Modelling of landslides propagation with SPH : effects of rheology and pore water pressure

El estudio desarrollado en este trabajo de tesis se centra en la modelización numérica de la fase de propagación de los deslizamientos rápidos de ladera a través del método sin malla Smoothed Particle Hydrodynamics (SPH). Este método tiene la gran ventaja de permitir el análisis de problemas de grandes deformaciones evitando operaciones costosas de remallado como en el caso de métodos numéricos con mallas tal como el método de los Elementos Finitos. En esta tesis, particular atención viene dada al rol que la reología y la presión de poros desempeñan durante estos eventos. El modelo matemático utilizado se basa en la formulación de Biot-Zienkiewicz v - pw, que representa el comportamiento, expresado en términos de velocidad del esqueleto sólido y presiones de poros, de la mezcla de partículas sólidas en un medio saturado. Las ecuaciones que gobiernan el problema son: • la ecuación de balance de masa de la fase del fluido intersticial, • la ecuación de balance de momento de la fase del fluido intersticial y de la mezcla, • la ecuación constitutiva y • una ecuación cinemática. Debido a sus propiedades geométricas, los deslizamientos de ladera se caracterizan por tener una profundidad muy pequeña frente a su longitud y a su anchura, y, consecuentemente, el modelo matemático mencionado anteriormente se puede simplificar integrando en profundidad las ecuaciones, pasando de un modelo 3D a 2D, el cual presenta una combinación excelente de precisión, sencillez y costes computacionales. El modelo propuesto en este trabajo se diferencia de los modelos integrados en profundidad existentes por incorporar un ulterior modelo capaz de proveer información sobre la presión del fluido intersticial a cada paso computacional de la propagación del deslizamiento. En una manera muy eficaz, la evolución de los perfiles de la presión de poros está numéricamente resuelta a través de un esquema explicito de Diferencias Finitas a cada nodo SPH. Este nuevo enfoque es capaz de tener en cuenta la variación de presión de poros debida a cambios de altura, de consolidación vertical o de cambios en las tensiones totales. Con respecto al comportamiento constitutivo, uno de los problemas principales al modelizar numéricamente deslizamientos rápidos de ladera está en la dificultad de simular con la misma ley constitutiva o reológica la transición de la fase de iniciación, donde el material se comporta como un sólido, a la fase de propagación donde el material se comporta como un fluido. En este trabajo de tesis, se propone un nuevo modelo reológico basado en el modelo viscoplástico de Perzyna, pensando a la viscoplasticidad como a la llave para poder simular tanto la fase de iniciación como la de propagación con el mismo modelo constitutivo. Con el fin de validar el modelo matemático y numérico se reproducen tanto ejemplos de referencia con solución analítica como experimentos de laboratorio. Finalmente, el modelo se aplica a casos reales, con especial atención al caso del deslizamiento de 1966 en Aberfan, mostrando como los resultados obtenidos simulan con éxito estos tipos de riesgos naturales. The study developed in this thesis focuses on the modelling of landslides propagation with the Smoothed Particle Hydrodynamics (SPH) meshless method which has the great advantage of allowing to deal with large deformation problems by avoiding expensive remeshing operations as happens for mesh methods such as, for example, the Finite Element Method. In this thesis, special attention is given to the role played by rheology and pore water pressure during these natural hazards. The mathematical framework used is based on the v - pw Biot-Zienkiewicz formulation, which represents the behaviour, formulated in terms of soil skeleton velocity and pore water pressure, of the mixture of solid particles and pore water in a saturated media. The governing equations are: • the mass balance equation for the pore water phase, • the momentum balance equation for the pore water phase and the mixture, • the constitutive equation and • a kinematic equation. Landslides, due to their shape and geometrical properties, have small depths in comparison with their length or width, therefore, the mathematical model aforementioned can then be simplified by depth integrating the equations, switching from a 3D to a 2D model, which presents an excellent combination of accuracy, computational costs and simplicity. The proposed model differs from previous depth integrated models by including a sub-model able to provide information on pore water pressure profiles at each computational step of the landslide's propagation. In an effective way, the evolution of the pore water pressure profiles is numerically solved through a set of 1D Finite Differences explicit scheme at each SPH node. This new approach is able to take into account the variation of the pore water pressure due to changes of height, vertical consolidation or changes of total stress. Concerning the constitutive behaviour, one of the main issues when modelling fast landslides is the difficulty to simulate with the same constitutive or rheological model the transition from the triggering phase, where the landslide behaves like a solid, to the propagation phase, where the landslide behaves in a fluid-like manner. In this work thesis, a new rheological model is proposed, based on the Perzyna viscoplastic model, thinking of viscoplasticity as the key to close the gap between the triggering and the propagation phase. In order to validate the mathematical model and the numerical approach, benchmarks and laboratory experiments are reproduced and compared to analytical solutions when possible. Finally, applications to real cases are studied, with particular attention paid to the Aberfan flowslide of 1966, showing how the mathematical model accurately and successfully simulate these kind of natural hazards.

