Límites de ductilidad y de servicio al cálculo en carga última de estructuras de hormigón armado y de fábrica

En este trabajo se aborda una cuestión central en el diseño en carga última de estructuras de hormigón armado y de fábrica: la posibilidad efectiva de que las deformaciones plásticas necesarias para verificar un estado de rotura puedan ser alcanzadas por las regiones de la estructura que deban desarrollar su capacidad última para verificar tal estado. Así, se parte de las decisiones de diseño que mediante mera estática aseguran un equilibrio de la estructura para las cargas últimas que deba resistir, pero determinando directamente el valor de las deformaciones necesarias para llegar a tal estado. Por tanto, no se acude a los teoremas de rotura sin más, sino que se formula el problema desde un punto de vista elastoplástico. Es decir, no se obvia el recorrido que la estructura deba realizar en un proceso de carga incremental monótono, de modo que las regiones no plastificadas contribuyen a coaccionar las libres deformaciones plásticas que, en la teoría de rotura, se suponen. En términos de trabajo y energía, se introduce en el balance del trabajo de las fuerzas externas y en el de la energía de deformación, aquella parte del sistema que no ha plastificado. Establecido así el balance energético como potencial del sistema es cuando la condición de estacionariedad del mismo hace determinados los campos de desplazamientos y, por tanto, el de las deformaciones plásticas también. En definitiva, se trata de un modo de verificar si la ductilidad de los diseños previstos es suficiente, y en qué medida, para verificar el estado de rotura previsto, para unas determinadas cargas impuestas. Dentro del desarrollo teórico del problema, se encuentran ciertas precisiones importantes. Entre ellas, la verificación de que el estado de rotura a que se llega de manera determinada mediante el balance energético elasto-plástico satisface las condiciones de la solución de rotura que los teoremas de carga última predicen, asegurando, por tanto, que la solución determinada -unicidad del problema elásticocoincide con el teorema de unicidad de la carga de rotura, acotando además cuál es el sistema de equilibrio y cuál es la deformada de colapso, aspectos que los teoremas de rotura no pueden asegurar, sino sólo el valor de la carga última a verificar. Otra precisión se basa en la particularidad de los casos en que el sistema presenta una superficie de rotura plana, haciendo infinitas las posibilidades de equilibrio para una misma deformada de colapso determinada, lo que está en la base de, aparentemente, poder plastificar a antojo en vigas y arcos. Desde el planteamiento anterior, se encuentra entonces que existe una condición inherente a cualquier sistema, definidas unas leyes constitutivas internas, que permite al mismo llegar al inicio del estado de rotura sin demandar deformación plástica alguna, produciéndose la plastificación simultánea de todas las regiones que hayan llegado a su solicitación de rotura. En cierto modo, se daría un colapso de apariencia frágil. En tal caso, el sistema conserva plenamente hasta el final su capacidad dúctil y tal estado actúa como representante canónico de cualquier otra solución de equilibrio que con idéntico criterio de diseño interno se prevea para tal estructura. En la medida que el diseño se acerque o aleje de la solución canónica, la demanda de ductilidad del sistema para verificar la carga última será menor o mayor. Las soluciones que se aparten en exceso de la solución canónica, no verificarán el estado de rotura previsto por falta de ductilidad: la demanda de deformación plástica de alguna región plastificada estará más allá de la capacidad de la misma, revelándose una carga de rotura por falta de ductilidad menor que la que se preveía por mero equilibrio. Para la determinación de las deformaciones plásticas de las rótulas, se ha tomado un modelo formulado mediante el Método de los Elementos de Contorno, que proporciona un campo continuo de desplazamientos -y, por ende, de deformaciones y de tensiones- incluso en presencia de fisuras en el contorno. Importante cuestión es que se formula la diferencia, nada desdeñable, de la capacidad de rotación plástica de las secciones de hormigón armado en presencia de cortante y en su ausencia. Para las rótulas de fábrica, la diferencia se establece para las condiciones de la excentricidad -asociadas al valor relativo de la compresión-, donde las diferencias entres las regiones plastificadas con esfuerzo normal relativo alto o bajo son reseñables. Por otro lado, si bien de manera un tanto secundaria, las condiciones de servicio también imponen un límite al diseño previo en carga última deseado. La plastificación lleva asociadas deformaciones considerables, sean locales como globales. Tal cosa impone que, en estado de servicio, si la plastificación de alguna región lleva asociadas fisuraciones excesivas para el ambiente del entorno, la solución sea inviable por ello. Asimismo, las deformaciones de las estructuras suponen un límite severo a las posibilidades de su diseño. Especialmente en edificación, las deformaciones activas son un factor crítico a la hora de decidirse por una u otra solución. Por tanto, al límite que se impone por razón de ductilidad, se debe añadir el que se imponga por razón de las condiciones de servicio. Del modo anterior, considerando las condiciones de ductilidad y de servicio en cada caso, se puede tasar cada decisión de diseño con la previsión de cuáles serán las consecuencias en su estado de carga última y de servicio. Es decir, conocidos los límites, podemos acotar cuáles son los diseños a priori que podrán satisfacer seguro las condiciones de ductilidad y de servicio previstas, y en qué medida. Y, en caso de no poderse satisfacer, qué correcciones debieran realizarse sobre el diseño previo para poderlas cumplir. Por último, de las consecuencias que se extraen de lo estudiado, se proponen ciertas líneas de estudio y de experimentación para poder llegar a completar o expandir de manera práctica los resultados obtenidos. ABSTRACT This work deals with a main issue for the ultimate load design in reinforced concrete and masonry structures: the actual possibility that needed yield strains to reach a ultimate state could be reached by yielded regions on the structure that should develop their ultimate capacity to fulfill such a state. Thus, some statically determined design decisions are posed as a start for prescribed ultimate loads to be counteracted, but finding out the determined value of the strains needed to reach the ultimate load state. Therefore, ultimate load theorems are not taken as they are, but a full elasto-plastic formulation point of view is used. As a result, the path the structure must develop in a monotonus increasing loading procedure is not neglected, leading to the fact that non yielded regions will restrict the supposed totally free yield strains under a pure ultimate load theory. In work and energy terms, in the overall account of external forces work and internal strain energy, those domains in the body not reaching their ultimate state are considered. Once thus established the energy balance of the system as its potential, by imposing on it the stationary condition, both displacements and yield strains appear as determined values. Consequently, what proposed is a means for verifying whether the ductility of prescribed designs is enough and the extent to which they are so, for known imposed loads. On the way for the theoretical development of the proposal, some important aspects have been found. Among these, the verification that the conditions for the ultimate state reached under the elastoplastic energy balance fulfills the conditions prescribed for the ultimate load state predicted through the ultimate load theorems, assuring, therefore, that the determinate solution -unicity of the elastic problemcoincides with the unicity ultimate load theorem, determining as well which equilibrium system and which collapse shape are linked to it, being these two last aspects unaffordable by the ultimate load theorems, that make sure only which is the value of the ultimate load leading to collapse. Another aspect is based on the particular case in which the yield surface of the system is flat -i.e. expressed under a linear expression-, turning out infinite the equilibrium possibilities for one determined collapse shape, which is the basis of, apparently, deciding at own free will the yield distribution in beams and arches. From the foresaid approach, is then found that there is an inherent condition in any system, once defined internal constitutive laws, which allows it arrive at the beginning of the ultimate state or collapse without any yield strain demand, reaching the collapse simultaneously for all regions that have come to their ultimate strength. In a certain way, it would appear to be a fragile collapse. In such a case case, the system fully keeps until the end its ductility, and such a state acts as a canonical representative of any other statically determined solution having the same internal design criteria that could be posed for the that same structure. The extent to which a design is closer to or farther from the canonical solution, the ductility demand of the system to verify the ultimate load will be higher or lower. The solutions being far in excess from the canonical solution, will not verify the ultimate state due to lack of ductility: the demand for yield strains of any yielded region will be beyond its capacity, and a shortcoming ultimate load by lack of ductility will appear, lower than the expected by mere equilibrium. For determining the yield strains of plastic hinges, a Boundary Element Method based model has been used, leading to a continuous displacement field -therefore, for strains and stresses as well- even if cracks on the boundary are present. An important aspect is that a remarkable difference is found in the rotation capacity between plastic hinges in reinforced concrete with or without shear. For masonry hinges, such difference appears when dealing with the eccentricity of axial forces -related to their relative value of compression- on the section, where differences between yield regions under high or low relative compressions are remarkable. On the other hand, although in a certain secondary manner, serviceability conditions impose limits to the previous ultimate load stated wanted too. Yield means always big strains and deformations, locally and globally. Such a thing imposes, for serviceability states, that if a yielded region is associated with too large cracking for the environmental conditions, the predicted design will be unsuitable due to this. Furthermore, displacements must be restricted under certain severe limits that restrain the possibilities for a free design. Especially in building structures, active displacements are a critical factor when chosing one or another solution. Then, to the limits due to ductility reasons, other limits dealing with serviceability conditions shoud be added. In the foresaid way, both considering ductility and serviceability conditions in every case, the results for ultimate load and serviceability to which every design decision will lead can be bounded. This means that, once the limits are known, it is possible to bound which a priori designs will fulfill for sure the prescribed ductility and serviceability conditions, and the extent to wich they will be fulfilled, And, in case they were not, which corrections must be performed in the previous design so that it will. Finally, from the consequences derived through what studied, several study and experimental fields are proposed, in order to achieve a completeness and practical expansion of the obtained results.

