Analysis of the static and dynamic behaviour of hydraulic fills

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(1)                                                                            .    . . E.T.S. DE INGENIEROS DE CAMINOS, CANALES Y PUERTOS GROUND ENGINEERING AND MORPHOLOGY DEPARTMENT / DEPARTAMENTO DE INGENIERÍA Y MORFOLOGÍA DEL TERRENO . . ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF HYDRAULIC FILLS . PhD THESIS   MANUEL DÁVILA MADRID Ingeniero de Caminos, Canales y Puertos MADRID, 2014 . PhD THESIS: ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF HYDRAULIC FILLS. . UNIVERSIDAD POLITÉCNICA DE MADRID .

(2)                                                                             .    . . E.T.S. DE INGENIEROS DE CAMINOS, CANALES Y PUERTOS DEPARTAMENTO DE INGENIERÍA Y MORFOLOGÍA DEL TERRENO .                . . ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF HYDRAULIC FILLS. . TESIS DOCTORAL MANUEL DÁVILA MADRID Ingeniero de Caminos, Canales y Puertos Directores de Tesis: CLAUDIO OLALLA MARAÑÓN Dr. Ingeniero de Caminos, Canales y Puertos ENRIQUE ASANZA IZQUIERDO Dr. Ingeniero de Caminos, Canales y Puertos MADRID, 2014 . PhD THESIS: ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF HYDRAULIC FILLS. . UNIVERSIDAD POLITÉCNICA DE MADRID .

(3)                                                                             .    . . Autor / Author:  . . D. Manuel Dávila Madrid . Directores / Directors:   D. Claudio Olalla Marañón D. Enrique Asanza Izquierdo Tribunal nombrado por el Mgfco. Y Excmo. Sr. Rector de la Universidad Politécnica de Madrid, el día …... de …………………………. de 2014.   Presidente D. …………………………………………………………………………….. Vocal 1º  D. ……………………………………………………………………………... Vocal 2º  D.…………………………………………………………………………………... Vocal 3º  D. ………………………………………………………………………………... Secretario D. ………………………………………………………………………………. Realizado el acto de defensa y lectura de la tesis el día ……. de ………………… de 2014 en   …………………………….,  los miembros del tribunal acuerdan otorgar la calificación de : ……………………………………………………………………………. . EL PRESIDENTE    LOS VOCALES      EL SECRETARIO . . PhD THESIS: ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF HYDRAULIC FILLS. . TÍTULO DE TESIS / THESIS TITLE: ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF HYDRAULIC FILLS / ANALISIS DEL COMPORTAMIENTO ESTÁTICO Y DINÁMICO DE RELLENOS HIDRÁULICOS .

