Simulation of the deformation of polycrystalline nanostructured Ti by computational homogenization

Computational homogenization by means of the finite element analysis of a representative volume element of the microstructure is used to simulate the deformation of nanostructured Ti. The behavior of each grain is taken into account using a single crystal elasto-viscoplastic model which includes the microscopic mechanisms of plastic deformation by slip along basal, prismatic and pyramidal systems. Two different representations of the polycrystal were used. Each grain was modeled with one cubic finite element in the first one while many cubic elements were used to represent each grain in the second one, leading to a model which includes the effect of grain shape and size in a limited number of grains due to the computational cost. Both representations were used to simulate the tensile deformation of nanostructured Ti processed by ECAP-C as well as the drawing process of nanostructured Ti billets. It was found that the first representation based in one finite element per grain led to a stiffer response in tension and was not able to predict the texture evolution during drawing because the strain gradient within each grain could not be captured. On the contrary, the second representation of the polycrystal microstructure with many finite elements per grain was able to predict accurately the deformation of nanostructured Ti.

Effect of Stress Level on the High Temperature Deformation and Fracture Mechanisms of Ti-45Al-2Nb-2Mn-0.8 vol. pct TiB2: An In Situ Experimental Study

The effect of the applied stress on the deformation and crack nucleation and propagation mechanisms of a c-TiAl intermetallic alloy (Ti-45Al-2Nb-2Mn (at. pct)-0.8 vol. pct TiB2) was examined by means of in situ tensile (constant strain rate) and tensile-creep (constant load) experiments performed at 973 K (700 �C) using a scanning electron microscope. Colony boundary cracking developed during the secondary stage in creep tests at 300 and 400 MPa and during the tertiary stage of the creep tests performed at higher stresses. Colony boundary cracking was also observed in the constant strain rate tensile test. Interlamellar ledges were only found during the tensile-creep tests at high stresses (r>400 MPa) and during the constant strain rate tensile test. Quantitative measurements of the nature of the crack propagation path along secondary cracks and along the primary crack indicated that colony boundaries were preferential sites for crack propagation under all the conditions investigated. The frequency of interlamellar cracking increased with stress, but this fracture mechanism was always of secondary importance. Translamellar cracking was only observed along the primary crack.

Finite elastic deformations of transversely isotropic circular cylindrical tubes

We consider the finite radially symmetric deformation of a circular cylindrical tube of a homogeneous transversely isotropic elastic material subject to axial stretch, radial deformation and torsion, supported by axial load, internal pressure and end moment. Two different directions of transverse isotropy are considered: the radial direction and an arbitrary direction in planes normal locally to the radial direction, the only directions for which the considered deformation is admissible in general. In the absence of body forces, formulas are obtained for the internal pressure, and the resultant axial load and torsional moment on the ends of the tube in respect of a general strain-energy function. For a specific material model of transversely isotropic elasticity, and material and geometrical parameters, numerical results are used to illustrate the dependence of the pressure, (reduced) axial load and moment on the radial stretch and a measure of the torsional deformation for a fixed value of the axial stretch.

Simplified Finite Element Assessment of Beams With and Without Shear Deformation

This paper presents a simplified finite element (FE) methodology for solving accurately beam models with (Timoshenko) and without (Bernoulli-Euler) shear deformation. Special emphasis is made on showing how it is possible to obtain the exact solution on the nodes and a good accuracy inside the element. The proposed simplifying concept, denominated as the equivalent distributed load (EDL) of any order, is based on the use of Legendre orthogonal polynomials to approximate the original or acting load for computing the results between the nodes. The 1-span beam examples show that this is a promising procedure that allows the aim of using either one FE and an EDL of slightly higher order or by using an slightly larger number of FEs leaving the EDL in the lowest possible order assumed by definition to be equal to 4 independently of how irregular the beam is loaded.

Raman spectroscopy in Group IV nanowires and nanowire axial heterostructures

The control of the SiGe NW composition is fundamental for the fabrication of high quality heterostructures. Raman spectroscopy has been used to analyse the composition of SiGe alloys. We present a study of the Raman spectrum of SiGe nanowires and SiGe/Si heterostructures. The inhomogeneity of the Ge composition deduced from the Raman spectrum is explained by the existence of a Ge-rich outer shell and by the interaction of the NW with the electromagnetic field associated with the laser beam.