Analysis, reliability and optimization of reinforced concrete 2-D structures

In this paper a consistent analysis of reinforced concrete (RC) two-dimensional (2-D) structures,namely slab structures subjected to in-plane and out-plane forces, is presented. By using this method of analysis the well established methodology for dimensioning and verifying RC sections of beam structures is extended to 2-D structures. The validity of the proposed analysis results is checked by comparing them with some published experimental test results. Several examples show some of these proposed analysis features, such as the influence of the reinforcement layout on the service and ultimate behavior of a slab structure and the non straightforward problem of the optimal dimension at a slab point subjected to several loading cases. Also, in these examples, the method applications to design situations as multiple steel families and non orthogonal reinforcement layout are commented.

Sharing analysis of arrays, collections, and recursive structures

Precise modeling of the program heap is fundamental for understanding the behavior of a program, and is thus of signiflcant interest for many optimization applications. One of the fundamental properties of the heap that can be used in a range of optimization techniques is the sharing relationships between the elements in an array or collection. If an analysis can determine that the memory locations pointed to by different entries of an array (or collection) are disjoint, then in many cases loops that traverse the array can be vectorized or transformed into a thread-parallel versión. This paper introduces several novel sharing properties over the concrete heap and corresponding abstractions to represent them. In conjunction with an existing shape analysis technique, these abstractions allow us to precisely resolve the sharing relations in a wide range of heap structures (arrays, collections, recursive data structures, composite heap structures) in a computationally efflcient manner. The effectiveness of the approach is evaluated on a set of challenge problems from the JOlden and SPECjvm98 suites. Sharing information obtained from the analysis is used to achieve substantial thread-level parallel speedups.