(4)                                                                             .    . . . En la actualidad existe un gran conocimiento en la caracterización de rellenos hidráulicos, tanto en su caracterización estática, como dinámica. Sin embargo, son escasos en la literatura estudios más generales y globales de estos materiales, muy relacionados con sus usos y principales problemáticas en obras portuarias y mineras. Los procedimientos semi‐empíricos para la evaluación del efecto silo en las celdas de cajones portuarios, así como para el potencial de licuefacción de estos suelos durantes cargas instantáneas y terremotos, se basan en estudios donde la influencia de los parámetros que los rigen no se conocen en gran medida, dando lugar a resultados con considerable dispersión. Este es el caso, por ejemplo, de los daños notificados por el grupo de investigación del Puerto de Barcelona, la rotura de los cajones portuarios en el Puerto de Barcelona en 2007.   Por estos motivos y otros, se ha decidido desarrollar un análisis para la evaluación de estos problemas mediante la propuesta de una metodología teórico‐numérica y empírica. El enfoque teórico‐numérico desarrollado en el presente estudio se centra en la determinación del marco teórico y las herramientas numéricas capaces de solventar los retos que presentan estos problemas. La complejidad del problema procede de varios aspectos fundamentales: el comportamiento no lineal de los suelos poco confinados o flojos en procesos de consolidación por preso propio; su alto potencial de licuefacción; la caracterización hidromecánica de los contactos entre estructuras y suelo (camino preferencial para el flujo de agua y consolidación lateral); el punto de partida de los problemas con un estado de tensiones efectivas prácticamente nulo. En cuanto al enfoque experimental, se ha propuesto una metodología de laboratorio muy sencilla para la caracterización hidromecánica del suelo y las interfaces, sin la necesidad de usar complejos aparatos de laboratorio o procedimientos excesivamente complicados. Este trabajo incluye por tanto un breve repaso a los aspectos relacionados con la ejecución de los rellenos hidráulicos, sus usos principales y los fenómenos relacionados, con el fin de establecer un punto de partida para el presente estudio. Este repaso abarca desde la evolución de las ecuaciones de consolidación tradicionales (Terzaghi, 1943), (Gibson, English & Hussey, 1967) y las metodologías de cálculo (Townsend & McVay, 1990) (Fredlund, Donaldson and Gitirana, 2009) hasta las contribuciones en relación al efecto silo (Ranssen, 1985) (Ravenet, 1977) y sobre el fenómeno de la licuefacción (Casagrande, 1936) (Castro, 1969) (Been & Jefferies, 1985) (Pastor & Zienkiewicz, 1986). Con motivo de este estudio se ha desarrollado exclusivamente un código basado en el método de los elementos finitos (MEF) empleando el programa MATLAB. Para ello, se ha esablecido un marco teórico (Biot, 1941) (Zienkiewicz & Shiomi, 1984) (Segura & Caron, 2004) y numérico (Zienkiewicz & Taylor, 1989) (Huerta & Rodríguez, 1992) (Segura & Carol, 2008) para resolver problemas de consolidación multidimensional con condiciones de contorno friccionales, y los correspondientes modelos constitutivos (Pastor & Zienkiewicz, 1986) (Fiu & Liu, 2011).   Asimismo, se ha desarrollado una metodología experimental a través de una serie de ensayos de laboratorio para la calibración de los modelos constitutivos y de la caracterización de parámetros índice y de flujo (Castro, 1969) (Bahda 1997) (Been & Jefferies, 2006). Para ello se han empleado arenas de Hostun como material (relleno hidráulico) de referencia. Como principal aportación se incluyen una serie de nuevos ensayos de corte directo para la caracterización hidromecánica de la interfaz suelo – estructura de hormigón, para diferentes tipos de encofrados y rugosidades.  . PhD THESIS: ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF HYDRAULIC FILLS. . RESUMEN .

(5)    . Finalmente, se han diseñado una serie de algoritmos específicos para la resolución del set de ecuaciones diferenciales de gobierno que definen este problema. Estos algoritmos son de gran importancia en este problema para tratar el procesamiento transitorio de la consolidación de los rellenos hidráulicos, y de otros efectos relacionados con su implementación en celdas de cajones, como el efecto silo y la licuefacciones autoinducida. Para ello, se ha establecido un modelo 2D axisimétrico, con formulación acoplada u‐p para elementos continuos y elementos interfaz (de espesor cero), que tratan de simular las condiciones de estos rellenos hidráulicos cuando se colocan en las celdas portuarias. Este caso de estudio hace referencia clara a materiales granulares en estado inicial muy suelto y con escasas tensiones efectivas, es decir, con prácticamente todas las sobrepresiones ocasionadas por el proceso de autoconsolidación (por peso propio). Por todo ello se requiere de algoritmos numéricos específicos, así como de modelos constitutivos particulares, para los elementos del continuo y para los elementos interfaz. En el caso de la simulación de diferentes procedimientos de puesta en obra de los rellenos se ha requerido la modificacion de los algoritmos empleados para poder así representar numéricamente la puesta en obra de estos materiales, además de poder realizar una comparativa de los resultados para los distintos procedimientos.   La constante actualización de los parámetros del suelo, hace también de este algoritmo una potente   herramienta que permite establecer un interesante juego de perfiles de variables, tales como la densidad, el índice de huecos, la fracción de sólidos, el exceso de presiones, y tensiones y deformaciones. En definitiva, el modelo otorga un mejor entendimiento del efecto silo, término comúnmente usado para definir el fenómeno transitorio del gradiente de presiones laterales en las estructuras de contención en forma de silo.   Finalmente se incluyen una serie de comparativas entre los resultados del modelo y de diferentes estudios de la literatura técnica, tanto para el fenómeno de las consolidaciones por preso propio (Fredlund, Donaldson & Gitirana, 2009) como para el estudio del efecto silo (Puertos del Estado, 2006, EuroCódigo (2006), Japan Tech, Stands. (2009), etc.). Para concluir, se propone el diseño de un prototipo de columna de decantación con paredes friccionales, como principal propuesta de futura línea de investigación. . . . PhD THESIS: ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF HYDRAULIC FILLS. .                                                                             .

