Maximum Likelihood Estimation of Modal Parameters in Structures Using the Expectation Maximization Algorithm

This paper presents a time-domain stochastic system identification method based on maximum likelihood estimation (MLE) with the expectation maximization (EM) algorithm. The effectiveness of this structural identification method is evaluated through numerical simulation in the context of the ASCE benchmark problem on structural health monitoring. The benchmark structure is a four-story, two-bay by two-bay steel-frame scale model structure built in the Earthquake Engineering Research Laboratory at the University of British Columbia, Canada. This paper focuses on Phase I of the analytical benchmark studies. A MATLAB-based finite element analysis code obtained from the IASC-ASCE SHM Task Group web site is used to calculate the dynamic response of the prototype structure. A number of 100 simulations have been made using this MATLAB-based finite element analysis code in order to evaluate the proposed identification method. There are several techniques to realize system identification. In this work, stochastic subspace identification (SSI)method has been used for comparison. SSI identification method is a well known method and computes accurate estimates of the modal parameters. The principles of the SSI identification method has been introduced in the paper and next the proposed MLE with EM algorithm has been explained in detail. The advantages of the proposed structural identification method can be summarized as follows: (i) the method is based on maximum likelihood, that implies minimum variance estimates; (ii) EM is a computational simpler estimation procedure than other optimization algorithms; (iii) estimate more parameters than SSI, and these estimates are accurate. On the contrary, the main disadvantages of the method are: (i) EM algorithm is an iterative procedure and it consumes time until convergence is reached; and (ii) this method needs starting values for the parameters. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using both the SSI method and the proposed MLE + EM method. The numerical results show that the proposed method identifies eigenfrequencies, damping ratios and mode shapes reasonably well even in the presence of 10% measurement noises. These modal parameters are more accurate than the SSI estimated modal parameters.

Comparative study of auxetic geometrics by means of computer-aided design and engineering

Auxetic materials (or metamaterials) are those with a negative Poisson ratio (NPR) and display the unexpected property of lateral expansion when stretched, as well as an equal and opposing densification when compressed. Such geometries are being progressively employed in the development of novel products, especially in the fields of intelligent expandable actuators, shape morphing structures and minimally invasive implantable devices. Although several auxetic and potentially auxetic geometries have been summarized in previous reviews and research, precise information regarding relevant properties for design tasks is not always provided. In this study we present a comparative study of two-dimensional and three-dimensional auxetic geometries carried out by means of computer-aided design and engineering tools (from now on CAD–CAE). The first part of the study is focused on the development of a CAD library of auxetics. Once the library is developed we simulate the behavior of the different auxetic geometries and elaborate a systematic comparison, considering relevant properties of these geometries, such as Poisson ratio(s), maximum volume or area reductions attainable and equivalent Young's modulus, hoping it may provide useful information for future designs of devices based on these interesting structures.

On soil-structure interaction in large non-slender partially buried structures

This paper addresses the seismic analysis of a deeply embedded non-slender structure hosting the pumping unit of a reservoir. The dynamic response in this type of problems is usually studied under the assumption of a perfectly rigid structure using a sub-structuring procedure (three-step solution) proposed specifically for this hypothesis. Such an approach enables a relatively simple assessment of the importance of some key factors influencing the structural response. In this work, the problem is also solved in a single step using a direct approach in which the structure and surrounding soil are modelled as a coupled system with its actual geometry and flexibility. Results indicate that, quite surprisingly, there are significant differences among prediction using both methods. Furthermore, neglecting the flexibility of the structure leads to a significant underestimation of the spectral accelerations at certain points of the structure.