Discontinuous solutions and boundary value problems for non-linearly elastic fibre-reinforced materials

En este trabajo se han analizado varios problemas en el contexto de la elasticidad no lineal basándose en modelos constitutivos representativos. En particular, se han analizado problemas relacionados con el fenómeno de perdida de estabilidad asociada con condiciones de contorno en el caso de material reforzados con fibras. Cada problema se ha formulado y se ha analizado por separado en diferentes capítulos. En primer lugar se ha mostrado el análisis del gradiente de deformación discontinuo para un material transversalmente isótropo, en particular, el modelo del material considerado consiste de una base neo-Hookeana isótropa incrustada con fibras de refuerzo direccional caracterizadas con un solo parámetro. La solución de este problema se vincula con instabilidades que dan lugar al mecanismo de fallo conocido como banda de cortante. La perdida de elipticidad de las ecuaciones diferenciales de equilibrio es una condición necesaria para que aparezca este tipo de soluciones y por tanto las inestabilidades asociadas. En segundo lugar se ha analizado una deformación combinada de extensión, inación y torsión de un tubo cilíndrico grueso donde se ha encontrado que la deformación citada anteriormente puede ser controlada solo para determinadas direcciones de las fibras refuerzo. Para entender el comportamiento elástico del tubo considerado se ha ilustrado numéricamente los resultados obtenidos para las direcciones admisibles de las fibras de refuerzo bajo la deformación considerada. En tercer lugar se ha estudiado el caso de un tubo cilíndrico grueso reforzado con dos familias de fibras sometido a cortante en la dirección azimutal para un modelo de refuerzo especial. En este problema se ha encontrado que las inestabilidades que aparecen en el material considerado están asociadas con lo que se llama soluciones múltiples de la ecuación diferencial de equilibrio. Se ha encontrado que el fenómeno de instabilidad ocurre en un estado de deformación previo al estado de deformación donde se pierde la elipticidad de la ecuación diferencial de equilibrio. También se ha demostrado que la condición de perdida de elipticidad y ^W=2 = 0 (la segunda derivada de la función de energía con respecto a la deformación) son dos condiciones necesarias para la existencia de soluciones múltiples. Finalmente, se ha analizado detalladamente en el contexto de elipticidad un problema de un tubo cilíndrico grueso sometido a una deformación combinada en las direcciones helicoidal, axial y radial para distintas geotermias de las fibras de refuerzo . In the present work four main problems have been addressed within the framework of non-linear elasticity based on representative constitutive models. Namely, problems related to the loss of stability phenomena associated with boundary value problems for fibre-reinforced materials. Each of the considered problems is formulated and analysed separately in different chapters. We first start with the analysis of discontinuous deformation gradients for a transversely isotropic material under plane deformation. In particular, the material model is an augmented neo-Hookean base with a simple unidirectional reinforcement characterised by a single parameter. The solution of this problem is related to material instabilities and it is associated with a shear band-type failure mode. The loss of ellipticity of the governing differential equations is a necessary condition for the existence of these material instabilities. The second problem involves a detailed analysis of the combined non-linear extension, inflation and torsion of a thick-walled circular cylindrical tube where it has been found that the aforementioned deformation is controllable only for certain preferred directions of transverse isotropy. Numerical results have been illustrated to understand the elastic behaviour of the tube for the admissible preferred directions under the considered deformation. The third problem deals with the analysis of a doubly fibre-reinforced thickwalled circular cylindrical tube undergoing pure azimuthal shear for a special class of the reinforcing model where multiple non-smooth solutions emerge. The associated instability phenomena are found to occur prior to the point where the nominal stress tensor changes monotonicity in a particular direction. It has been also shown that the loss of ellipticity condition that arises from the equilibrium equation and ^W=2 = 0 (the second derivative of the strain-energy function with respect to the deformation) are equivalent necessary conditions for the emergence of multiple solutions for the considered material. Finally, a detailed analysis in the basis of the loss of ellipticity of the governing differential equations for a combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube is carried out.

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 influence of axial microgravity on the breakage of axisymmetric slender liquid bridges

The dynamics of inviscid, axisymmetric liquid bridges permits a simplified treatment if the bridge is long enough. Under such condition the evolution of the liquid zone is satisfactorily explained through a non-linear one-dimensional model. In the case of breaking, the one-dimensional model fails when the neck radius of the liquid column is close to zero; however, the model allows the calculation of the time variation of the liquid-bridge interface as well as of the fluid velocity field and, because the last part of the evolution is not needed, the overall results such as the breaking time and the volume of each of the two drops resulting after breakage can be calculated. In this paper numerical results concerning the behavior of clinical liquid bridges subjected to a small axial gravitational field are presented.