(6)                                                                             .    . . Wide research is nowadays available on the characterization of hydraulic fills in terms of either static or dynamic behavior. However, reported comprehensive analyses of these soils when meant for port or mining works are scarce. Moreover, the semi‐empirical procedures for assessing the silo effect on cells in floating caissons, and the liquefaction potential of these soils during sudden loads or earthquakes are based on studies where the underlying influence parameters are not well known, yielding results with significant scatter. This is the case, for instance, of hazards reported by the Barcelona Liquefaction working group, with the failure of harbor walls in 2007.   By virtue of this, a complex approach has been undertaken to evaluate the problem by a proposal of numerical and laboratory methodology. Within a theoretical and numerical scope, the study is focused on the numerical tools capable to face the different challenges of this problem. The complexity is manifold; the highly non‐linear behavior of consolidating soft soils; their potentially liquefactable nature, the significance of the hydromechanics of the soil‐structure contact, the discontinuities as preferential paths for water flow, setting “negligible” effective stresses as initial conditions. Within an experimental scope, a straightforward laboratory methodology is introduced for the hydromechanical characterization of the soil and the interface without the need of complex laboratory devices or cumbersome procedures. Therefore, this study includes a brief overview of the hydraulic filling execution, main uses (land reclamation, filled cells, tailing dams, etc.) and the underlying phenomena (self‐weight consolidation, silo effect, liquefaction, etc.). It comprises from the evolution of the traditional consolidation equations (Terzaghi, 1943), (Gibson, English, & Hussey, 1967) and solving methodologies (Townsend & McVay, 1990) (Fredlund, Donaldson and Gitirana, 2009) to the contributions in terms of silo effect (Ranssen, 1895) (Ravenet, 1977) and liquefaction phenomena (Casagrande, 1936) (Castro, 1969) (Been & Jefferies, 1985) (Pastor & Zienkiewicz, 1986). The novelty of the study lies on the development of a Finite Element Method (FEM) code, exclusively formulated for this problem. Subsequently, a theoretical (Biot, 1941) (Zienkiewicz and Shiomi, 1984) (Segura and Carol, 2004) and numerical approach (Zienkiewicz and Taylor, 1989) (Huerta, A. & Rodriguez, A., 1992) (Segura, J.M. & Carol, I., 2008) is introduced for multidimensional consolidation problems with frictional contacts and the corresponding constitutive models (Pastor & Zienkiewicz, 1986) (Fu & Liu, 2011).   An experimental methodology is presented for the laboratory test and material characterization (Castro 1969) (Bahda 1997) (Been & Jefferies 2006) using Hostun sands as reference hydraulic fill. A series of singular interaction shear tests for the interface calibration is included. Finally, a specific model algorithm for the solution of the set of differential equations governing the problem is presented. The process of consolidation and settlements involves a comprehensive simulation of the transient process of decantation and the build‐up of the silo effect in cells and certain phenomena related to self‐compaction and liquefaction. For this, an implementation of a 2D axi‐syimmetric coupled model with continuum and interface elements, aimed at simulating conditions and self‐weight consolidation of hydraulic fills once placed into floating caisson cells or close to retaining structures. This basically concerns a loose granular soil with a negligible initial effective stress level at the onset of the process. The implementation requires a specific numerical algorithm as well as specific constitutive models for both the continuum and the interface elements. The simulation of implementation procedures for the fills has required the modification of the . PhD THESIS: ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF HYDRAULIC FILLS. . ABSTRACT .

(7)                                                                             .    . . Furthermore, the continuous updating of the model provides an insightful logging of variable profiles such as density, void ratio and solid fraction profiles, total and excess pore pressure, stresses and strains. This will lead to a better understanding of complex phenomena such as the transient gradient in lateral pressures due to silo effect in saturated soils. Interesting model and literature comparisons for the self‐weight consolidation (Fredlund, Donaldson, & Gitirana, 2009) and the silo effect results (Puertos del Estado (2006), EuroCode (2006), Japan Tech, Stands. (2009)). This study closes with the design of a decantation column prototype with frictional walls as the main future line of research. . PhD THESIS: ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF HYDRAULIC FILLS. . algorithm so that a numerical representation of these procedures is carried out. A comparison of the results for the different procedures is interesting for the global analysis. .