Computational Methods for Identification of Vibrating Structures

System identification deals with the problem of building mathematical models of dynamical systems based on observed data from the system" [1]. In the context of civil engineering, the system refers to a large scale structure such as a building, bridge, or an offshore structure, and identification mostly involves the determination of modal parameters (the natural frequencies, damping ratios, and mode shapes). This paper presents some modal identification results obtained using a state-of-the-art time domain system identification method (data-driven stochastic subspace algorithms [2]) applied to the output-only data measured in a steel arch bridge. First, a three dimensional finite element model was developed for the numerical analysis of the structure using ANSYS. Modal analysis was carried out and modal parameters were extracted in the frequency range of interest, 0-10 Hz. The results obtained from the finite element modal analysis were used to determine the location of the sensors. After that, ambient vibration tests were conducted during April 23-24, 2009. The response of the structure was measured using eight accelerometers. Two stations of three sensors were formed (triaxial stations). These sensors were held stationary for reference during the test. The two remaining sensors were placed at the different measurement points along the bridge deck, in which only vertical and transversal measurements were conducted (biaxial stations). Point estimate and interval estimate have been carried out in the state space model using these ambient vibration measurements. In the case of parametric models (like state space), the dynamic behaviour of a system is described using mathematical models. Then, mathematical relationships can be established between modal parameters and estimated point parameters (thus, it is common to use experimental modal analysis as a synonym for system identification). Stable modal parameters are found using a stabilization diagram. Furthermore, this paper proposes a method for assessing the precision of estimates of the parameters of state-space models (confidence interval). This approach employs the nonparametric bootstrap procedure [3] and is applied to subspace parameter estimation algorithm. Using bootstrap results, a plot similar to a stabilization diagram is developed. These graphics differentiate system modes from spurious noise modes for a given order system. Additionally, using the modal assurance criterion, the experimental modes obtained have been compared with those evaluated from a finite element analysis. A quite good agreement between numerical and experimental results is observed.

Damage assessment on building structures subjected to the recent near-fault earthquake in Lorca (Spain)

The city of Lorca (Spain) was hit on May 11th 2011 by two consecutive earthquakes with 4.6 and 5.2 Mw respectively, causing casualties and important damage in buildings. Lorca is located in the south-east region of Spain and settled on the trace of the Murcia-Totana-Lorca fault. Although the magnitudes of these ground motions were not severe, the damage observed was considerable over a great amount of buildings. More than 300 of them have been demolished and many others are being retrofitted. This paper reports a field study on the damage caused by these earthquakes. The observed damage is related with the structural typology. Further, prototypes of the damaged buildings are idealized with nonlinear numerical models and their seismic behavior and proneness to damage concentration is further investigated through dynamic response analyses.

A damage model for seismic retrofitting of structures

Numerous damage models have been developed in order to analyse the seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of Continuum Damage Mechanics are more consistent with the definition of damage like a phenomenon with mechanical consequences as they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, many of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Flórez is made in order to include the low cycle fatigue. Such model employs in its formulation irreversible thermodynamics and internal state variable theory.

Crack width control in RC elements with recycled steel fibres and applications to integral structures : theoretical and experimental study