Análisis de elementos viga-columna en régimen no lineal con deformación por cortante

El hormigón estructural sigue siendo sin duda uno de los materiales más utilizados en construcción debido a su resistencia, rigidez y flexibilidad para diseñar estructuras. El cálculo de estructuras de hormigón, utilizando vigas y vigas-columna, es complejo debido a los fenómenos de acoplamiento entre esfuerzos y al comportamiento no lineal del material. Los modelos más empleados para su análisis son el de Bernoulli-Euler y el de Timoshenko, indicándose en la literatura la conveniencia de usar el segundo cuando la relación canto/luz no es pequeña o los elementos están fuertemente armados. El objetivo fundamental de esta tesis es el análisis de elementos viga y viga-columna en régimen no lineal con deformación por cortante, aplicando el concepto de Pieza Lineal Equivalente (PLE). Concepto éste que consiste básicamente en resolver el problema de una pieza en régimen no lineal, transformándolo en uno lineal equivalente, de modo que ambas piezas tengan la misma deformada y los mismos esfuerzos. Para ello, se hizo en primer lugar un estudio comparado de: las distintas propuestas que aplican la deformación por cortante, de los distintos modelos constitutivos y seccionales del hormigón estructural y de los métodos de cálculo no lineal aplicando el método de elementos finitos (MEF). Teniendo en cuenta que la resolución del problema no lineal se basa en la resolución de sucesivos problemas lineales empleando un proceso de homotopía, los problemas lineales de la viga y viga-columna de Timoshenko, se resuelven mediante MEF, utilizando soluciones nodalmente exactas (SNE) y acción repartida equivalente de cualquier orden. Se obtiene así, con muy pocos elementos finitos, una excelente aproximación de la solución, no sólo en los nodos sino en el interior de los elementos. Se introduce el concepto PLE para el análisis de una barra, de material no lineal, sometida a acciones axiales, y se extiende el mismo para el análisis no lineal de vigas y vigas-columna con deformación por cortante. Cabe señalar que para estos últimos, la solución de una pieza en régimen no lineal es igual a la de una en régimen lineal, cuyas rigideces son constantes a trozos, y donde además hay que añadir momentos y cargas puntuales ficticias en los nodos, así como, un momento distribuido ficticio en toda la pieza. Se han desarrollado dos métodos para el análisis: uno para problemas isostáticos y otro general, aplicable tanto a problemas isostáticos como hiperestáticos. El primero determina de entrada la PLE, realizándose a continuación el cálculo por MEF-SNE de dicha pieza, que ahora está en régimen lineal. El general utiliza una homotopía que transforma de manera iterativa, unas leyes constitutivas lineales en las leyes no lineales del material. Cuando se combina con el MEF, la pieza lineal equivalente y la solución del problema original quedan determinadas al final de todo el proceso. Si bien el método general es un procedimiento próximo al de Newton- Raphson, presenta sobre éste la ventaja de permitir visualizar las deformaciones de la pieza en régimen no lineal, de manera tanto cualitativa como cuantitativa, ya que es posible observar en cada paso del proceso la modificación de rigideces (a flexión y cortante) y asimismo la evolución de las acciones ficticias. Por otra parte, los resultados obtenidos comparados con los publicados en la literatura, indican que el concepto PLE ofrece una forma directa y eficiente para analizar con muy buena precisión los problemas asociados a vigas y vigas-columna en las que por su tipología los efectos del cortante no pueden ser despreciados. ABSTRACT The structural concrete clearly remains the most used material in construction due to its strength, rigidity and structural design flexibility. The calculation of concrete structures using beams and beam-column is complex as consequence of the coupling phenomena between stresses and of its nonlinear behaviour. The models most commonly used for analysis are the Bernoulli-Euler and Timoshenko. The second model is strongly recommended when the relationship thickness/span is not small or in case the elements are heavily reinforced. The main objective of this thesis is to analyse the beam and beam-column elements with shear deformation in nonlinear regime, applying the concept of Equivalent Linear Structural Element (ELSE). This concept is basically to solve the problem of a structural element in nonlinear regime, transforming it into an equivalent linear structural element, so that both elements have the same deformations and the same stresses. Firstly, a comparative study of the various proposals of applying shear deformation, of various constitutive and sectional models of structural concrete, and of the nonlinear calculation methods (using finite element methods) was carried out. Considering that the resolution of nonlinear problem is based on solving the successive linear problem, using homotopy process, the linear problem of Timoshenko beam and beam-columns is resolved by FEM, using the exact nodal solutions (ENS) and equivalent distributed load of any order. Thus, the accurate solution approximation can be obtained with very few finite elements for not only nodes, but also for inside of elements. The concept ELSE is introduced to analyse a bar of nonlinear material, subjected to axial forces. The same bar is then used for other nonlinear beam and beam-column analysis with shear deformation. It is noted that, for the last analyses, the solution of a structural element in nonlinear regime is equal to that of linear regime, in which the piecewise-stiffness is constant, the moments and fictitious point loads need to be added at nodes of each element, as well as the fictitious distributed moment on element. Two methods have been developed for analysis: one for isostatic problem and other more general, applicable for both isostatic and hiperstatic problem. The first method determines the ELSE, and then the calculation of this piece is performed by FEM-ENS that now is in linear regime. The general method uses the homotopy that transforms iteratively linear constitutive laws into nonlinear laws of material. When combined with FEM, the ELSE and the solution of the original problem are determined at the end of the whole process. The general method is well known as a procedure closed to Newton-Raphson procedure but presents an advantage that allows displaying deformations of the piece in nonlinear regime, in both qualitative and quantitative way. Since it is possible to observe the modification of stiffness (flexural and shear) in each step of process and also the evolution of the fictitious actions. Moreover, the results compared with those published in the literature indicate that the ELSE concept offers a direct and efficient way to analyze with very good accuracy the problems associated with beams and beams columns in which, by typology, the effects of shear cannot be neglected.