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.

Dynamic Studies of Shell and Spatial Structures

For the past 20 years, dynamic analysis of shells has been one of the most fascinating fields for research. Using the new light materials the building engineer soon discovered that the subsequent reduction of gravity forces produced not only the desired shape freedom but the appearance of ecologic loads as the first factor of design; loads which present strong random properties and marked dynamic influence. On the other hand, the technological advance in the aeronautical and astronautical field placed the engineers in front of shell structures of nonconventional shape and able to sustain substantialy dynamic loads. The response to the increasingly challenger problems of the last two decades has been very bright; new forms, new materials and new methods of analysis have arosen in the design of off-shore platforms, nuclear vessels, space crafts, etc. Thanks to the intensity of the lived years we have at our disposition a coherent and homogeneous amount of knowledge which enable us to face problems of inconceivable complexity when IASS was founded. The open minded approach to classical problems and the impact of the computer are, probably, important factors in the Renaissance we have enjoyed these years, and a good proof of this are the papers presented to the previous IASS meetings as well as that we are going to consider in this one. Particularly striking is the great number of papers based on a mathematical modeling in front of the meagerness of those treating laboratory experiments on physical models. The universal entering of the computer into almost every phase of our lifes, and the cost of physical models, are –may be- reasons for this lack of experimental methods. Nevertheless they continue offering useful results as are those obtained with the shaking-table in which the computer plays an essential role in the application of loads as well as in the instantaneous treatment of control data. Plates 1 and 2 record the papers presented under dynamic heading, 40% of them are from Japan in good correlation with the relevance that Japanese research has traditionally showed in this area. Also interesting is to find old friends as profesors Tanaka, Nishimura and Kostem who presented valuable papers in previous IASS conferences. As we see there are papers representative of all tendencies, even purely analytical! Better than discuss them in detail, which can be done after the authors presentation, I think we can comment in the general pattern of the dynamical approach are summarized in plate 3.

Condicionantes de la adherencia y anclaje en el refuerzo de muros de fábrica con elementos de fibras