El presente trabajo trata de elementos reforzados con barras de armadura y Fibras Metálicas Recicladas (FMR). El objetivo principal es mejorar el comportamiento a fisuración de elementos sometidos a flexión pura y a flexión compuesta, aumentando en consecuencia las prestaciones en servicio de aquellas estructuras con requerimientos estrictos con respecto al control de fisuración. Entre éstas últimas se encuentran las estructuras integrales, es decir aquellas estructuras sin juntas (puentes o edificios), sometidas a cargas gravitatorias y deformaciones impuestas en los elementos horizontales debidas a retracción, fluencia y temperatura. Las FMR son obtenidas a partir de los neumáticos fuera de uso, y puesto que el procedimiento de reciclado se centra en el caucho en vez que en el acero, su forma es aleatoria y con longitud variable. A pesar de que la eficacia del fibrorefuerzo mediante FMR ha sido demostrada en investigaciones anteriores, la innovación que representa este trabajo consiste en proponer la acción combinada de barras convencionales y FMR en la mejora del comportamiento a fisuración. El objetivo es por tanto mejorar la sostenibilidad del proyecto de la estructura en HA al utilizar materiales reciclados por un lado, y aumentando por el otro la durabilidad. En primer lugar, se presenta el estado del arte con respecto a la fisuración en elementos de HA, que sucesivamente se amplía a elementos reforzados con barras y fibras. Asimismo, se resume el método simplificado para el análisis de columnas de estructuras sin juntas ya propuesto por Pérez et al., con particular énfasis en aquellos aspectos que son incompatibles con la acción de las fibras a nivel seccional. A continuación, se presenta un modelo para describir la deformabilidad seccional y la fisuración en elementos en HA, que luego se amplía a aquellos elementos reforzados con barras y fibras, teniendo en cuenta también los efectos debidos a la retracción (tension stiffening negativo). El modelo es luego empleado para ampliar el método simplificado para el análisis de columnas. La aportación consiste por tanto en contar con una metodología amplia de análisis para este tipo de elementos. Seguidamente, se presenta la campaña experimental preliminar que ha involucrado vigas a escala reducida sometidas a flexión simple, con el objetivo de validar la eficiencia y la usabilidad en el hormigón de las FMR de dos diferentes tipos, y su comportamiento con respecto a fibras de acero comerciales. Se describe a continuación la campaña principal, consistente en ensayos sobre ocho vigas en flexión simple a escala 1:1 (variando contenido en FRM, Ø/s,eff y recubrimiento) y doce columnas a flexión compuesta (variando contenido en FMR, Ø/s,eff y nivel de fuerza axil). Los resultados obtenidos en la campaña principal son presentados y comentados, resaltando las mejoras obtenidas en el comportamiento a fisuración de las vigas y columnas, y la rigidez estructural de las columnas. Estos resultados se comparan con las predicciones del modelo propuesto. Los principales parámetros estudiados para describir la fisuración y el comportamiento seccional de las vigas son: la separación entre fisuras, el alargamiento medio de las armaduras y la abertura de fisura, mientras que en los ensayos de las columnas se ha contrastado las leyes momento/curvatura, la tensión en las barras de armadura y la abertura de fisura en el empotramiento en la base. La comparación muestra un buen acuerdo entre las predicciones y los resultados experimentales. Asimismo, se nota la mejora en el comportamiento a fisuración debido a la incorporación de FMR en aquellos elementos con cuantías de armadura bajas en flexión simple, en elementos con axiles bajos y para el control de la fisuración en elementos con grandes recubrimientos, siendo por tanto resultados de inmediato impacto en la práctica ingenieril (diseño de losas, tanques, estructuras integrales, etc.). VIIIComo punto final, se presentan aplicaciones de las FMR en estructuras reales. Se discuten dos casos de elementos sometidos a flexión pura, en particular una viga simplemente apoyada y un tanque para el tratamiento de agua. En ambos casos la adicción de FMR al hormigón lleva a mejoras en el comportamiento a fisuración. Luego, utilizando el método simplificado para el análisis en servicio de columnas de estructuras sin juntas, se calcula la máxima longitud admisible en casos típicos de puentes y edificación. En particular, se demuestra que las limitaciones de la práctica ingenieril actual (sobre todo en edificación) pueden ser aumentadas considerando el comportamiento real de las columnas en HA. Finalmente, los mismos casos son modificados para considerar el uso de MFR, y se presentan las mejoras tanto en la máxima longitud admisible como en la abertura de fisura para una longitud y deformación impuesta. This work deals with elements reinforced with both rebars and Recycled Steel Fibres (RSFs). Its main objective is to improve cracking behaviour of elements subjected to pure bending and bending and axial force, resulting in better serviceability conditions for these structures demanding keen crack width control. Among these structures a particularly interesting type are the so-called integral structures, i.e. long jointless structures (bridges and buildings) subjected to gravitational loads and imposed deformations due to shrinkage, creep and temperature. RSFs are obtained from End of Life Tyres, and due to the recycling process that is focused on the rubber rather than on the steel they come out crooked and with variable length. Although the effectiveness of RSFs had already been proven by previous research, the innovation of this work consists in the proposing the combined action of conventional rebars and RSFs to improve cracking behaviour. Therefore, the objective is to improve the sustainability of RC structures by, on the one hand, using recycled materials, and on the other improving their durability. A state of the art on cracking in RC elements is firstly drawn. It is then expanded to elements reinforced with both rebars and fibres (R/FRC elements). Finally, the simplified method for analysis of columns of long jointless structures already proposed by Pérez et al. is resumed, with a special focus on the points that conflict when taking into account the action of fibres. Afterwards, a model to describe sectional deformability and cracking of R/FRC elements is presented, taking also into account the effect of shrinkage (negative tension stiffening). The model is then used to implement the simplified method for columns. The novelty represented by this is that a comprehensive methodology to analyse this type of elements is presented. A preliminary experimental campaign consisting in small beams subjected to pure bending is described, with the objective of validating the effectiveness and usability in concrete of RSFs of two different types, and their behaviour when compared with commercial steel fibres. With the results and lessons learnt from this campaign in mind, the main experimental campaign is then described, consisting in cracking tests of eight unscaled beams in pure bending (varying RSF content, Ø/s,eff and concrete cover) and twelve columns subjected to imposed displacement and axial force (varying RSF content, Ø/s,eff and squashing load ratio). The results obtained from the main campaign are presented and discussed, with particular focus on the improvement in cracking behaviour for the beams and columns, and structural stiffness for the columns. They are then compared with the proposed model. The main parameters studied to describe cracking and sectional behaviours of the beam tests are crack spacing, mean steel strain and crack width, while for the column tests these were moment/curvature, stress in rebars and crack with at column embedment. The comparison showed satisfactory agreement between experimental results and model predictions. Moreover, it is pointed out the improvement in cracking behaviour due to the addition of RSF for elements with low reinforcement ratios, elements with low squashing load ratios and for crack width control of elements with large concrete covers, thus representing results with a immediate impact in engineering practice (slab design, tanks, integral structures, etc.). Applications of RSF to actual structures are finally presented. Two cases of elements in pure bending are presented, namely a simple supported beam and a water treatment tank. In both cases the addition of RSF to concrete leads to improvements in cracking behaviour. Then, using the simplified model for the serviceability analysis of columns of jointless structures, the maximum achievable jointless length of typical cases of a bridge and building is obtained. In XIIparticular, it is shown how the limitations of current engineering practice (this is especially the case of buildings) can be increased by considering the actual behaviour of RC supports. Then, the same cases are modified considering the use of RSF, and the improvements both in maximum achievable length and in crack width for a given length and imposed strain at the deck/first floor are shown.