Mechanical behavior and deformation micromechanisms of polypropylene nonwoven fabrics as a function of temperature and strain rate

The mechanical behavior and the deformation and failure micromechanisms of a thermally-bonded polypropylene nonwoven fabric were studied as a function of temperature and strain rate. Mechanical tests were carried out from 248 K (below the glass transition temperature) up to 383 K at strain rates in the range ≈10−3 s−1 to 10−1 s−1. In addition, individual fibers extracted from the nonwoven fabric were tested under the same conditions. Micromechanisms of deformation and failure at the fiber level were ascertained by means of mechanical tests within the scanning electron microscope while the strain distribution at the macroscopic level upon loading was determined by means of digital image correlation. It was found that the nonwoven behavior was mainly controlled by the properties of the fibers and of the interfiber bonds. Fiber properties determined the nonlinear behavior before the peak load while the interfiber bonds controlled the localization of damage after the peak load. The influence of these properties on the strength, ductility and energy absorbed during deformation is discussed from the experimental observations.

A gradient-enhanced large-deformation continuum damage model for fibre-reinforced materials

A non-local gradient-based damage formulation within a geometrically non-linear setting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre-reinforced material, respectively. The inelastic constitutive response is governed by a scalar [1–d]-type damage formulation, where only the anisotropic elastic part is assumed to be affected by the damage. Following the concept in Dimitrijević and Hackl [28], the local free energy function is enhanced by a gradient-term. This term essentially contains the gradient of the non-local damage variable which, itself, is introduced as an additional independent variable. In order to guarantee the equivalence between the local and non-local damage variable, a penalisation term is incorporated within the free energy function. Based on the principle of minimum total potential energy, a coupled system of Euler–Lagrange equations, i.e., the balance of linear momentum and the balance of the non-local damage field, is obtained and solved in weak form. The resulting coupled, highly non-linear system of equations is symmetric and can conveniently be solved by a standard incremental-iterative Newton–Raphson-type solution scheme. Several three-dimensional displacement- and force-driven boundary value problems—partially motivated by biomechanical application—highlight the mesh-objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed

Permanent deformation estimates of dynamic equipment foundations: Application to a gas turbine in granular soils

Permanent displacements of a gas turbine founded on a fine, poorly graded, and medium density sand are studied. The amplitudes and modes of vibration are computed using Barkan´s formulation, and the “High-Cycle Accumulation” (HCA) model is employed to account for accumulated deformations due to the high number of cycles. The methodology is simple: it can be easily incorporated into standard mathematical software, and HCA model parameters can be estimated based on granulometry and index properties. Special attention is devoted to ‘transient’ situations at equipment´s start-up, during which a range of frequencies – including frequencies that could be similar to the natural frequencies of the ground – is traversed. Results show that such transient situations could be more restrictive than stationary situations corresponding to normal operation. Therefore, checking the stationary situation only might not be enough, and studying the influence of transient situations on computed permanent displacements is needed to produce a proper foundation design

Values of the deformation modulus of soil at different ways of determining this amount

In accordance with Russian, Kazakh and European building regulations, the deformation modulus of soil should be determined in the laboratory and also apply in situ soil tests on the stages of engineering geology prospecting. In this paper we present data on the determination and adjustment of the deformation characteristics at different stages of construction

Minimum volume stability limits for axisymmetric liquid bridges subject to steady axial acceleration

In this paper the influence of an axial microgravity on the minimum volume stability limit of axisymmetric liquid bridges between unequal disks is analyzed both theoretically and experimentally. The results here presented extend the knowledge of the static behaviour of liquid bridges to fluid configurations different from those studied up to now (almost equal disks). Experimental results, obtained by simulating microgravity conditions by the neutral buoyancy technique, are also presented and are shown to be in complete agreement with theoretical ones.