Es cada vez más frecuente la rehabilitación de patrimonio construido, tanto de obras deterioradas como para la adecuación de obras existentes a nuevos usos o solicitaciones. Se ha considerado el estudio del refuerzo de obras de fábrica ya que constituyen un importante número dentro del patrimonio tanto de edificación como de obra civil (sistemas de muros de carga o en estructuras principales porticadas de acero u hormigón empleándose las fábricas como cerramiento o distribución con elementos autoportantes). A la hora de reparar o reforzar una estructura es importante realizar un análisis de las deficiencias, caracterización mecánica del elemento y solicitaciones presentes o posibles; en el apartado 1.3 del presente trabajo se refieren acciones de rehabilitación cuando lo que se precisa no es refuerzo estructural, así como las técnicas tradicionales más habituales para refuerzo de fábricas que suelen clasificarse según se trate de refuerzos exteriores o interiores. En los últimos años se ha adoptado el sistema de refuerzo de FRP, tecnología con origen en los refuerzos de hormigón tanto de elementos a flexión como de soportes. Estos refuerzos pueden ser de láminas adheridas a la fábrica soporte (SM), o de barras incluidas en rozas lineales (NSM). La elección de un sistema u otro depende de la necesidad de refuerzo y tipo de solicitación predominante, del acceso para colocación y de la exigencia de impacto visual. Una de las mayores limitaciones de los sistemas de refuerzo por FRP es que no suele movilizarse la resistencia del material de refuerzo, produciéndose previamente fallo en la interfase con el soporte con el consecuente despegue o deslaminación; dichos fallos pueden tener un origen local y propagarse a partir de una discontinuidad, por lo que es preciso un tratamiento cuidadoso de la superficie soporte, o bien como consecuencia de una insuficiente longitud de anclaje para la transferencia de los esfuerzos en la interfase. Se considera imprescindible una caracterización mecánica del elemento a reforzar. Es por ello que el trabajo presenta en el capítulo 2 métodos de cálculo de la fábrica soporte de distintas normativas y también una formulación alternativa que tiene en cuenta la fábrica histórica ya que su caracterización suele ser más complicada por la heterogeneidad y falta de clasificación de sus materiales, especialmente de los morteros. Una vez conocidos los parámetros resistentes de la fábrica soporte es posible diseñar el refuerzo; hasta la fecha existe escasa normativa de refuerzos de FRP para muros de fábrica, consistente en un protocolo propuesto por la ACI 440 7R-10 que carece de mejoras por tipo de anclaje y aporta valores muy conservadores de la eficacia del refuerzo. Como se ha indicado, la problemática principal de los refuerzos de FRP en muros es el modo de fallo que impide un aprovechamiento óptimo de las propiedades del material. Recientemente se están realizando estudios con distintos métodos de anclaje para estos refuerzos, con lo que se incremente la capacidad última y se mantenga el soporte ligado al refuerzo tras la rotura. Junto con sistemas de anclajes por prolongación del refuerzo (tanto para láminas como para barras) se han ensayado anclajes con llaves de cortante, barras embebidas, o anclajes mecánicos de acero o incluso de FRP. Este texto resume, en el capítulo 4, algunas de las campañas experimentales llevadas a cabo entre los años 2000 y 2013 con distintos anclajes. Se observan los parámetros fundamentales para medir la eficacia del anclajes como son: el modo de fallo, el incremento de resistencia, y los desplazamientos que permite observar la ductilidad del refuerzo; estos datos se analizan en función de la variación de: tipo de refuerzo incluyéndose el tipo de fibra y sistema de colocación, y tipo de anclaje. Existen también parámetros de diseño de los propios anclajes. En el caso de barras embebidas se resumen en diámetro y material de la barra, acabado superficial, dimensiones y forma de la roza, tipo de adhesivo. En el caso de anclajes de FRP tipo pasador la caracterización incluye: tipo de fibra, sistema de fabricación del anclajes y diámetro del mismo, radio de expansión del abanico, espaciamiento longitudinal de anclajes, número de filas de anclajes, número de láminas del refuerzo, longitud adherida tras el anclaje; es compleja la sistematización de resultados de los autores de las campañas expuestas ya que algunos de estos parámetros varían impidiendo la comparación. El capítulo 5 presenta los ensayos empleados para estas campañas de anclajes, distinguiéndose entre ensayos de modo I, tipo tracción directa o arrancamiento, que servirían para sistemas NSM o para cuantificar la resistencia individual de anclajes tipo pasador; ensayos de modo II, tipo corte simple, que se asemeja más a las condiciones de trabajo de los refuerzos. El presente texto se realiza con objeto de abrir una posible investigación sobre los anclajes tipo pasador, considerándose que junto con los sistemas de barra embebida son los que permiten una mayor versatilidad de diseño para los refuerzos de FRP y siendo su eficacia aún difícil de aislar por el número de parámetros de diseño. Rehabilitation of built heritage is becoming increasingly frequent, including repair of damaged works and conditioning for a new use or higher loads. In this work it has been considered the study of masonry wall reinforcement, as most buildings and civil works have load bearing walls or at least infilled masonry walls in concrete and steel structures. Before repairing or reinforcing an structure, it is important to analyse its deficiencies, its mechanical properties and both existing and potential loads; chapter 1, section 4 includes the most common rehabilitation methods when structural reinforcement is not needed, as well as traditional reinforcement techniques (internal and external reinforcement) In the last years the FRP reinforcement system has been adopted for masonry walls. FRP materials for reinforcement were initially used for concrete pillars and beams. FRP reinforcement includes two main techniques: surface mounted laminates (SM) and near surface mounted bars (NSM); one of them may be more accurate according to the need for reinforcement and main load, accessibility for installation and aesthetic requirements. One of the main constraints of FRP systems is not reaching maximum load for material due to premature debonding failure, which can be caused by surface irregularities so surface preparation is necessary. But debonding (or delamination for SM techniques) can also be a consequence of insufficient anchorage length or stress concentration. In order to provide an accurate mechanical characterisation of walls, chapter 2 summarises the calculation methods included in guidelines as well as alternative formulations for old masonry walls as historic wall properties are more complicated to obtain due to heterogeneity and data gaps (specially for mortars). The next step is designing reinforcement system; to date there are scarce regulations for walls reinforcement with FRP: ACI 440 7R-10 includes a protocol without considering the potential benefits provided by anchorage devices and with conservative values for reinforcement efficiency. As noted above, the main problem of FRP masonry walls reinforcement is failure mode. Recently, some authors have performed studies with different anchorage systems, finding that these systems are able to delay or prevent debonding . Studies include the following anchorage systems: Overlap, embedded bars, shear keys, shear restraint and fiber anchors. Chapter 4 briefly describes several experimental works between years 2000 and 2013, concerning different anchorage systems. The main parameters that measure the anchorage efficiency are: failure mode, failure load increase, displacements (in order to evaluate the ductility of the system); all these data points strongly depend on: reinforcement system, FRP fibers, anchorage system, and also on the specific anchorage parameters. Specific anchorage parameters are a function of the anchorage system used. The embedded bar system have design variables which can be identified as: bar diameter and material, surface finish, groove dimensions, and adhesive. In FRP anchorages (spikes) a complete design characterisation should include: type of fiber, manufacturing process, diameter, fan orientation, anchor splay width, anchor longitudinal spacing and number or rows, number or FRP sheet plies, bonded length beyond anchorage devices,...the parameters considered differ from some authors to others, so the comparison of results is quite complicated. Chapter 5 includes the most common tests used in experimental investigations on bond-behaviour and anchorage characterisation: direct shear tests (with variations single-shear and double-shear), pullout tests and bending tests. Each of them may be used according to the data needed. The purpose of this text is to promote further investigation of anchor spikes, accepting that both FRP anchors and embedded bars are the most versatile anchorage systems of FRP reinforcement and considering that to date its efficiency cannot be evaluated as there are too many design uncertainties.

Simplified serviceability design of jointless structures. Experimental verification and application to typical bridge and building structures

In this article an experimental campaign aimed at validating a previously published simplified serviceability design method of the columns of long jointless structures is presented. The proposed method is also extended to include tension stiffening effects which proved to be significant in structures with small amount of reinforcement subjected to small axial loading. This extension allows significant improvement of predictions for this type of element. The campaign involved columns with different reinforcement and squashing load ratios, given that these parameters had been identified as crucial when designing columns subjected to imposed displacements. Experimental results are presented and discussed, with particular regard to cracking behaviour and structural stiffness. Considerations on tension stiffening effects are also made. Finally, the application of the method to typical bridge and building cases is presented, showing the feasibility of jointless construction, and the limits which should be respected.