Storm evolution characterization for analysing stone armour damage progression

Storm evolution is fundamental for analysing the damage progression of the different failure modes and establishing suitable protocols for maintaining and optimally sizing structures. However, this aspect has hardly been studied and practically the whole of the studies dealing with the subject adopt the Equivalent triangle storm. As against this approach, two new ones are proposed. The first is the Equivalent Triangle Magnitude Storm model (ETMS), whose base, the triangular storm duration, D, is established such that its magnitude (area describing the storm history above the reference threshold level which sets the storm condition),HT, equals the real storm magnitude. The other is the Equivalent Triangle Number of Waves Storm (ETNWS), where the base is referred in terms of the real storm's number of waves,Nz. Three approaches are used for estimating the mean period, Tm, associated to each of the sea states defining the storm evolution, which is necessary to determine the full energy flux withstood by the structure in the course of the extreme event. Two are based on the Jonswap spectrum representativity and the other uses the bivariate Gumbel copula (Hs, Tm), resulting from adjusting the storm peaks. The representativity of the approaches proposed and those defined in specialised literature are analysed by comparing the main armour layer's progressive loss of hydraulic stability caused by real storms and that relating to theoretical ones. An empirical maximum energy flux model is used for this purpose. The agreement between the empirical and theoretical results demonstrates that the representativity of the different approaches depends on the storm characteristics and point towards a need to investigate other geometrical shapes to characterise the storm evolution associated with sea states heavily influenced by swell wave components.

Neuroanatomic-based detection algorithm for automatic labeling of brain structures in brain injury

The number and grade of injured neuroanatomic structures and the type of injury determine the degree of impairment after a brain injury event and the recovery options of the patient. However, the body of knowledge and clinical intervention guides are basically focused on functional disorder and they still do not take into account the location of injuries. The prognostic value of location information is not known in detail either. This paper proposes a feature-based detection algorithm, named Neuroanatomic-Based Detection Algorithm (NBDA), based on SURF (Speeded Up Robust Feature) to label anatomical brain structures on cortical and sub-cortical areas. Themain goal is to register injured neuroanatomic structures to generate a database containing patient?s structural impairment profile. This kind of information permits to establish a relation with functional disorders and the prognostic evolution during neurorehabilitation procedures.

Estimation of modal parameters in structures using multiple time history records

In Operational Modal Analysis of structures we often have multiple time history records of vibrations measured at different time instants. This work presents a procedure for estimating the modal parameters of the structure processing all the records, that is, using all available information to obtain a single estimate of the modal parameters. The method uses Maximum Likelihood Estimation and the Expectation Maximization algorithm. Finally, it has been applied to various problems for both simulated and real structures and the results show the advantage of the joint analysis proposed.