Nonlinear models for lateral dynamics of railway vehicles on bridges subject to wind action

The study of lateral dynamics of running trains on bridges is of importance mainly for the safety of the traffic, and may be relevant for laterally compliant bridges. These studies require threedimensional coupled vehicle-bridge models, wheree consideration of wheel to rail contact is a key aspect. Furthermore, an adequate evaluation of safety of rail traffic requires nonlinear models. A nonlinear coupled model is proposed here for vehicle-structure vertical and lateral dynamics. Vehicles are considered as fully three-dimensional multibody systems including gyroscopic terms and large rotation effects. The bridge structure is modeled by means of finite elements which may be of beam, shell or continuum type and may include geometric or material nonlinearities. The track geometry includes distributed track alignment irregularities. Both subsystems (bridge and vehicles) are described with coordinates in absolute reference frames, as opposed to alternative approaches which describe the multibody system with coordinates relative to the base bridge motion. The wheelrail contact employed is a semi-Hertzian model based on realistic wheel-rail profiles. It allows a detailed geometrical description of the contact patch under each wheel including multiple-point contact, flange contact and uplift. Normal and tangential stresses in each contact are integrated at each time-step to obtain the resultant contact forces. The models have been implemented within an existing finite element analysis software with multibody capabilities, Abaqus (Simulia Ltd., 2010). Further details of the model are presented in Antolín et al. (2012). Representative applications are presented for railway vehicles under lateral wind action on laterally compliant viaducts, showing the relevance of the nonlinear wheel-rail contact model as well as the interaction between bridge and vehicle.

Modifications in the Dynamic Properties of a Structure due to Human Actions

The interest for modelling of human actions acting on structures has been recurrent since the first accidents on suspension bridges in the nineteenth century such as Broughton (1831) in the U.K. or Angers (1850) in France. Stadiums, gymnasiums are other types of structure where human induced vibration is very important. In these structures a particular phenomenon appears such as the interaction personstructure (lock-in), the person-person synchronization, and the influence of the mass and damping of the people in the structural behaviour. This paper focuses on the latter topic. In order to evaluate these property modifications several tests have been carried out on a stand-alone building. For the test an electro-dynamic shaker was installed at a fixed point of the gym slab and different groups of people were located around the shaker. The dynamic characteristics of the structure without people inside have been calculated by two methods: using a three-dimensional finite element model of the building and by operational modal analysis. These calculated experimental and numerical values are the reference values used to evaluate the modifications in the dynamic properties of the structure.