Sobre el comportamiento de micropilotes trabajando a flexión y/o cortante en estructuras de tierra

El empleo de los micropilotes en la ingeniería civil ha revolucionado las técnicas de estabilización de terraplenes a media ladera, ya que aunque los pilotes pueden ser la opción más económica, el uso de micropilotes permite llegar a sitios inaccesibles con menor coste de movimientos de tierras, realización de plataformas de trabajo de dimensiones reducidas, maquinaria necesaria es mucho más pequeña, liviana y versátil en su uso, incluyendo la posibilidad de situar la fabricación de morteros o lechadas a distancias de varias decenas de metros del elemento a ejecutar. Sin embargo, realizando una revisión de la documentación técnica que se tiene en el ámbito ingenieril, se comprobó que los sistemas de diseño de algunos casos (micropilotes en terraplenes a media ladera, micropilotes en pantallas verticales, micropilotes como “paraguas” en túneles, etc.) eran bastante deficientes o poco desarrollados. Premisa que permite concluir que el constructor ha ido por delante (como suele ocurrir en ingeniería geotécnica) del cálculo o de su análisis teórico. Del mismo modo se determinó que en su mayoría los micropilotes se utilizan en labores de recalce o como nueva solución de cimentación en condiciones de difícil acceso, casos en los que el diseño de los micropilotes viene definido por cargas axiales, de compresión o de tracción, consideraciones que se contemplan en reglamentaciones como la “Guía para el proyecto y la ejecución de micropilotes en obras de carretera” del Ministerio de Fomento. En los micropilotes utilizados para estabilizar terraplenes a media ladera y micropilotes actuando como muros pantalla, en los que éstos trabajan a esfuerzo cortante y flexión, no se dispone de sistemas de análisis fiables o no se introduce adecuadamente el problema de interacción terreno-micropilote. Además en muchos casos, los parámetros geotécnicos que se utilizan no tienen una base técnico-teórica adecuada por lo que los diseños pueden quedar excesivamente del lado de la seguridad, en la mayoría de los casos, o todo lo contrario. Uno de los objetivos principales de esta investigación es estudiar el comportamiento de los micropilotes que están sometidos a esfuerzos de flexión y cortante, además de otros objetivos de gran importancia que se describen en el apartado correspondiente de esta tesis. Cabe indicar que en este estudio no se ha incluido el caso de micropilotes quasi-horizontales trabajando a flexion (como los “paraguas” en túneles), por considerarse que estos tienen un comportamiento y un cálculo diferente, que está fuera del alcance de esta investigación. Se ha profundizado en el estudio del empleo de micropilotes en taludes, presentando casos reales de obras ejecutadas, datos estadísticos, problemas de diseño y ejecución, métodos de cálculo simplificados y modelación teórica en cada caso, efectuada mediante el empleo de elementos finitos con el Código Plaxis 2D. Para llevar a cabo los objetivos que se buscan con esta investigación, se ha iniciado con el desarrollo del “Estado del Arte” que ha permitido establecer tipología, aplicaciones, características y cálculo de los micropilotes que se emplean habitualmente. Seguidamente y a efectos de estudiar el problema dentro de un marco geotécnico real, se ha seleccionado una zona española de actuación, siendo ésta Andalucía, en la que se ha utilizado de manera muy importante la técnica de micropilotes sobre todo en problemas de estabilidad de terraplenes a media ladera. A partir de ahí, se ha realizado un estudio de las propiedades geotécnicas de los materiales (principalmente suelos y rocas muy blandas) que están presentes en esta zona geográfica, estudio que ha sido principalmente bibliográfico o a partir de la experiencia en la zona del Director de esta tesis. Del análisis realizado se han establecido ordenes de magnitud de los parámetros geotécnicos, principalmente la cohesión y el ángulo de rozamiento interno (además del módulo de deformación aparente o de un módulo de reacción lateral equivalente) para los diversos terrenos andaluces. Con el objeto de conocer el efecto de la ejecución de un micropilote en el terreno (volumen medio real del micropilote, una vez ejecutado; efecto de la presión aplicada en las propiedades del suelo circundante, etc.) se ha realizado una encuesta entre diversas empresas españolas especializadas en la técnica de los micropilotes, a efectos de controlar los volúmenes de inyección y las presiones aplicadas, en función de la deformabilidad del terreno circundante a dichos micropilotes, con lo que se ha logrado definir una rigidez a flexión equivalente de los mismos y la definición y características de una corona de terreno “mejorado” lograda mediante la introducción de la lechada y el efecto de la presión alrededor del micropilote. Con las premisas anteriores y a partir de los parámetros geotécnicos determinados para los terrenos andaluces, se ha procedido a estudiar la estabilidad de terraplenes apoyados sobre taludes a media ladera, mediante el uso de elementos finitos con el Código Plaxis 2D. En el capítulo 5. “Simulación del comportamiento de micropilotes estabilizando terraplenes”, se han desarrollado