Smart aeronautical structures: development and experimental validation of a structural health monitoring system for damage detection

En muchas áreas de la ingeniería, la integridad y confiabilidad de las estructuras son aspectos de extrema importancia. Estos son controlados mediante el adecuado conocimiento de danos existentes. Típicamente, alcanzar el nivel de conocimiento necesario que permita caracterizar la integridad estructural implica el uso de técnicas de ensayos no destructivos. Estas técnicas son a menudo costosas y consumen mucho tiempo. En la actualidad, muchas industrias buscan incrementar la confiabilidad de las estructuras que emplean. Mediante el uso de técnicas de última tecnología es posible monitorizar las estructuras y en algunos casos, es factible detectar daños incipientes que pueden desencadenar en fallos catastróficos. Desafortunadamente, a medida que la complejidad de las estructuras, los componentes y sistemas incrementa, el riesgo de la aparición de daños y fallas también incrementa. Al mismo tiempo, la detección de dichas fallas y defectos se torna más compleja. En años recientes, la industria aeroespacial ha realizado grandes esfuerzos para integrar los sensores dentro de las estructuras, además de desarrollar algoritmos que permitan determinar la integridad estructural en tiempo real. Esta filosofía ha sido llamada “Structural Health Monitoring” (o “Monitorización de Salud Estructural” en español) y este tipo de estructuras han recibido el nombre de “Smart Structures” (o “Estructuras Inteligentes” en español). Este nuevo tipo de estructuras integran materiales, sensores, actuadores y algoritmos para detectar, cuantificar y localizar daños dentro de ellas mismas. Una novedosa metodología para detección de daños en estructuras se propone en este trabajo. La metodología está basada en mediciones de deformación y consiste en desarrollar técnicas de reconocimiento de patrones en el campo de deformaciones. Estas últimas, basadas en PCA (Análisis de Componentes Principales) y otras técnicas de reducción dimensional. Se propone el uso de Redes de difracción de Bragg y medidas distribuidas como sensores de deformación. La metodología se validó mediante pruebas a escala de laboratorio y pruebas a escala real con estructuras complejas. Los efectos de las condiciones de carga variables fueron estudiados y diversos experimentos fueron realizados para condiciones de carga estáticas y dinámicas, demostrando que la metodología es robusta ante condiciones de carga desconocidas. ABSTRACT In many engineering fields, the integrity and reliability of the structures are extremely important aspects. They are controlled by the adequate knowledge of existing damages. Typically, achieving the level of knowledge necessary to characterize the structural integrity involves the usage of nondestructive testing techniques. These are often expensive and time consuming. Nowadays, many industries look to increase the reliability of the structures used. By using leading edge techniques it is possible to monitoring these structures and in some cases, detect incipient damage that could trigger catastrophic failures. Unfortunately, as the complexity of the structures, components and systems increases, the risk of damages and failures also increases. At the same time, the detection of such failures and defects becomes more difficult. In recent years, the aerospace industry has done great efforts to integrate the sensors within the structures and, to develop algorithms for determining the structural integrity in real time. The ‘philosophy’ has being called “Structural Health Monitoring” and these structures have been called “smart structures”. These new types of structures integrate materials, sensors, actuators and algorithms to detect, quantify and locate damage within itself. A novel methodology for damage detection in structures is proposed. The methodology is based on strain measurements and consists in the development of strain field pattern recognition techniques. The aforementioned are based on PCA (Principal Component Analysis) and other dimensional reduction techniques. The use of fiber Bragg gratings and distributed sensing as strain sensors is proposed. The methodology have been validated by using laboratory scale tests and real scale tests with complex structures. The effects of the variable load conditions were studied and several experiments were performed for static and dynamic load conditions, demonstrating that the methodology is robust under unknown load conditions.

