Nonlinear seismic behaviour of concrete arch bridges

Arch bridge structural solution has been known for centuries, in fact the simple nature of arch that require low tension and shear strength was an advantage as the simple materials like stone and brick were the only option back in ancient centuries. By the pass of time especially after industrial revolution, the new materials were adopted in construction of arch bridges to reach longer spans. Nowadays one long span arch bridge is made of steel, concrete or combination of these two as "CFST", as the result of using these high strength materials, very long spans can be achieved. The current record for longest arch belongs to Chaotianmen bridge over Yangtze river in China with 552 meters span made of steel and the longest reinforced concrete type is Wanxian bridge which also cross the Yangtze river through a 420 meters span. Today the designer is no longer limited by span length as long as arch bridge is the most applicable solution among other approaches, i.e. cable stayed and suspended bridges are more reasonable if very long span is desired. Like any super structure, the economical and architectural aspects in construction of a bridge is extremely important, in other words, as a narrower bridge has better appearance, it also require smaller volume of material which make the design more economical. Design of such bridge, beside the high strength materials, requires precise structural analysis approaches capable of integrating the combination of material behaviour and complex geometry of structure and various types of loads which may be applied to bridge during its service life. Depend on the design strategy, analysis may only evaluates the linear elastic behaviour of structure or consider the nonlinear properties as well. Although most of structures in the past were designed to act in their elastic range, the rapid increase in computational capacity allow us to consider different sources of nonlinearities in order to achieve a more realistic evaluations where the dynamic behaviour of bridge is important especially in seismic zones where large movements may occur or structure experience P - _ effect during the earthquake. The above mentioned type of analysis is computationally expensive and very time consuming. In recent years, several methods were proposed in order to resolve this problem. Discussion of recent developments on these methods and their application on long span concrete arch bridges is the main goal of this research. Accordingly available long span concrete arch bridges have been studied to gather the critical information about their geometrical aspects and properties of their materials. Based on concluded information, several concrete arch bridges were designed for further studies. The main span of these bridges range from 100 to 400 meters. The Structural analysis methods implemented in in this study are as following: Elastic Analysis: Direct Response History Analysis (DRHA): This method solves the direct equation of motion over time history of applied acceleration or imposed load in linear elastic range. Modal Response History Analysis (MRHA): Similar to DRHA, this method is also based on time history, but the equation of motion is simplified to single degree of freedom system and calculates the response of each mode independently. Performing this analysis require less time than DRHA. Modal Response Spectrum Analysis (MRSA): As it is obvious from its name, this method calculates the peak response of structure for each mode and combine them using modal combination rules based on the introduced spectra of ground motion. This method is expected to be fastest among Elastic analysis. Inelastic Analysis: Nonlinear Response History Analysis (NL-RHA): The most accurate strategy to address significant nonlinearities in structural dynamics is undoubtedly the nonlinear response history analysis which is similar to DRHA but extended to inelastic range by updating the stiffness matrix for every iteration. This onerous task, clearly increase the computational cost especially for unsymmetrical buildings that requires to be analyzed in a full 3D model for taking the torsional effects in to consideration. Modal Pushover Analysis (MPA): The Modal Pushover Analysis is basically the MRHA but extended to inelastic stage. After all, the MRHA cannot solve the system of dynamics because the resisting force fs(u; u_ ) is unknown for inelastic stage. The solution of MPA for this obstacle is using the previously recorded fs to evaluate system of dynamics. Extended Modal Pushover Analysis (EMPA): Expanded Modal pushover is a one of very recent proposed methods which evaluates response of structure under multi-directional excitation using the modal pushover analysis strategy. In one specific mode,the original pushover neglect the contribution of the directions different than characteristic one, this is reasonable in regular symmetric building but a structure with complex shape like long span arch bridges may go through strong modal coupling. This method intend to consider modal coupling while it take same time of computation as MPA. Coupled Nonlinear Static Pushover Analysis (CNSP): The EMPA includes the contribution of non-characteristic direction to the formal MPA procedure. However the static pushovers in EMPA are performed individually for every mode, accordingly the resulted values from different modes can be combined but this is only valid in elastic phase; as soon as any element in structure starts yielding the neutral axis of that section is no longer fixed for both response during the earthquake, meaning the longitudinal deflection unavoidably affect the transverse one or vice versa. To overcome this drawback, the CNSP suggests executing pushover analysis for governing modes of each direction at the same time. This strategy is estimated to be more accurate than MPA and EMPA, moreover the calculation time is reduced because only one pushover analysis is required. Regardless of the strategy, the accuracy of structural analysis is highly dependent on modelling and numerical integration approaches used in evaluation of each method. Therefore the widely used Finite Element Method is implemented in process of all analysis performed in this research. In order to address the study, chapter 2, starts with gathered information about constructed long span arch bridges, this chapter continuous with geometrical and material definition of new models. Chapter 3 provides the detailed information about structural analysis strategies; furthermore the step by step description of procedure of all methods is available in Appendix A. The document ends with the description of results and conclusion of chapter 4.