The Future of the Technologies of Shell and spatial Structures. Bridges

The objective of this lecture is try to predict the future of this important type of spatial structures. In this way the activities of the different IASS Technical Working Groups can be stimulated and coordinated in order to play a more relevant role in this future. To grasp a possible evolution of bridges it is convenient a reflection on the bridge history and on their present situation, particularly in relation to the different existing achievements.

I.A.S.S. Symposium on Practical Aspects in the Computation on Shell and Spatial Structures

This work is the outcome of the interest that the Board of Executives of the lASS showed on the papers presented at the lASS-Symposium in Osaka (1986)

Evaluación de la profundidad de la fisuración superficial descendente en pavimentos asfálticos mediante técnicas de ultrasonidos. Validación teórico-práctica y modelos

La fisuración iniciada en la superficie de los pavimentos asfálticos constituye uno de los más frecuentes e importantes modos de deterioro que tienen lugar en los firmes bituminosos, como han demostrado los estudios teóricos y experimentales llevados a cabo en la última década. Sin embargo, este mecanismo de fallo no ha sido considerado por los métodos tradicionales de diseño de estos firmes. El concepto de firmes de larga duración se fundamenta en un adecuado seguimiento del proceso de avance en profundidad de estos deterioros y la intervención en el momento más apropiado para conseguir mantenerlos confinados como fisuras de profundidad parcial en la capa superficial más fácilmente accesible y reparable, de manera que pueda prolongarse la durabilidad y funcionalidad del firme y reducir los costes generalizados de su ciclo de vida. Por lo tanto, para la selección de la estrategia óptima de conservación de los firmes resulta esencial disponer de metodologías que posibiliten la identificación precisa in situ de la fisuración descendente, su seguimiento y control, y que además permitan una determinación fiable y con alto rendimiento de su profundidad y extensión. En esta Tesis Doctoral se presentan los resultados obtenidos mediante la investigación sistemática de laboratorio e in situ llevada a cabo para la obtención de datos sobre fisuración descendente en firmes asfálticos y para el estudio de procedimientos de evaluación de la profundidad de este tipo de fisuras empleando técnicas de ultrasonidos. Dichos resultados han permitido comprobar que la metodología no destructiva propuesta, de rápida ejecución, bajo coste y sencilla implementación (principalmente empleada hasta el momento en estructuras metálicas y de hormigón, debido a las dificultades que introduce la naturaleza viscoelástica de los materiales bituminosos) puede ser aplicada con suficiente fiabilidad y repetibilidad sobre firmes asfálticos. Las medidas resultan asimismo independientes del espesor total del firme. Además, permite resolver algunos de los inconvenientes frecuentes que presentan otros métodos de diagnóstico de las fisuras de pavimentos, tales como la extracción de testigos (sistema destructivo, de alto coste y prolongados tiempos de interrupción del tráfico) o algunas otras técnicas no destructivas como las basadas en medidas de deflexiones o el georradar, las cuales no resultan suficientemente precisas para la investigación de fisuras superficiales. Para ello se han realizado varias campañas de ensayos sobre probetas de laboratorio en las que se han estudiado diferentes condiciones empíricas como, por ejemplo, distintos tipos de mezclas bituminosas en caliente (AC, SMA y PA), espesores de firme y adherencias entre capas, temperaturas, texturas superficiales, materiales de relleno y agua en el interior de las grietas, posición de los sensores y un amplio rango de posibles profundidades de fisura. Los métodos empleados se basan en la realización de varias medidas de velocidad o de tiempo de transmisión del pulso ultrasónico sobre una única cara o superficie accesible del material, de manera que resulte posible obtener un coeficiente de transmisión de la señal (mediciones relativas o autocompensadas). Las mediciones se han realizado a bajas frecuencias de excitación mediante dos equipos de ultrasonidos diferentes dotados, en un caso, de transductores de contacto puntual seco (DPC) y siendo en el otro instrumento de contacto plano a través de un material especialmente seleccionado para el acoplamiento (CPC). Ello ha permitido superar algunos de los tradicionales inconvenientes que presenta el uso de los transductores convencionales y no precisar preparación previa de las superficies. La técnica de autocalibración empleada elimina los errores sistemáticos y la necesidad de una calibración local previa, demostrando el potencial de esta tecnología. Los resultados experimentales han sido comparados con modelos teóricos simplificados que simulan la propagación de las ondas ultrasónicas en estos materiales bituminosos fisurados, los cuales han sido deducidos previamente mediante un planteamiento analítico y han permitido la correcta interpretación de dichos datos empíricos. Posteriormente, estos modelos se han calibrado mediante los resultados de laboratorio, proporcionándose sus expresiones matemáticas generalizadas y gráficas para su uso rutinario en las aplicaciones prácticas. Mediante los ensayos con ultrasonidos efectuados en campañas llevadas a cabo in situ, acompañados de la extracción de testigos del firme, se han podido evaluar los modelos propuestos. El máximo error relativo promedio en la estimación de la profundidad de las fisuras al aplicar dichos modelos no ha superado el 13%, con un nivel de confianza del 95%, en el conjunto de todos los ensayos realizados. La comprobación in situ de los modelos ha permitido establecer los criterios y las necesarias recomendaciones para su utilización sobre firmes en servicio. La experiencia obtenida posibilita la integración de esta metodología entre las técnicas de auscultación para la gestión de su conservación. Abstract Surface-initiated cracking of asphalt pavements constitutes one of the most frequent and important types of distress that occur in flexible bituminous pavements, as clearly has been demonstrated in the technical and experimental studies done over the past decade. However, this failure mechanism has not been taken into consideration for traditional methods of flexible pavement design. The concept of long-lasting pavements is based on adequate monitoring of the depth and extent of these deteriorations and on intervention at the most appropriate moment so as to contain them in the surface layer in the form of easily-accessible and repairable partial-depth topdown cracks, thereby prolonging the durability and serviceability of the pavement and reducing the overall cost of its life cycle. Therefore, to select the optimal maintenance strategy for perpetual pavements, it becomes essential to have access to methodologies that enable precise on-site identification, monitoring and control of top-down propagated cracks and that also permit a reliable, high-performance determination of the extent and depth of cracking. This PhD Thesis presents the results of systematic laboratory and in situ research carried out to obtain information about top-down cracking in asphalt pavements and to study methods of depth evaluation of this type of cracking using ultrasonic techniques. These results have demonstrated that the proposed non-destructive methodology –cost-effective, fast and easy-to-implement– (mainly used to date for concrete and metal structures, due to the difficulties caused by the viscoelastic nature of bituminous materials) can be applied with sufficient reliability and repeatability to asphalt pavements. Measurements are also independent of the asphalt thickness. Furthermore, it resolves some of the common inconveniences presented by other methods used to evaluate pavement cracking, such as core extraction (a destructive and expensive procedure that requires prolonged traffic interruptions) and other non-destructive techniques, such as those based on deflection measurements or ground-penetrating radar, which are not sufficiently precise to measure surface cracks. To obtain these results, extensive tests were performed on laboratory specimens. Different empirical conditions were studied, such as various types of hot bituminous mixtures (AC, SMA and PA), differing thicknesses of asphalt and adhesions between layers, varied temperatures, surface textures, filling materials and water within the crack, different sensor positions, as well as an ample range of possible crack depths. The methods employed in the study are based on a series of measurements of ultrasonic pulse velocities or transmission times over a single accessible side or surface of the material that make it possible to obtain a signal transmission coefficient (relative or auto-calibrated readings). Measurements were taken at low frequencies by two short-pulse ultrasonic devices: one equipped with dry point contact transducers (DPC) and the other with flat contact transducers that require a specially-selected coupling material (CPC). In this way, some of the traditional inconveniences presented by the use of conventional transducers were overcome and a prior preparation of the surfaces was not required. The auto-compensating technique eliminated systematic errors and the need for previous local calibration, demonstrating the potential for this technology. The experimental results have been compared with simplified theoretical models that simulate ultrasonic wave propagation in cracked bituminous materials, which had been previously deduced using an analytical approach and have permitted the correct interpretation of the aforementioned empirical results. These models were subsequently calibrated using the laboratory results, providing generalized mathematical expressions and graphics for routine use in practical applications. Through a series of on-site ultrasound test campaigns, accompanied by asphalt core extraction, it was possible to evaluate the proposed models, with differences between predicted crack depths and those measured in situ lower than 13% (with a confidence level of 95%). Thereby, the criteria and the necessary recommendations for their implementation on in-service asphalt pavements have been established. The experience obtained through this study makes it possible to integrate this methodology into the evaluation techniques for pavement management systems.