(8)                                                                             .    . . I would like to take this opportunity to thank the people who contributed to this research and without whom this would not have gone ahead and had success. I would like to particularly thank my Thesis directors and supervisors, Dr Professor Claudio Olalla and Dr Enrique Asanza. Their practical knowledge and attention to detail taught me many valuable lessons and furthered my understanding of geotechnical engineering greatly. Their assistance and continue motivation in editing and analyzing the research performed was essential for the success of my doctoral programme. Special thanks also go to Dr Professor Manuel Pastor and Dr Pablo Mira and the rest of the members of the Computational Geomechanics Group in CEDEX, Ana Sofía Benítez and Silvia Sancho, who share their time of research with me. I am very thankful for their practical support in completing the aspects of this research related to the numerical computation and software programming. I greatly enjoyed my time with them at the office in CEDEX, where their assistance greatly improved my understanding in this field, as well as the enjoyment of our free time in the laboratory. I would also like to thank the members of “Applied Geotechnics” Department in CEDEX that I was part: Dr Roberto Fernández, Dr Áurea Perucho, José Antonio Díez and specially Dr José Manuel Martínez Santamaría, for their constant assistance in analysing and improving of the research performed and for the search of financial aid. I have benefited greatly from their insights and assistance.   Special thanks go also to Institute of Geotechnical Engineering and Construction Management of the Hamburg University of Technology (TUHH), particularly in the figure of Prof. Dr. Ing. Jürgen Grabe for the global support given, to carry out a short stay in Hamburg. The Geotechnical Laboratory of the National Public Works and Engineering Research Centre (CEDEX), throughout the figure of its Director Dr Fernando Pardo, also deserves acknowledgement for the financial support provided for this project through a four year scholarship – research staff training contract. I also would like to highlight the special aid received by the laboratory staff, especially José María Toledo, Clemente Arias and J. Luis Miranda, and the Responsible of the Triaxials Laboratory, Dr. Jose Estaire, who put their trust on me to carry out the test laboratory campaign necessary to achieve the empirical goals of this research. Also special thanks to Dr Marta Sánchez, from Central Structures Laboratory in CEDEX, for the collaboration in the preparation of concrete specimen for the laboratory tests. My enduring gratitude goes to all my family; specially my parents, Manolo and María, and my sister Isabel who supported and encouraged me throughout my education. Finally, I would like to thank all my closer friends, whose encouragement and support enabled me to pursue my interest in this research. . PhD THESIS: ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF HYDRAULIC FILLS. . ACKNOWLEDGEMENTS .

(9) . INDEX RESUMEN ..................................................................................................................... 4 ABSTRACT ..................................................................................................................... 6 ACKNOWLEDGEMENTS ................................................................................................ 8 1. INTRODUCTION AND TARGETS ............................................................................. 1 1.1 . INTRODUCTION. ........................................................................................... 1 . 1.2 . MAIN TARGETS............................................................................................. 1 . 2. HYDRAULIC FILLS. STATE OF KNOWLEDGE. .......................................................... 5 2.1 2.1.1 2.1.2 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.4 2.4.1 2.4.2 . A GENERAL HYDRAULIC FILLS SCOPE. .......................................................... 5 Hydraulic fills main uses. Construction methods reclamation. ............. 5 Fill mass properties and general classifications..................................... 8 SELF WEIGHT LARGE STRAIN CONSOLIDATION. ........................................ 15 Literature overview. Significant additions. .......................................... 15 Coordinate Systems. ............................................................................ 19 Theory review. The Dependent Variable. ............................................ 20 Constitutive Equations. ........................................................................ 25 Conclusions. ......................................................................................... 25 ARCH‐SILO EFFECT. FLOATING CAISSON CELLS. ........................................ 26 Introduction ......................................................................................... 26 Construction aspects. .......................................................................... 28 Actions affection of caisson cells. ........................................................ 31 Actions estimations.............................................................................. 33 LIQUEFACTION OF HYDRAULIC FILLS. ........................................................ 35 Historical review of liquefaction phenomena. .................................... 35 Theory review. ..................................................................................... 41 . 3. NUMERICAL MODELING. ..................................................................................... 51 3.1 . INTRODUCTION .......................................................................................... 51 . Manual Pequeñas Presas para Países en Desarrollo . . I | P a g e .