Dynamic analysis of payloads and structures with intermediate modal density

La necesidad de desarrollar técnicas para predecir la respuesta vibroacústica de estructuras espaciales lia ido ganando importancia en los últimos años. Las técnicas numéricas existentes en la actualidad son capaces de predecir de forma fiable el comportamiento vibroacústico de sistemas con altas o bajas densidades modales. Sin embargo, ambos rangos no siempre solapan lo que hace que sea necesario el desarrollo de métodos específicos para este rango, conocido como densidad modal media. Es en este rango, conocido también como media frecuencia, donde se centra la presente Tesis doctoral, debido a la carencia de métodos específicos para el cálculo de la respuesta vibroacústica. Para las estructuras estudiadas en este trabajo, los mencionados rangos de baja y alta densidad modal se corresponden, en general, con los rangos de baja y alta frecuencia, respectivamente. Los métodos numéricos que permiten obtener la respuesta vibroacústica para estos rangos de frecuencia están bien especificados. Para el rango de baja frecuencia se emplean técnicas deterministas, como el método de los Elementos Finitos, mientras que, para el rango de alta frecuencia las técnicas estadísticas son más utilizadas, como el Análisis Estadístico de la Energía. En el rango de medias frecuencias ninguno de estos métodos numéricos puede ser usado con suficiente precisión y, como consecuencia -a falta de propuestas más específicas- se han desarrollado métodos híbridos que combinan el uso de métodos de baja y alta frecuencia, intentando que cada uno supla las deficiencias del otro en este rango medio. Este trabajo propone dos soluciones diferentes para resolver el problema de la media frecuencia. El primero de ellos, denominado SHFL (del inglés Subsystem based High Frequency Limit procedure), propone un procedimiento multihíbrido en el cuál cada subestructura del sistema completo se modela empleando una técnica numérica diferente, dependiendo del rango de frecuencias de estudio. Con este propósito se introduce el concepto de límite de alta frecuencia de una subestructura, que marca el límite a partir del cual dicha subestructura tiene una densidad modal lo suficientemente alta como para ser modelada utilizando Análisis Estadístico de la Energía. Si la frecuencia de análisis es menor que el límite de alta frecuencia de la subestructura, ésta se modela utilizando Elementos Finitos. Mediante este método, el rango de media frecuencia se puede definir de una forma precisa, estando comprendido entre el menor y el mayor de los límites de alta frecuencia de las subestructuras que componen el sistema completo. Los resultados obtenidos mediante la aplicación de este método evidencian una mejora en la continuidad de la respuesta vibroacústica, mostrando una transición suave entre los rangos de baja y alta frecuencia. El segundo método propuesto se denomina HS-CMS (del inglés Hybrid Substructuring method based on Component Mode Synthesis). Este método se basa en la clasificación de la base modal de las subestructuras en conjuntos de modos globales (que afectan a todo o a varias partes del sistema) o locales (que afectan a una única subestructura), utilizando un método de Síntesis Modal de Componentes. De este modo es posible situar espacialmente los modos del sistema completo y estudiar el comportamiento del mismo desde el punto de vista de las subestructuras. De nuevo se emplea el concepto de límite de alta frecuencia de una subestructura para realizar la clasificación global/local de los modos en la misma. Mediante dicha clasificación se derivan las ecuaciones globales del movimiento, gobernadas por los modos globales, y en las que la influencia del conjunto de modos locales se introduce mediante modificaciones en las mismas (en su matriz dinámica de rigidez y en el vector de fuerzas). Las ecuaciones locales se resuelven empleando Análisis Estadístico de Energías. Sin embargo, este último será un modelo híbrido, en el cual se introduce la potencia adicional aportada por la presencia de los modos globales. El método ha sido probado para el cálculo de la respuesta de estructuras sometidas tanto a cargas estructurales como acústicas. Ambos métodos han sido probados inicialmente en estructuras sencillas para establecer las bases e hipótesis de aplicación. Posteriormente, se han aplicado a estructuras espaciales, como satélites y reflectores de antenas, mostrando buenos resultados, como se concluye de la comparación de las simulaciones y los datos experimentales medidos en ensayos, tanto estructurales como acústicos. Este trabajo abre un amplio campo de investigación a partir del