An embedded cohesive crack model for finite element analysis of quasi-brittle materials

This paper presents a numerical implementation of the cohesive crack model for the anal-ysis of quasibrittle materials based on the strong discontinuity approach in the framework of the finite element method. A simple central force model is used for the stress versus crack opening curve. The additional degrees of freedom defining the crack opening are determined at the crack level, thus avoiding the need for performing a static condensation at the element level. The need for a tracking algorithm is avoided by using a consistent pro-cedure for the selection of the separated nodes. Such a model is then implemented into a commercial program by means of a user subroutine, consequently being contrasted with the experimental results. The model takes into account the anisotropy of the material. Numerical simulations of well-known experiments are presented to show the ability of the proposed model to simulate the fracture of quasibrittle materials such as mortar, concrete and masonry.

Ethics and materials: Some Spanish Cases

The problem is general: modern architects and engineers are trying to understand historic structures using the wrong theoretical frame, the classic (elastic) thery of structures developed in the 19th Century for iron and stell, and in the 20th century for reinforced concrete, disguised with "modern" computer packages, mainly FEM, but also others. Masonry is an essentially different material, and the structural equations must be adapted accordingly. It is not a matter of "taste" or "opinion", and the consequences are before us. Since, say 1920s, historic monuments have suffered the aggression of generations of archietcts and engineers, trying to transform masonry in reinfored concrete or steel. The damage to the monuments and the expense has been, and is, enormous. However, as we have an adequate theory (modern limit analysis of masonry structures, Heyman 1966) which encompasses the "old theory" used successfully by the 18th and 19th Century practical engineers (from Perronet to Sejourné), it is a matter of "Ethics" not to use the wrong approach. It is also "contra natura" to modify the material masonry with indiscriminate injections, stitchings, etc. It is insane to consider, suddenly, that buildings which are Centuries or milennia old, are suddenly in danger of collapse. Maintenance is necessary but not the actual destruction of the constructive essence of the monument. A cocktail of "ignorance, fear and greed" is acting under the best of intentions.