(10) . 3.2 3.2.1 3.2.2 3.3 3.3.1 3.3.2 3.3.3 3.4 3.4.1 3.4.2 3.5 3.5.1 3.5.2 3.6 3.6.1 3.6.2 . HYDRO‐MECHANICAL DESCRIPTION. ......................................................... 51 Continuous elements ........................................................................... 51 Interface elements ............................................................................... 59 FEM IMPLEMENTATION. ............................................................................ 61 Continuous elements ........................................................................... 61 Interface elements and discontinuous porous media. ........................ 69 FEM implementation particularities. ................................................... 77 CONSTITUTIVE MODELS. CLASSIC AND GENERALIZED PLASTICITY. .......... 82 Continuous elements. .......................................................................... 82 Interface elements. ............................................................................ 108 ALGORITHM ADAPTION TO THE HIGHLY NON‐LINEAR PROBLEM. ......... 114 Continuous elements ......................................................................... 114 Interface elements ............................................................................. 123 FEM IMPLEMENTATION OF THE DYNAMIC PROBLEM. ........................... 130 Continuous elements ......................................................................... 130 Interface elements ............................................................................. 135 . 4. LABORATORY CHARACTERISATION CAMPAIGN................................................ 140 4.1 . INTRODUCTION ........................................................................................ 140 . 4.2 . HOSTUN SANDS AS MATERIAL EMPLOYEED. ........................................... 140 . 4.3 . FILLS LABORATORY CHARACTERISTATION. .............................................. 141 . 4.3.1 Triaxial Tests. ..................................................................................... 141 4.3.2 Triaxial Test Results. Strength, deformational and flux characterisation. ............................................................................................... 155 4.3.3 Isotropic consolidation in the triaxial cell. Deformational and flux characterisation. ............................................................................................... 158 4.3.4 Oedometers Test results. Deformational and Flux characterisation. 163 4.4 4.4.1 4.4.2 4.4.3 . CONSTITUTIVE MODEL ASIGNATION FOR THE INTERFACE. .................... 168 Direct Shear Test. ............................................................................... 168 Shear Test results. Strength and deformational characterisation. ... 174 Shear Test results. Flow characterisation. ......................................... 179 . 5. CALIBRATION OF THE FEM MODEL AND CALCULATIONS. ................................ 183 5.1 . FEM MODEL VERIFICATIONS.................................................................... 183 . Manual Pequeñas Presas para Países en Desarrollo . . II | P a g e .

(11) . 5.2 . GENERAL CONSOLIDATION AND SETTLEMENTS. ..................................... 183 . 5.3 . LIMIT LOAD PROBLEM BY DISPLACEMENT CONTROL ............................. 185 . 5.4 . INTERFACE CONSOLIDATION ................................................................... 197 . 5.5 . DYNAMIC ELASTIC PROBLEM ................................................................... 199 . 5.6 . SELF‐WEIGHT CONSOLIDATION PROBLEM .............................................. 207 . 5.7 . SILO EFFECT CHECKING ............................................................................ 213 . 5.7.1 5.7.2 5.7.3 5.7.4 . Introduction to the problem .............................................................. 213 Silo effect analysis for wooden formwork concrete walls ................. 219 Silo effect analysis for metal formwork concrete walls..................... 221 Analysis of Silo effect results ............................................................. 224 . 5.8 . IMPLEMENTATION PROCEDURE AND EXTERNAL LOAD APPLICATION. .. 226 . 5.9 . JACOBIAN MATRIX MODIFICATION ......................................................... 231 . 5.10 . NUMERICAL VERIFICATIONS OF THE MODEL .......................................... 235 . 6. DESIGN AND SETUP OF A FULLY INSTRUMENTED COLUMN OF FILLS DECANTATION. ......................................................................................................... 237 6.1 6.1.1 6.1.2 6.2 6.2.1 6.2.2 6.3 6.3.1 6.3.2 6.3.3 6.4 6.4.1 . BACKGROUND. ......................................................................................... 237 Introduction. ...................................................................................... 237 Research experiences. ....................................................................... 238 THEORETICAL LAYOUT. ............................................................................ 240 General description. .......................................................................... 240 Operating scheme. ............................................................................. 243 TECHNICAL DETAILS LAYOUT. .................................................................. 245 Mechanical layout .............................................................................. 245 Instrumentation and monitoring ....................................................... 250 Data acquisition system ..................................................................... 251 COLUMN SETUP. ...................................................................................... 252 Equipment setup steps: ..................................................................... 252 . 7. CONCLUSIONS AND FUTURE RESEARCH LINES. ................................................ 256 7.1 . CONCLUSIONS. ......................................................................................... 256 . Manual Pequeñas Presas para Países en Desarrollo . . III | P a g e .