diversas simulaciones. Para empezar se simplificó el problema simulando casos similares a algunos reales en los que se conocía que los terraplenes habían llegado hasta su situación límite (de los que se disponía información de movimientos medidos con inclinómetros), a partir de ahí se inició la simulación de la inestabilidad para establecer el valor de los parámetros de resistencia al corte del terreno (mediante un análisis retrospectivo – back-análisis) comprobando a su vez que estos valores eran similares a los deducidos del estudio bibliográfico. Seguidamente se han introducido los micropilotes en el borde de la carretera y se ha analizado el comportamiento de éstos y del talud del terraplén (una vez construidos los micropilotes), con el objeto de establecer las bases para su diseño. De este modo y adoptando los distintos parámetros geotécnicos establecidos para los terrenos andaluces, se simularon tres casos reales (en Granada, Málaga y Ceuta), comparando los resultados de dichas simulaciones numéricas con los resultados de medidas reales de campo (desplazamientos del terreno, medidos con inclinómetros), obteniéndose una reproducción bastante acorde a los movimientos registrados. Con las primeras simulaciones se concluye que al instalar los micropilotes la zona más insegura de la ladera es la de aguas abajo. La superficie de rotura ya no afecta a la calzada que protegen los micropilotes. De ahí que se deduzca que esta solución sea válida y se haya aplicado masivamente en Andalucía. En esas condiciones, podría decirse que no se está simulando adecuadamente el trabajo de flexión de los micropilotes (en la superficie de rotura, ya que no les corta), aunque se utilicen elementos viga. Por esta razón se ha realizado otra simulación, basada en las siguientes hipótesis: − Se desprecia totalmente la masa potencialmente deslizante, es decir, la que está por delante de la fila exterior de micros. − La estratigrafía del terreno es similar a la considerada en las primeras simulaciones. − La barrera de micropilotes está constituida por dos elementos inclinados (uno hacia dentro del terraplén y otro hacia fuera), con inclinación 1(H):3(V). − Se puede introducir la rigidez del encepado. − Los micros están separados 0,556 m ó 1,00 m dentro de la misma alineación. − El empotramiento de los micropilotes en el sustrato resistente puede ser entre 1,5 y 7,0 m. Al “anular” el terreno que está por delante de los micropilotes, a lo largo del talud, estos elementos empiezan claramente a trabajar, pudiendo deducirse los esfuerzos de cortante y de flexión que puedan actuar sobre ellos (cota superior pero prácticamente muy cerca de la solución real). En esta nueva modelación se ha considerado tanto la rigidez equivalente (coeficiente ϴ) como la corona de terreno tratado concéntrico al micropilote. De acuerdo a esto último, y gracias a la comparación de estas modelaciones con valores reales de movimientos en laderas instrumentadas con problemas de estabilidad, se ha verificado que existe una similitud bastante importante entre los valores teóricos obtenidos y los medidos en campo, en relación al comportamiento de los micropilotes ejecutados en terraplenes a media ladera. Finalmente para completar el análisis de los micropilotes trabajando a flexión, se ha estudiado el caso de micropilotes dispuestos verticalmente, trabajando como pantallas discontinuas provistas de anclajes, aplicado a un caso real en la ciudad de Granada, en la obra “Hospital de Nuestra Señora de la Salud”. Para su análisis se utilizó el código numérico CYPE, basado en que la reacción del terreno se simula con muelles de rigidez Kh o “módulo de balasto” horizontal, introduciendo en la modelación como variables: a) Las diferentes medidas obtenidas en campo; b) El espesor de terreno cuaternario, que por lo que se pudo determinar, era variable, c) La rigidez y tensión inicial de los anclajes. d) La rigidez del terreno a través de valores relativos de Kh, recopilados en el estudio de los suelos de Andalucía, concretamente en la zona de Granada. Dicha pantalla se instrumentó con 4 inclinómetros (introducidos en los tubos de armadura de cuatro micropilotes), a efectos de controlar los desplazamientos horizontales del muro de contención durante las excavaciones pertinentes, a efectos de comprobar la seguridad del conjunto. A partir del modelo de cálculo desarrollado, se ha comprobado que el valor de Kh pierde importancia debido al gran número de niveles de anclajes, en lo concerniente a las deformaciones horizontales de la pantalla. Por otro lado, los momentos flectores son bastante sensibles a la distancia entre anclajes, al valor de la tensión inicial de los mismos y al valor de Kh. Dicho modelo también ha permitido reproducir de manera fiable los valores de desplazamientos medidos en campo y deducir los parámetros de deformabilidad del terreno, Kh, con valores del orden de la mitad de los medidos en el Metro Ligero de Granada, pero visiblemente superiores a los deducibles de ábacos que permiten obtener Kh para suelos granulares con poca cohesión (gravas y cuaternario superior de Sevilla) como es el caso del ábaco de Arozamena, debido, a nuestro juicio, a la cementación de los materiales presentes en Granada. En definitiva, de las