Experimental and numerical analysis of reinforced concrete elements subjected to blast loading

El hormigón es uno de los materiales de construcción más empleados en la actualidad debido a sus buenas prestaciones mecánicas, moldeabilidad y economía de obtención, entre otras ventajas. Es bien sabido que tiene una buena resistencia a compresión y una baja resistencia a tracción, por lo que se arma con barras de acero para formar el hormigón armado, material que se ha convertido por méritos propios en la solución constructiva más importante de nuestra época. A pesar de ser un material profusamente utilizado, hay aspectos del comportamiento del hormigón que todavía no son completamente conocidos, como es el caso de su respuesta ante los efectos de una explosión. Este es un campo de especial relevancia, debido a que los eventos, tanto intencionados como accidentales, en los que una estructura se ve sometida a una explosión son, por desgracia, relativamente frecuentes. La solicitación de una estructura ante una explosión se produce por el impacto sobre la misma de la onda de presión generada en la detonación. La aplicación de esta carga sobre la estructura es muy rápida y de muy corta duración. Este tipo de acciones se denominan cargas impulsivas, y pueden ser hasta cuatro órdenes de magnitud más rápidas que las cargas dinámicas impuestas por un terremoto. En consecuencia, no es de extrañar que sus efectos sobre las estructuras y sus materiales sean muy distintos que las que producen las cargas habitualmente consideradas en ingeniería. En la presente tesis doctoral se profundiza en el conocimiento del comportamiento material del hormigón sometido a explosiones. Para ello, es crucial contar con resultados experimentales de estructuras de hormigón sometidas a explosiones. Este tipo de resultados es difícil de encontrar en la literatura científica, ya que estos ensayos han sido tradicionalmente llevados a cabo en el ámbito militar y los resultados obtenidos no son de dominio público. Por otra parte, en las campañas experimentales con explosiones llevadas a cabo por instituciones civiles el elevado coste de acceso a explosivos y a campos de prueba adecuados no permite la realización de ensayos con un elevado número de muestras. Por este motivo, la dispersión experimental no es habitualmente controlada. Sin embargo, en elementos de hormigón armado sometidos a explosiones, la dispersión experimental es muy acusada, en primer lugar, por la propia heterogeneidad del hormigón, y en segundo, por la dificultad inherente a la realización de ensayos con explosiones, por motivos tales como dificultades en las condiciones de contorno, variabilidad del explosivo, o incluso cambios en las condiciones atmosféricas. Para paliar estos inconvenientes, en esta tesis doctoral se ha diseñado un novedoso dispositivo que permite ensayar hasta cuatro losas de hormigón bajo la misma detonación, lo que además de proporcionar un número de muestras estadísticamente representativo, supone un importante ahorro de costes. Con este dispositivo se han ensayado 28 losas de hormigón, tanto armadas como en masa, de dos dosificaciones distintas. Pero además de contar con datos experimentales, también es importante disponer de herramientas de cálculo para el análisis y diseño de estructuras sometidas a explosiones. Aunque existen diversos métodos analíticos, hoy por hoy las técnicas de simulación numérica suponen la alternativa más avanzada y versátil para el cálculo de elementos estructurales sometidos a cargas impulsivas. Sin embargo, para obtener resultados fiables es crucial contar con modelos constitutivos de material que tengan en cuenta los parámetros que gobiernan el comportamiento para el caso de carga en estudio. En este sentido, cabe destacar que la mayoría de los modelos constitutivos desarrollados para el hormigón a altas velocidades de deformación proceden del ámbito balístico, donde dominan las grandes tensiones de compresión en el entorno local de la zona afectada por el impacto. En el caso de los elementos de hormigón sometidos a explosiones, las tensiones de compresión son mucho más moderadas, siendo las tensiones de tracción generalmente las causantes de la rotura del material. En esta tesis doctoral se analiza la validez de algunos de los modelos disponibles, confirmando que los parámetros que gobiernan el fallo de las losas de hormigón armado ante explosiones son la resistencia a tracción y su ablandamiento tras rotura. En base a los resultados anteriores se ha desarrollado un modelo constitutivo para el hormigón ante altas velocidades de deformación, que sólo tiene en cuenta la rotura por tracción. Este modelo parte del de fisura cohesiva embebida con discontinuidad fuerte, desarrollado por Planas y Sancho, que ha demostrado su capacidad en la predicción de la rotura a tracción de elementos de hormigón en masa. El modelo ha sido modificado para su implementación en el programa comercial de integración explícita LS-DYNA, utilizando elementos finitos hexaédricos e incorporando la dependencia de la velocidad de deformación para permitir su utilización en el ámbito dinámico. El modelo es estrictamente local y no requiere de remallado ni conocer previamente la trayectoria de la fisura. Este modelo constitutivo ha sido utilizado para simular dos campañas experimentales, probando la hipótesis de que el fallo de elementos de hormigón ante explosiones está gobernado por el comportamiento a tracción, siendo de especial relevancia el ablandamiento del hormigón. Concrete is nowadays one of the most widely used building materials because of its good mechanical properties, moldability and production economy, among other advantages. As it is known, it has high compressive and low tensile strengths and for this reason it is reinforced with steel bars to form reinforced concrete, a material that has become the most important constructive solution of our time. Despite being such a widely used material, there are some aspects of concrete performance that are not yet fully understood, as it is the case of its response to the effects of an explosion. This is a topic of particular relevance because the events, both intentional and accidental, in which a structure is subjected to an explosion are, unfortunately, relatively common. The loading of a structure due to an explosive event occurs due to the impact of the pressure shock wave generated in the detonation. The application of this load on the structure is very fast and of very short duration. Such actions are called impulsive loads, and can be up to four orders of magnitude faster than the dynamic loads imposed by an earthquake. Consequently, it is not surprising that their effects on structures and materials are very different than those that cause the loads usually considered in engineering. This thesis broadens the knowledge about the material behavior of concrete subjected to explosions. To that end, it is crucial to have experimental results of concrete structures subjected to explosions. These types of results are difficult to find in the scientific literature, as these tests have traditionally been carried out by armies of different countries and the results obtained are classified. Moreover, in experimental campaigns with explosives conducted by civil institutions the high cost of accessing explosives and the lack of proper test fields does not allow for the testing of a large number of samples. For this reason, the experimental scatter is usually not controlled. However, in reinforced concrete elements subjected to explosions the experimental dispersion is very pronounced. First, due to the heterogeneity of concrete, and secondly, because of the difficulty inherent to testing with explosions, for reasons such as difficulties in the boundary conditions, variability of the explosive, or even atmospheric changes. To overcome these drawbacks, in this thesis we have designed a novel device that allows for testing up to four concrete slabs under the same detonation, which apart from providing a statistically representative number of samples, represents a significant saving in costs. A number of 28 slabs were tested using this device. The slabs were both reinforced and plain concrete, and two different concrete mixes were used. Besides having experimental data, it is also important to have computational tools for the analysis and design of structures subjected to explosions. Despite the existence of several analytical methods, numerical simulation techniques nowadays represent the most advanced and versatile alternative for the assessment of structural elements subjected to impulsive loading. However, to obtain reliable results it is crucial to have material constitutive models that take into account the parameters that govern the behavior for the load case under study. In this regard it is noteworthy that most of the developed constitutive models for concrete at high strain rates arise from the ballistic field, dominated by large compressive stresses in the local environment of the area affected by the impact. In the case of concrete elements subjected to an explosion, the compressive stresses are much more moderate, while tensile stresses usually cause material failure. This thesis discusses the validity of some of the available models, confirming that the parameters governing the failure of reinforced concrete slabs subjected to blast are the tensile strength and softening behaviour after failure. Based on these results we have developed a constitutive model for concrete at high strain rates, which only takes into account the ultimate tensile strength. This model is based on the embedded Cohesive Crack Model with Strong Discontinuity Approach developed by Planas and Sancho, which has proved its ability in predicting the tensile fracture of plain concrete elements. The model has been modified for its implementation in the commercial explicit integration program LS-DYNA, using hexahedral finite elements and incorporating the dependence of the strain rate, to allow for its use in dynamic domain. The model is strictly local and does not require remeshing nor prior knowledge of the crack path. This constitutive model has been used to simulate two experimental campaigns, confirming the hypothesis that the failure of concrete elements subjected to explosions is governed by their tensile response, being of particular relevance the softening behavior of concrete.