cual es posible obtener metodologías precisas y eficientes para reproducir el comportamiento vibroacústico de sistemas en el rango de la media frecuencia. ABSTRACT Over the last years an increasing need of novel prediction techniques for vibroacoustic analysis of space structures has arisen. Current numerical techniques arc able to predict with enough accuracy the vibro-acoustic behaviour of systems with low and high modal densities. However, space structures are, in general, very complex and they present a range of frequencies in which a mixed behaviour exist. In such cases, the full system is composed of some sub-structures which has low modal density, while others present high modal density. This frequency range is known as the mid-frequency range and to develop methods for accurately describe the vibro-acoustic response in this frequency range is the scope of this dissertation. For the structures under study, the aforementioned low and high modal densities correspond with the low and high frequency ranges, respectively. For the low frequency range, deterministic techniques as the Finite Element Method (FEM) are used while, for the high frequency range statistical techniques, as the Statistical Energy Analysis (SEA), arc considered as more appropriate. In the mid-frequency range, where a mixed vibro-acoustic behaviour is expected, any of these numerical method can not be used with enough confidence level. As a consequence, it is usual to obtain an undetermined gap between low and high frequencies in the vibro-acoustic response function. This dissertation proposes two different solutions to the mid-frequency range problem. The first one, named as The Subsystem based High Frequency Limit (SHFL) procedure, proposes a multi-hybrid procedure in which each sub-structure of the full system is modelled with the appropriate modelling technique, depending on the frequency of study. With this purpose, the concept of high frequency limit of a sub-structure is introduced, marking out the limit above which a substructure has enough modal density to be modelled by SEA. For a certain analysis frequency, if it is lower than the high frequency limit of the sub-structure, the sub-structure is modelled through FEM and, if the frequency of analysis is higher than the high frequency limit, the sub-structure is modelled by SEA. The procedure leads to a number of hybrid models required to cover the medium frequency range, which is defined as the frequency range between the lowest substructure high frequency limit and the highest one. Using this procedure, the mid-frequency range can be define specifically so that, as a consequence, an improvement in the continuity of the vibro-acoustic response function is achieved, closing the undetermined gap between the low and high frequency ranges. The second proposed mid-frequency solution is the Hybrid Sub-structuring method based on Component Mode Synthesis (HS-CMS). The method adopts a partition scheme based on classifying the system modal basis into global and local sets of modes. This classification is performed by using a Component Mode Synthesis, in particular a Craig-Bampton transformation, in order to express the system modal base into the modal bases associated with each sub-structure. Then, each sub-structure modal base is classified into global and local set, fist ones associated with the long wavelength motion and second ones with the short wavelength motion. The high frequency limit of each sub-structure is used as frequency frontier between both sets of modes. From this classification, the equations of motion associated with global modes are derived, which include the interaction of local modes by means of corrections in the dynamic stiffness matrix and the force vector of the global problem. The local equations of motion are solved through SEA, where again interactions with global modes arc included through the inclusion of an additional input power into the SEA model. The method has been tested for the calculation of the response function of structures subjected to structural and acoustic loads. Both methods have been firstly tested in simple structures to establish their basis and main characteristics. Methods are also verified in space structures, as satellites and antenna reflectors, providing good results as it is concluded from the comparison with experimental results obtained in both, acoustic and structural load tests. This dissertation opens a wide field of research through which further studies could be performed to obtain efficient and accurate methodologies to appropriately reproduce the vibro-acoustic behaviour of complex systems in the mid-frequency range.