anteriores deducciones se podría pensar en la optimización del diseño de los micropilotes en las obras que se prevean ejecutar en Granada, con similares características al caso de la pantalla vertical arriostrada mediante varios niveles de anclajes y en las que los materiales de emplazamiento tengan un comportamiento geotécnico similar a los estudiados, con el consiguiente ahorro económico. Con todo ello, se considera que se ha hecho una importante aportación para el diseño de futuras obras de micropilotes, trabajando a flexión y cortante, en obras de estabilización de laderas o de excavaciones. Using micropiles in civil engineering has transformed the techniques of stabilization of embankments on the natural or artificial slopes, because although the piles may be the cheapest option, the use of micropiles can reach inaccessible places with lower cost of earthworks, carrying out small work platforms. Machinery used is smaller, lightweight and versatile, including the possibility of manufacturing mortars or cement grouts over distances of several tens of meters of the element to build. However, making a review of the technical documentation available in the engineering field, it was found that systems designed in some cases (micropiles in embankments on the natural slopes, micropiles in vertical cut-off walls, micropiles like "umbrella" in tunnels, etc.) were quite poor or underdeveloped. Premise that concludes the builder has gone ahead (as usually happen in geotechnical engineering) of calculation or theoretical analysis. In the same way it was determined that most of the micropiles are used in underpinning works or as a new foundation solution in conditions of difficult access, in which case the design of micropiles is defined by axial, compressive or tensile loads, considered in regulations as the " Handbook for the design and execution of micropiles in road construction" of the Ministry of Development. The micropiles used to stabilize embankments on the slopes and micropiles act as retaining walls, where they work under shear stress and bending moment, there are not neither reliable systems analysis nor the problem of soil-micropile interaction are properly introduced. Moreover, in many cases, the geotechnical parameters used do not have a proper technical and theoretical basis for what designs may be excessively safe, or the opposite, in most cases. One of the main objectives of this research is to study the behavior of micro piles which are subjected to bending moment and shear stress, as well as other important objectives described in the pertinent section of this thesis. It should be noted that this study has not included the case of quasi-horizontal micropiles working bending moment (as the "umbrella" in tunnels), because it is considered they have a different behavior and calculation, which is outside the scope of this research. It has gone in depth in the study of using micropiles on slopes, presenting real cases of works made, statistics, problems of design and implementation, simplified calculation methods and theoretical modeling in each case, carried out by using FEM (Finite Element Method) Code Plaxis 2D. To accomplish the objectives of this research, It has been started with the development of the "state of the art" which stipulate types, applications, characteristics and calculation of micropiles that are commonly used. In order to study the problem in a real geotechnical field, it has been selected a Spanish zone of action, this being Andalusia, in which it has been used in a very important way, the technique of micropiles especially in embankments stability on natural slopes. From there, it has made a study of the geotechnical properties of the materials (mainly very soft soils and rocks) that are found in this geographical area, which has been mainly a bibliographic study or from the experience in the area of the Director of this thesis. It has been set orders of magnitude of the geotechnical parameters from analyzing made, especially the cohesion and angle of internal friction (also apparent deformation module or a side reaction module equivalent) for various typical Andalusian ground. In order to determine the effect of the implementation of a micropile on the ground (real average volume of micropile once carried out, effect of the pressure applied on the properties of the surrounding soil, etc.) it has conducted a survey among various skilled companies in the technique of micropiles, in order to control injection volumes and pressures applied, depending on the deformability of surrounding terrain such micropiles, whereby it has been possible to define a bending stiffness and the definition and characteristics of a crown land "improved" achieved by introducing the slurry and the effect of the pressure around the micropile. With the previous premises and from the geotechnical parameters determined for the Andalusian terrain, we proceeded to study the stability of embankments resting on batters on the slope, using FEM Code Plaxis 2D. In the fifth chapter "Simulation of the behavior of micropiles stabilizing embankments", there were several different numerical simulations. To begin the problem was simplified simulating similar to some real in which it