(12) . 7.1.1 7.1.2 7.1.3 7.2 7.2.1 7.2.2 . Theoretical and numerical approach. ................................................ 256 Laboratory approach. ........................................................................ 257 Algorithm implementation and results. ............................................ 258 FUTURE RESEARCH LINES. ....................................................................... 261 Decantation column........................................................................... 261 Future theoretical and laboratory research lines. ............................. 261 . APPENDIXES ............................................................................................................. 273 APPENDIX A .............................................................................................................. 274 APPENDIX B .............................................................................................................. 287 . . Manual Pequeñas Presas para Países en Desarrollo . . IV | P a g e .

(13) . FIGURE INDEX Figure 1. Trailing Suction Hopper Dredger, TSHD (Hydraulic Fill Manual, 2012). ................................... 6 Figure 2. Rainbowing (Hydraulic Fill Manual, 2012). .............................................................................. 7 Figure 3. Staged bund construction under water using a grab dredger (Hydraulic Fill Manual, 2012). . 8 Figure 4. Fines / Water Content / Solid Content diagram (Scott & Cymerman, 1984). ........................ 11 Figure 5. Formation of clay balls on the reclamation area (Hydraulic Fill Manual, 2012). ................... 12 Figure 6. Pre‐loading of subsoil and effect of vertical drains (Hydraulic Fill Manual, 2012). ............... 13 Figure 7. Crane mounted with tandem vibratory probes (Hydraulic Fill Manual, 2012). ..................... 14 Figure 8. Dynamic compaction machine (Hydraulic Fill Manual, 2012). ............................................... 14 Figure 9. Behavior scheme proposed by Imai (1981). .......................................................................... 17 Figure 10. Comparison of Eulerian and Lagrangian coordinate systems (Schiffman, Vick, & Gibson, 1988). .......................................................................................................................................... 19 Figure 11. Different relationships of describing soil deformations. ..................................................... 22 Figure 12. Comparative of lateral pressures. ........................................................................................ 27 Figure 13. 3D perspective of a floating caisson. ................................................................................... 28 Figure 14. Floating dock construction process sequences. ................................................................... 29 Figure 15. Continuum sliding process. .................................................................................................. 29 Figure 16. Caisson installation procedures. .......................................................................................... 30 Figure 17. Filling of the caisson cells with rainbowing techniques. ...................................................... 31 Figure 18. Final layout / section of a floating dock. .............................................................................. 31 Figure 19. Pressures exerted when filling a cell (Silo Effect). ............................................................... 32 Figure 20. Dock : Loads exerted on the outer wall at the service stage (Silo Effect). ........................... 32 Figure 21. Compression stresses exerted upon the inner wall (Silo Effect). ......................................... 33 Figure 22. Pressures distribution when filling a cell (Silo Effect) according to Spanish code. .............. 34 Figure 23. Aerial view of Fort Peck failure (U.S. Army Corps of Engineers, 1939)). .............................. 36 Figure 24. Nerlerk B‐67 berm and foundation cross section (from Been et al., 1987, with permission NRC of Canada). .......................................................................................................................... 37 Figure 25. Apartment building at Kawagishi‐cho in 1964 Niigata earthquake (Kawasumi‐Hirosi, 1968). ..................................................................................................................................................... 37 Figure 26. Liquefaction failure of Lower San Fernando Dam after the 1971 earthquake (University of California, Berkeley). ................................................................................................................... 38 Figure 27. Aerial view of the Merriespruit tailings dam failure showing the path of the mudflow (Fourie et al., 2001). .................................................................................................................... 39 Figure 28. Gulf Canada’s Molikpaq structure in the Beaufort Sea. ....................................................... 40 . Manual Pequeñas Presas para Países en Desarrollo . . V | P a g e .