Mechanical behavior of 2G REBCO HTS at 77 and 300 K

El gran esfuerzo realizado durante la última década con el fin de integrar los diferentes materiales superconductores en el campo de los sistemas eléctricos y en otras aplicaciones tecnológicas ha dado lugar a un campo de investigación amplio y prometedor. El comportamiento eléctrico de los Superconductores de Alta Temperatura (SAT) crítica (masivo y cintas) depende de diferentes parámetros desde su fabricación hasta la aplicación final con imanes o cables. Sin embargo, las aplicaciones prácticas de estos materiales están fuertemente vinculadas con su comportamiento mecánico tanto a temperatura ambiente (manipulación durante fabricación o instalación) como a temperaturas criogénicas (condiciones de servicio). En esta tesis se ha estudiado el comportamiento mecánico de materiales masivos y cintas de alta temperatura crítica a 300 y 77 K (utilizando nitrógeno líquido). Se han obtenido la resistencia en flexión, la tenacidad de fractura y la resistencia a tracción a la temperatura de servicio y a 300 K. Adicionalmente, se ha medido la dureza mediante el ensayo Vickers y nanoindentación. El módulo Young se midió mediante tres métodos diferentes: 1) nanoindentación, 2) ensayos de flexión en tres puntos y 3) resonancia vibracional mediante grindosonic. Para cada condición de ensayo, se han analizado detalladamente las superficies de fractura y los micromecanismos de fallo. Las propiedades mecánicas de los materiales se han comparado con el fin de entender la influencia de las técnicas de procesado y de las características microestructurales de los monocristales en su comportamiento mecánico. Se ha estudiado el comportamiento electromecánico de cintas comerciales superconductoras de YBCO mediante ensayos de tracción y fatiga a 77 y 300 K. El campo completo de deformaciones en la superficie del material se ha obtenido utilizando Correlación Digital de Imágenes (DIC, por sus siglas en inglés) a 300 K. Además, se realizaron ensayos de fragmentación in situ dentro de un microscopio electrónico con el fin de estudiar la fractura de la capa superconductora y determinar la resistencia a cortante de la intercara entre el substrato y la capa cerámica. Se ha conseguido ver el proceso de la fragmentación aplicando tensión axial y finalmente, se han implementado simulaciones mediante elementos finitos para reproducir la delaminación y el fenómeno de la fragmentación. Por último, se han preparado uniones soldadas entre las capas de cobre de dos cintas superconductoras. Se ha medido la resistencia eléctrica de las uniones con el fin de evaluar el metal de soldadura y el proceso. Asimismo, se ha llevado a cabo la caracterización mecánica de las uniones mediante ensayos "single lap shear" a 300 y 77 K. El efecto del campo magnético se ha estudiado aplicando campo externo hasta 1 T perpendicular o paralelo a la cinta-unión a la temperatura de servicio (77 K). Finalmente, la distribución de tensiones en cada una de las capas de la cinta se estudió mediante simulaciones de elementos finitos, teniendo en cuenta las capas de la cinta mecánicamente más representativas (Cu-Hastelloy-Cu) que influyen en su comportamiento mecánico. The strong effort that has been made in the last years to integrate the different superconducting materials in the field of electrical power systems and other technological applications led to a wide and promising research field. The electrical behavior of High Temperature Superconducting (HTS) materials (bulk and coated conductors) depends on different parameters since their processing until their final application as magnets or cables. However, practical applications of such materials are strongly related with their mechanical performance at room temperature (handling) as well as at cryogenic temperatures (service conditions). In this thesis, the mechanical behavior of HTS bulk and coated conductors was investigated at 300 and 77 K (by immersion in liquid nitrogen). The flexural strength, the fracture toughness and the tensile strength were obtained at service temperature as well as at 300 K. Furthermore, their hardness was determined by Vickers measurements and nanoindentation and the Young's modulus was measured by three different techniques: 1) nanoindentation, 2) three-point bending tests and 3) vibrational resonance with a grindosonic device. The fracture and deformation micromechanics have been also carefully analyzed for each testing condition. The comparison between the studied materials has been performed in order to understand the influence of the main sintering methods and the microstructural characteristics of the single grains on the macroscopic mechanical behavior. The electromechanical behavior of commercial YBCO coated conductors was studied. The mechanical behavior of the tapes was studied under tensile and fatigue tests at 77 and 300 K. The complete strain field on the surface of the sample was obtained by applying Digital Image Correlation (DIC) at 300 K. Addionally, in situ fragmentation tests inside a Scanning Electron Microscope (SEM) were carried out in order to study the fragmentation of the superconducting layer and determine the interfacial shear strength between substrate and ceramic layer. The fragmentation process upon loading of the YBCO layer has been observed and finally, Finite Element Simulations were employed to reproduce delamination and fragmentation phenomena. Finally, joints between the stabilizing Cu sides of two coated conductors have been prepared. The electrical resistivity of the joints was measured for the purpose of qualifying the soldering material and evaluating the soldering process. Additionally, mechanical characterization under single lap shear tests at 300 and 77 K has been carried out. The effect of the applied magnetic field has been studied by applying external magnetic field up to 1 T perpendicular and parallel to the tape-joint at service temperature (77 K). Finally, finite element simulations were employed to study the distribution of the stresses in earch layer, taking into account the three mechanically relevant layers of the coated conductor (Cu-Hastelloy-Cu) that affect its mechanical behavior