Uncertainties in the modal estimation from output-only data in civil structures

Cualquier estructura vibra según unas frecuencias propias definidas por sus parámetros modales (frecuencias naturales, amortiguamientos y formas modales). A través de las mediciones de la vibración en puntos clave de la estructura, los parámetros modales pueden ser estimados. En estructuras civiles, es difícil excitar una estructura de manera controlada, por lo tanto, las técnicas que implican la estimación de los parámetros modales sólo registrando su respuesta son de vital importancia para este tipo de estructuras. Esta técnica se conoce como Análisis Modal Operacional (OMA). La técnica del OMA no necesita excitar artificialmente la estructura, atendiendo únicamente a su comportamiento en servicio. La motivación para llevar a cabo pruebas de OMA surge en el campo de la Ingeniería Civil, debido a que excitar artificialmente con éxito grandes estructuras no sólo resulta difícil y costoso, sino que puede incluso dañarse la estructura. Su importancia reside en que el comportamiento global de una estructura está directamente relacionado con sus parámetros modales, y cualquier variación de rigidez, masa o condiciones de apoyo, aunque sean locales, quedan reflejadas en los parámetros modales. Por lo tanto, esta identificación puede integrarse en un sistema de vigilancia de la integridad estructural. La principal dificultad para el uso de los parámetros modales estimados mediante OMA son las incertidumbres asociadas a este proceso de estimación. Existen incertidumbres en el valor de los parámetros modales asociadas al proceso de cálculo (internos) y también asociadas a la influencia de los factores ambientales (externas), como es la temperatura. Este Trabajo Fin de Máster analiza estas dos fuentes de incertidumbre. Es decir, en primer lugar, para una estructura de laboratorio, se estudian y cuantifican las incertidumbres asociadas al programa de OMA utilizado. En segundo lugar, para una estructura en servicio (una pasarela de banda tesa), se estudian tanto el efecto del programa OMA como la influencia del factor ambiental en la estimación de los parámetros modales. Más concretamente, se ha propuesto un método para hacer un seguimiento de las frecuencias naturales de un mismo modo. Este método incluye un modelo de regresión lineal múltiple que permite eliminar la influencia de estos agentes externos. A structure vibrates according to some of its vibration modes, defined by their modal parameters (natural frequencies, damping ratios and modal shapes). Through the measurements of the vibration at key points of the structure, the modal parameters can be estimated. In civil engineering structures, it is difficult to excite structures in a controlled manner, thus, techniques involving output-only modal estimation are of vital importance for these structure. This techniques are known as Operational Modal Analysis (OMA). The OMA technique does not need to excite artificially the structure, this considers its behavior in service only. The motivation for carrying out OMA tests arises in the area of Civil Engineering, because successfully artificially excite large structures is difficult and expensive. It also may even damage the structure. The main goal is that the global behavior of a structure is directly related to their modal parameters, and any variation of stiffness, mass or support conditions, although it is local, is also reflected in the modal parameters. Therefore, this identification may be within a Structural Health Monitoring system. The main difficulty for using the modal parameters estimated by an OMA is the uncertainties associated to this estimation process. Thus, there are uncertainties in the value of the modal parameters associated to the computing process (internal) and the influence of environmental factors (external), such as the temperature. This Master’s Thesis analyzes these two sources of uncertainties. That is, firstly, for a lab structure, the uncertainties associated to the OMA program used are studied and quantified. Secondly, for an in-service structure (a stress-ribbon footbridge), both the effect of the OMA program and the influence of environmental factor on the modal parameters estimation are studied. More concretely, a method to track natural frequencies of the same mode has been proposed. This method includes a multiple linear regression model that allows to remove the influence of these external agents.

Space structures for sports buildings: Tien T. Lan and Yuan Zhilian (eds). Elsevier Applied Science Publishers, The Netherlands, 1987

This book review states that parts of this interesting volume may prove useful as a reference for designers and researchers in the field, though it lacks somewhat in unity and various important topics are not covered.

Seismic soil-interaction on earth retaining structures. Performance-based seismic design of a Retaining Wall

The design of containment walls suffering seismic loads traditionally has been realized with methods based on pseudoanalitic procedures such as Mononobe- Okabe's method, which it has led in certain occasions to insecure designs, that they have produced the ruin of many containment walls suffering the action of an earthquake. A method is proposed in this papers for the design of containment walls in different soils, suffering to the action of an earthquake, based on the Performance-Based Seismic Design.

Analysis of the static and dynamic behaviour of hydraulic fills

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. 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. 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 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. 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.