was known that the embankments had reached their limit situation (for which information of movements measured with inclinometers were available), from there the simulation of instability is initiated to set the value of the shear strength parameters of the ground (by a retrospective analysis or back-analysis) checking these values were similar to those deduced from the bibliographical study Then micropiles have been introduced along the roadside and its behavior was analyzed as well as the slope of embankment (once micropiles were built ), in order to establish the basis for its design. In this way and taking the different geotechnical parameters for the Andalusian terrain, three real cases (in Granada, Malaga and Ceuta) were simulated by comparing the results of these numerical simulations with the results of real field measurements (ground displacements measured with inclinometers), getting quite consistent information according to registered movements. After the first simulations it has been concluded that after installing the micropiles the most insecure area of the natural slope is the downstream. The failure surface no longer affects the road that protects micropiles. Hence it is inferred that this solution is acceptable and it has been massively applied in Andalusia. Under these conditions, one could say that it is not working properly simulating the bending moment of micropiles (on the failure surface, and that does not cut them), although beam elements are used. Therefore another simulation was performed based on the following hypotheses: − The potentially sliding mass is totally neglected, that is, which is ahead of the outer row of micropiles. − Stratigraphy field is similar to the one considered in the first simulations. − Micropiles barrier is constituted by two inclined elements (one inward and one fill out) with inclination 1 (H): 3 (V). − You can enter the stiffness of the pile cap. − The microlies lines are separated 0.556 m or 1.00 m in the same alignment. − The embedding of the micropiles in the tough substrate can be between 1.5 and 7.0 m. To "annul" the ground that is in front of the micro piles, along the slope, these elements clearly start working, efforts can be inferred shear stress and bending moment which may affect them (upper bound but pretty close to the real) solution. In this new modeling it has been considered both equivalent stiffness coefficient (θ) as the treated soil crown concentric to the micropile. According to the latter, and by comparing these values with real modeling movements on field slopes instrumented with stability problems, it was verified that there is quite a significant similarity between the obtained theoretical values and the measured field in relation to the behavior of micropiles executed in embankments along the natural slope. Finally to complete the analysis of micropiles working in bending conditions, we have studied the case of micropiles arranged vertically, working as discontinued cut-off walls including anchors, applied to a real case in the city of Granada, in the play "Hospital of Our Lady of the Health ". CYPE numeric code, based on the reaction of the ground is simulated spring stiffness Kh or "subgrade" horizontal, introduced in modeling was used as variables for analysis: a) The different measurements obtained in field; b) The thickness of quaternary ground, so that could be determined, was variable, c) The stiffness and the prestress of the anchors. d) The stiffness of the ground through relative values of Kh, collected in the study of soils in Andalusia, particularly in the area of Granada. (previously study of the Andalusia soils) This cut-off wall was implemented with 4 inclinometers (introduced in armor tubes four micropiles) in order to control the horizontal displacements of the retaining wall during the relevant excavations, in order to ensure the safety of the whole. From the developed model calculation, it was found that the value of Kh becomes less important because a large number of anchors levels, with regard to the horizontal deformation of the cut-off wall. On the other hand, the bending moments are quite sensitive to the distance between anchors, the initial voltage value thereof and the value of Kh. This model has also been reproduced reliably displacement values measured in the field and deduce parameters terrain deformability, Kh, with values around half the measured Light Rail in Granada, but visibly higher than deductible of abacuses which can obtain Kh for granular soils with low cohesion (upper Quaternary gravels and Sevilla) such as Abacus Arozamena, because, in our view, to cementing materials in Granada. In short, previous deductions you might think on optimizing the design of micropiles in the works that are expected to perform in Granada, with similar characteristics to the case of the vertical cut-off wall braced through several levels of anchors and in which materials location have a geotechnical behavior similar to those studied, with the consequent economic savings. With all this, it is considered that a significant contribution have been made for the design of future works of micropiles, bending moment and shear stress working in slope stabilization works or excavations.