Low-cost retrofitting solutions for RC frames using masonry infill panels

A large number of reinforced concrete (RC) frame structures built in earthquake-prone areas such as Haiti are vulnerable to strong ground motions. Structures in developing countries need low-cost seismic retrofit solutions to reduce their vulnerability. This paper investigates the feasibility of using masonry infill walls to reduce deformations and damage caused by strong ground motions in brittle and weak RC frames designed only for gravity loads. A numerical experiment was conducted in which several idealized prototypes representing RC frame structures of school buildings damaged during the Port-au-Prince earthquake (Haiti, 2010) were strengthened by adding elements representing masonry infill walls arranged in different configurations. Each configuration was characterized by the ratio Rm of the area of walls in the direction of the ground motion (in plan) installed in each story to the total floor area. The numerical representations of these idealized RC frame structures with different values of Rm were (hypothetically) subjected to three major earthquakes with peak ground accelerations of approximately 0.5g. The results of the non-linear dynamic response analyses were summarized in tentative relationships between Rm and four parameters commonly used to characterize the seismic response of structures: interstory drift, Park and Ang indexes of damage, and total amount of energy dissipated by the main frame. It was found that Rm=4% is a reasonable minimum design value for seismic retrofitting purposes in cases in which available resources are not sufficient to afford conventional retrofit measures.

Experimental and numerical analysis of concrete Slabs subjected to Blast

This paper summarizes the research activities focused on the behaviour of concrete and concrete structures subjected to blast loading carried out by the Department of Materials Science of the Technical University of Madrid (PUM). These activities comprise the design and construction of a test bench that allows for testing up to four planar concrete specimens with one single explosion, the study of the performance of different protection concepts for concrete structures and, finally, the development of a numerical model for the simulation of concrete structural elements subjected to blast. Up to date 6 different types of concrete have been studied, from plain normal strength concrete, to high strength concrete, including also fibre reinforced concretes with different types of fibres. The numerical model is based on the Cohesive Crack Model approach, and has been developed for the LSDYNA finite element code through a user programmed subroutine. Despite its simplicity, the model is able to predict the failure patterns of the concrete slabs tested with a high level of accuracy