(14) . Figure 29. Details of cyclic ice loading and excess pore pressure (Jefferies & Been, 2006). ................ 40 Figure 30. Failure of embankment on Ackermann Lake triggered by vibroseis trucks (from Hryciw et al., 1990). ..................................................................................................................................... 41 Figure 31. Triaxial tests on dense and loose sands (Zienkiewicz et al., 1999). ..................................... 42 Figure 32. Difference between rate and absolute definitions of dilatancy (Jefferies & Been, 2006). .. 42 Figure 33. Critical void ratio hypothesis from direct shear tests (Casagrande, 1975). ......................... 43 Figure 34. Definición del Parámetro de estado (después de Been & Jefferies, 1985). ......................... 44 Figure 35. Instability or flow liquefaction line for onset of liquefaction (after Yang, 2002). ................ 45 Figure 36. Collapse surface representation for onset of liquefaction (after Yang, 2002). .................... 46 Figure 37. Liquefaction types according to Robertson & Fear (1996). ................................................. 47 Figure 38. Scheme for soil undrained behaviour for triaxial compression under static load. (Robertson y Wride, 1998). ............................................................................................................................ 47 Figure 39. Scheme for soil cyclic undrained behaviour illustrating cyclic liquefaction in a sample with initial shear stress. (adapatada de Robertson y Wride, 1998). ................................................... 49 Figure 40. Scheme of the aperture and u variable for the interface. ................................................... 60 Figure 41. Elements implemented in the hydraulic fills model. ........................................................... 63 Figure 42. Eight‐node quadratic and four‐node linear quadrilateral elements. ................................... 64 Figure 43. Zero‐thickness interface elements for the contact. ............................................................. 70 Figure 44. Scheme of the axi‐symmetry of the model. ......................................................................... 80 Figure 45. Capped DP model. Yield surface (De Souza et al., 2008). .................................................... 84 Figure 46. Capped DP model. Flow vectors (De Souza et al., 2008). .................................................... 85 Figure 47. Drucker‐Prager model. Return mapping to cone and apex. ................................................ 90 Figure 48. Modified Cam‐Clay model. Yield surface. ............................................................................ 91 Figure 49. CDP model. Algorithm for selection of the correct return‐mapping procedure (De Souza et al., 2008). ..................................................................................................................................... 97 Figure 50. Theoretical yield surface for Pastor Zienkiewicz model..................................................... 104 Figure 51. Schematic behaviour of undrained sand for different Dr (in % per one)........................... 105 Figure 52. Coulomb yield locus for an interface element. .................................................................. 110 Figure 53. Shear behaviour predicted by the Fu‐Liu model. ............................................................... 114 Figure 54. Empirical Relationships for Estimating Hydraulic Conductivity. ........................................ 118 Figure 55. Hostun sands size grain curve. ........................................................................................... 141 Figure 56. Triaxial Cell with Tubular Load cell Mounted Directly in the Loading Piston (Garlanger, 1970). ........................................................................................................................................ 142 Figure 57. Illustration of sample preparation methods for clean sands (from Ishihara 1993). .......... 144 Figure 58. Sample preparation process. ............................................................................................. 146 . Manual Pequeñas Presas para Países en Desarrollo . . VI | P a g e .

(15) . Figure 59. CO2 flushing process for the fully saturation. .................................................................... 147 Figure 60. Skempton’s B values verification process. ......................................................................... 148 Figure 61. CO2 Isotropic consolidation and volumetric strain monitoring process. ........................... 149 Figure 62. Deviatoric stress application with piston displacement in triaxial cell. ............................. 150 Figure 63. Volume changes during triaxial test (for a drained test on a dilatant sample). ................. 150 Figure 64. Potential error in void ratio during saturation (from Sladen and Handford, 1987). .......... 151 Figure 65. Saturation influence on the void ratio (Bahloul, 1990). ..................................................... 152 Figure 66. Isotropic compressibility curves (El Hachem, 1987). ......................................................... 152 Figure 67. Membrane penetration scheme. ....................................................................................... 153 Figure 68. Normalized membrane penetration vs grain size (Salden et al., 1985). ............................ 154 Figure 69. Comparison of CSL determined from load controlled and strain rate controlled triaxial compression tests (Been & Jefferies, 2006). ............................................................................. 154 Figure 70. Lubricated end platen for triaxial testing of sands. ........................................................... 155 Figure 71. Drained behavior of Hostun Sand in compression triaxial test; the variation of deviatoric stress with axial strain, for Dr = 60 %. ....................................................................................... 157 Figure 72. Hostun sand stress paths for PZ model calibration for different ranges of Dr. Loose (a) and Medium Dense (b) (some tests from Bahda F. PhD Thesis, 1997). ........................................... 158 Figure 73. Isotropic consolidation process for a sample ICC‐1. .......................................................... 159 Figure 74. Isotropic consolidation graph for Hostun Sand. ................................................................ 160 Figure 75. Determination of t90 through the consolidation curve. Taylor Method. .......................... 162 Figure 76. Graph with the permeability – void ratio relationship for Hostun Sand. .......................... 163 Figure 77. Oedometer graph for Hostun Sands tests. ........................................................................ 164 Figure 78. Taylor method application to time curves. ........................................................................ 166 Figure 79. Medium loose Hostun sand permeability evolution with void ratio. ................................ 168 Figure 80. Stress conditions in the simple shear test. ........................................................................ 169 Figure 81. Formwork specimen preparation (wooden and metallic formwork). ............................... 172 Figure 82. Specimen preparation for Direct Shear Test. ..................................................................... 173 Figure 83. Hostun sand – concrete structure (wooden formwork) test results calibration with Fu‐Liu model. ....................................................................................................................................... 176 Figure 84. Hostun sand – concrete structure (metal formwork) test results calibration with Fu‐Liu model. ....................................................................................................................................... 177 Figure 85. Soil‐concrete interfaces strength. ...................................................................................... 178 Figure 86. Soil‐concrete interfaces normal strain behaviour (b). ....................................................... 178 Figure 87. Deformational results for initial consolidation in shear tests. ........................................... 180 Figure 88. Taylor method application to time curves. ........................................................................ 181 . Manual Pequeñas Presas para Países en Desarrollo . . VII | P a g e .