The use of non-reflecting boundary conditions in soil dynamics

In this paper some aspects of the use of non-reflecting boundaries in dynamic problems, analyzed in time domain, are considered. Current trends for treating the above mentioned problems are summarized with a particular emphasis on the use of numerical techniques, such as Boundary Element Method (BEM) or mixed and hybrid formulations, Finite Element Method (FEM) plus BEM. As an alternative to these methods, an easy time domain boundary condition, obtained from the well known consistent transmitting boundary developed by Waas for frequency domain analysis, can be applied to represent the reactions of the unbounded soil on the interest zone. The behaviour of this proposed boundary condition is studied when waves of different frequency to the one used for its obtention are acting on the physical edge of the model. As an application example,an analysis is made of the soil-structure interaction of a rigid strip foundation on a horizontal non-linear elastic layer on bed rock. The results obtained suggest the need of time domain solutions for this type of problem

Modelos sin malla en simulación numérica de estructuras aeroespaciales

La presente Tesis Doctoral aborda la introducción de la Partición de Unidad de Bernstein en la forma débil de Galerkin para la resolución de problemas de condiciones de contorno en el ámbito del análisis estructural. La familia de funciones base de Bernstein conforma un sistema generador del espacio de funciones polinómicas que permite construir aproximaciones numéricas para las que no se requiere la existencia de malla: las funciones de forma, de soporte global, dependen únicamente del orden de aproximación elegido y de la parametrización o mapping del dominio, estando las posiciones nodales implícitamente definidas. El desarrollo de la formulación está precedido por una revisión bibliográfica que, con su punto de partida en el Método de Elementos Finitos, recorre las principales técnicas de resolución sin malla de Ecuaciones Diferenciales en Derivadas Parciales, incluyendo los conocidos como Métodos Meshless y los métodos espectrales. En este contexto, en la Tesis se somete la aproximación Bernstein-Galerkin a validación en tests uni y bidimensionales clásicos de la Mecánica Estructural. Se estudian aspectos de la implementación tales como la consistencia, la capacidad de reproducción, la naturaleza no interpolante en la frontera, el planteamiento con refinamiento h-p o el acoplamiento con otras aproximaciones numéricas. Un bloque importante de la investigación se dedica al análisis de estrategias de optimización computacional, especialmente en lo referente a la reducción del tiempo de máquina asociado a la generación y operación con matrices llenas. Finalmente, se realiza aplicación a dos casos de referencia de estructuras aeronáuticas, el análisis de esfuerzos en un angular de material anisotrópico y la evaluación de factores de intensidad de esfuerzos de la Mecánica de Fractura mediante un modelo con Partición de Unidad de Bernstein acoplada a una malla de elementos finitos. ABSTRACT This Doctoral Thesis deals with the introduction of Bernstein Partition of Unity into Galerkin weak form to solve boundary value problems in the field of structural analysis. The family of Bernstein basis functions constitutes a spanning set of the space of polynomial functions that allows the construction of numerical approximations that do not require the presence of a mesh: the shape functions, which are globally-supported, are determined only by the selected approximation order and the parametrization or mapping of the domain, being the nodal positions implicitly defined. The exposition of the formulation is preceded by a revision of bibliography which begins with the review of the Finite Element Method and covers the main techniques to solve Partial Differential Equations without the use of mesh, including the so-called Meshless Methods and the spectral methods. In this context, in the Thesis the Bernstein-Galerkin approximation is subjected to validation in one- and two-dimensional classic benchmarks of Structural Mechanics. Implementation aspects such as consistency, reproduction capability, non-interpolating nature at boundaries, h-p refinement strategy or coupling with other numerical approximations are studied. An important part of the investigation focuses on the analysis and optimization of computational efficiency, mainly regarding the reduction of the CPU cost associated with the generation and handling of full matrices. Finally, application to two reference cases of aeronautic structures is performed: the stress analysis in an anisotropic angle part and the evaluation of stress intensity factors of Fracture Mechanics by means of a coupled Bernstein Partition of Unity - finite element mesh model.

Influencia de la configuración geométrica de placas prefabricadas para forjados en las tensiones originadas por la transferencia del pretensado en elementos realizados con armaduras pretesas ancladas por adherencia

Las piezas pretensadas de hormigón presentan zonas muy solicitadas correspondientes a la zona de transferencia. En muchos casos se ha detectado figuración en tales zonas cuyo origen está ligado a la transferencia de la fuerza de pretensado, pudiendo llegar a causar el rechazo de la pieza. En el caso de las piezas prefabricadas con armaduras pretesas adherentes, no siempre es posible disponer armado transversal para controlar esta fisuración, ya sea por el proceso constructivo, ya sea por disponer en general de secciones transversales muy optimizadas. Recientemente se desarrolló una nueva tipología de piezas de hormigón prefabricado para forjados unidireccionales pretensadas con armadura activa pretesa y sin armadura transversal. La tipología se asimila a una sección en PI invertida, con alas de gran envergadura en comparación con el ancho de nervio, y armadura activa distribuida en las alas. Este diseño parece propenso a la aparición de fisuración en el momento de la transferencia del pretensado. Así, se han producido fallos de carácter frágil: colapso de piezas ya colocadas en obra, separándose la losa inferior de los nervios y cayendo sobre el piso. Las herramientas de análisis usuales han resultado inútiles al aplicarse a la investigación de esta patología. Para afrontar el estudio de los problemas detectados en la tipología, se ha analizado el fenómeno de las tensiones de tracción en la zona de transferencia, usualmente denominadas exfoliación y estallido, así como los métodos de análisis aplicables a elementos pretesos sin armadura transversal. En algunas ocasiones se trata del resultado de trabajos desarrollados para piezas postesadas, o para calcular cuantías de armadura transversal, adaptados a posteriori. También existen métodos desarrollados específicamente para piezas pretesas sin armadura transversal. Junto a los factores considerados en los métodos existentes se han localizado otros, no tenidos en cuenta habitualmente, pero que pueden ser determinantes en piezas no convencionales, como son: la existencia de pretensado superior e inferior, la falta de simetría de la sección transversal, el ancho variable de las piezas, una relación entre el ancho del ala y el espesor de los nervios elevada, la distribución transversal del pretensado en relación al ancho variable. Además, la mayoría de los métodos se han basado en simplificaciones bidimensionales. Para tener en cuenta la influencia de estos factores, se han modelizado piezas en las que varían tanto la geometría de la sección transversal y la cuantía de pretensado, como la ley de adherencia o la distribución de armadura activa en la sección. Estos modelos se han analizado mediante el método de elementos finitos, efectuándose u análisis elástico lineal tridimensional. En general, los métodos existentes no han predicho adecuadamente las tensiones obtenidas mediante elementos finitos. Sobre los resultados obtenidos por elementos finitos se ha desarrollado un ajuste experimental, que presentan un alto grado de correlación y de significación, así como una reducida dispersión y error relativo. En consecuencia, se propone un método de obtención de la tensión máxima de exfoliación, consistente en varias ecuaciones, que tienen en cuenta las peculiaridades de la configuración de las piezas citadas y permiten considerar cualquier ley de adherencia, manteniendo la coherencia con la longitud de transmisión. Las ecuaciones se emplean para la obtención de la tensión máxima de exfoliación en piezas de la tipología estudiada cuya armadura activa se sitúe fuera del núcleo central de la sección transversal. Respecto al estallido, se propone una modificación de los métodos existentes que, comparado con los resultados del análisis por elementos finitos, mejora el valor medio y la dispersión a valores admisibles y del lado de la seguridad. El método considera la geometría de la sección y la distribución del pretensado en la losa inferior. Finalmente, se ofrecen estrategias de diseño para piezas de la tipología o semejantes. End zones of prestressed concrete members are highly stressed. Cracking have often appeared at end zone, and its beginning is related to prestress release. Some members become rejected because of these cracks. Sometimes it is not possible having transverse reinforcement in order to control cracking, when referring to pretensioned precast members. The reason may be the construction process or highly optimized crosssections. A new typology of precast concrete members designed for one-way composite floors was recently developed. The members, without transverse reinforcement, are prestressed with pretensioned wires or strands. This typology is similar to an inverted TT slab, with a large flange related to the web thickness and prestressing reinforcement spread across the flange. This design is highly susceptible to appear cracking at prestress release. Therefore, brittle failures have been reported: fail of slabs laid in place on a construction site, resulting in the separation of the flange from the webs,, and the subsequent fall on the lower floor. Usual analytical methods have been useless to study the failure. End zone tensile stresses have been analysed to study the detected typology problems. These tensile stresses are usually called spalling and bursting (also called splitting in the U.S.). Analysis methods applicable to pretensioned members without transverse reinforcement have been analysed too. Some methods were originally developed for postensioned concrete or for obtaining the amount of transverse reinforcement. In addition, there are methods developed specifically for pretensioned members without transverse reinforcement. Some factors, frequently ignored, have been found, such as lower and upper prestress, lack of symmetry in the cross section, variable width, a high ratio between flange width and web thickness or prestressing reinforcement location related to variable width. They can play a decisive role in non-conventional members. In addition, most methods are based on 2D simplifications. Finite Element modelling has been conducted in order to consider the influence of these factors. A linear 3D approach has been used. The modelled members vary according to cross section geometry, bond behaviour, or prestressing reinforcement location. In general, the obtained tensile stresses don’t agree with existing methods. An experimental adjustment has been conducted on the obtained results, with a high correlation ratio and significance level as well as a low dispersion and relative error. Therefore, a method to obtain the maximum spalling stress is proposed. The proposal consists on some equations that consider the special features of the typology and bond behaviour. Consistency between transmission length and bond behaviour is considered too. The equations are used to calculate maximum spalling stress for the studied typology members whose prestressing reinforcement is located out of the core of the cross section. In relation to bursting, a modification of existing methods is proposed. Compared to finite element results, the proposal improves mean value and dispersion, whose ranges are considered acceptable and secure. The method takes into account cross section geometry and location of prestressing reinforcement across the lower flange. Finally, strategies to design members of this typology or similar are proposed.