(16) . Figure 89. Graph with the permeability – void ratio relationship for Hostun Sands. ......................... 182 Figure 90. Scheme of the settlement – consolidation problem. ........................................................ 184 Figure 91. Analytical and FEM results comparison. ............................................................................ 185 Figure 92. Non linear coupled FE code structure based on the Newton‐Raphson method. .............. 185 Figure 93. Limit load for a FEM problem. ........................................................................................... 186 Figure 94. Geometry of the limit load analysis for a circular footing. ................................................ 192 Figure 95. Approximated failure shape due to a bearing pressure. ................................................... 193 Figure 96. Limit load by the FEM model problem for the Von Mises case. ........................................ 194 Figure 97. Failure shape due to a bearing pressure with the FEM model for the Von Mises case. .... 194 Figure 98. Load‐displacements curves by the Drucker‐Prager perfectly plastic models with different material constants (Chen, W.F. & Liu, X.L. “Limit Analysis in Soil Mechanics”, 1990). ............. 195 Figure 99. Limit load by the FEM model for the CDP model for the compression (a) and extension (b) case............................................................................................................................................ 195 Figure 100. Failure shape due to a bearing pressure with the FEM model for the CPD in extension. 196 Figure 101. Initial failure wedge (represented by plastic strains) due to bearing pressure with the FEM model for the CPD in extension. ....................................................................................... 196 Figure 102. Discontinuity consolidation problem geometry. ............................................................. 197 Figure 103. Fluid pressure distributions at different times from FEM model and analytically. ......... 199 Figure 104. Discontinuity settlements evolution with time from FEM model. ................................... 199 Figure 105. Scheme for one‐dimensional dynamic stress equilibrium. .............................................. 200 Figure 106. Scheme for one‐dimensional wave transmission. ........................................................... 202 Figure 107. Geometry of the dynamic problem for a P wave input at the base. ............................... 203 Figure 108. Geometry of the dynamic problem for an S wave input at the base. .............................. 203 Figure 109. P and S waves with time for the dynamic problem. ........................................................ 204 Figure 110. P and S waves with space for the dynamic problem. ...................................................... 205 Figure 111. Graphic results with P wave displacement versus time from dynamic FEM model. ....... 206 Figure 112. Graphic results with S wave displacement versus time from dynamic FEM model. ....... 206 Figure 113. Schematic soil/discontinuity index parameters. .............................................................. 208 Figure 114. Schematic FEM algorithm structure for self‐weight large strain consolidation problems. ................................................................................................................................................... 209 Figure 115. FEM model and FSConsol polynomial relationship for compressibility. .......................... 210 Figure 116. FEM model and FSConsol polynomial relationship for permeability ............................... 211 Figure 117. FSConsol analysis input parameters in compressibility and permeability. ...................... 211 Figure 118. FEM model and FSConsol results for void ratio versus height with time. ....................... 212 Figure 119. FEM model and FSConsol results for pore pressure dissipation along the vertical. ........ 212 . Manual Pequeñas Presas para Países en Desarrollo . . VIII | P a g e .

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