Numerical analysis of shell and spatial structures

Since the advent of the computer into the engineering field, the application of the numerical methods to the solution of engineering problems has grown very rapidly. Among the different computer methods of structural analysis the Finite Element (FEM) has been predominantly used. Shells and space structures are very attractive and have been constructed to solve a large variety of functional problems (roofs, industrial building, aqueducts, reservoirs, footings etc). In this type of structures aesthetics, structural efficiency and concept play a very important role. This class of structures can be divided into three main groups, namely continuous (concrete) shells, space frames and tension (fabric, pneumatic, cable etc )structures. In the following only the current applications of the FEM to the analysis of continuous shell structures will be discussed. However, some of the comments on this class of shells can be also applied to some extend to the others, but obviously specific computational problems will be restricted to the continuous shells. Different aspects, such as, the type of elements,input-output computational techniques etc, of the analysis of shells by the FEM will be described below. Clearly, the improvements and developments occurring in general for the FEM since its first appearance in the fifties have had a significative impact on the particular class of structures under discussion.

Beam Spectral Element with FRP Debonding

The behaviour of the interface between the FRP and the concrete is the key factor controlling debonding failures in FRP-strengthened RC structures. This defect can cause reductions in static strength, structural integrity and the change in the dynamic behavior of the structure. The adverse effect on the dynamic behavior of the defects can be utilized as an effective means for identifying and assessing both the location and size of debonding at its earliest stages. The presence of debonding changes the structural dynamic characteristics and might be traced in modal parameters, dynamic strain and wave patterns etc. Detection of minor local defects, as those origin of a future debonding, requires working at high frequencies so that the wavelength of the excited is small and sensitive enough to detect local damage. The development of a spectral element method gives a large potential in high-frequency structural modeling. In contrast to the conventional finite element, since inertial properties are modeled exactly few elements are necessary to capture very accurate solutions at the highest frequencies in large regions. A wide variety of spectral elements have been developed for structural members over finite and semi-infinite regions. The objective of this paper is to develop a Spectral Finite Element Model to efficiently capture the behavior of intermediate debonding of a FRP strengthened RC beam during wave-based diagnostics.

Stabilization of embankments on inclined surfaces by micropiles

Embankments constructed on hillsides can have serious problems of stability, generally created by the action of water com-bined with the inclination of the hillside. In order to increase the stability or correct problems of instability already present, there are various methods that can be used: surface and deep drainage, reinforcements with anchored beams, medium and large diameter piles, etc. Standing out among these systems (for its versatility) is the use of micropiles which ?sew? the embankment to a non-unstable area of the hillside. This paper presents research undertaken by means of a finite element code for studying the effect and stress of the micropiles, comparing the results with real measurements taken in the south of Spain.