Modelos de elementos finitos explícitos para explosiones en estructuras reticuladas de hormigón armado : aplicaciones al estudio del colapso de edificios

La frecuencia con la que se producen explosiones sobre edificios, ya sean accidentales o intencionadas, es reducida, pero sus efectos pueden ser catastróficos. Es deseable poder predecir de forma suficientemente precisa las consecuencias de estas acciones dinámicas sobre edificaciones civiles, entre las cuales las estructuras reticuladas de hormigón armado son una tipología habitual. En esta tesis doctoral se exploran distintas opciones prácticas para el modelado y cálculo numérico por ordenador de estructuras de hormigón armado sometidas a explosiones. Se emplean modelos numéricos de elementos finitos con integración explícita en el tiempo, que demuestran su capacidad efectiva para simular los fenómenos físicos y estructurales de dinámica rápida y altamente no lineales que suceden, pudiendo predecir los daños ocasionados tanto por la propia explosión como por el posible colapso progresivo de la estructura. El trabajo se ha llevado a cabo empleando el código comercial de elementos finitos LS-DYNA (Hallquist, 2006), desarrollando en el mismo distintos tipos de modelos de cálculo que se pueden clasificar en dos tipos principales: 1) modelos basados en elementos finitos de continuo, en los que se discretiza directamente el medio continuo mediante grados de libertad nodales de desplazamientos; 2) modelos basados en elementos finitos estructurales, mediante vigas y láminas, que incluyen hipótesis cinemáticas para elementos lineales o superficiales. Estos modelos se desarrollan y discuten a varios niveles distintos: 1) a nivel del comportamiento de los materiales, 2) a nivel de la respuesta de elementos estructurales tales como columnas, vigas o losas, y 3) a nivel de la respuesta de edificios completos o de partes significativas de los mismos. Se desarrollan modelos de elementos finitos de continuo 3D muy detallados que modelizan el hormigón en masa y el acero de armado de forma segregada. El hormigón se representa con un modelo constitutivo del hormigón CSCM (Murray et al., 2007), que tiene un comportamiento inelástico, con diferente respuesta a tracción y compresión, endurecimiento, daño por fisuración y compresión, y rotura. El acero se representa con un modelo constitutivo elastoplástico bilineal con rotura. Se modeliza la geometría precisa del hormigón mediante elementos finitos de continuo 3D y cada una de las barras de armado mediante elementos finitos tipo viga, con su posición exacta dentro de la masa de hormigón. La malla del modelo se construye mediante la superposición de los elementos de continuo de hormigón y los elementos tipo viga de las armaduras segregadas, que son obligadas a seguir la deformación del sólido en cada punto mediante un algoritmo de penalización, simulando así el comportamiento del hormigón armado. En este trabajo se denominarán a estos modelos simplificadamente como modelos de EF de continuo. Con estos modelos de EF de continuo se analiza la respuesta estructural de elementos constructivos (columnas, losas y pórticos) frente a acciones explosivas. Asimismo se han comparado con resultados experimentales, de ensayos sobre vigas y losas con distintas cargas de explosivo, verificándose una coincidencia aceptable y permitiendo una calibración de los parámetros de cálculo. Sin embargo estos modelos tan detallados no son recomendables para analizar edificios completos, ya que el elevado número de elementos finitos que serían necesarios eleva su coste computacional hasta hacerlos inviables para los recursos de cálculo actuales. Adicionalmente, se desarrollan modelos de elementos finitos estructurales (vigas y láminas) que, con un coste computacional reducido, son capaces de reproducir el comportamiento global de la estructura con una precisión similar. Se modelizan igualmente el hormigón en masa y el acero de armado de forma segregada. El hormigón se representa con el modelo constitutivo del hormigón EC2 (Hallquist et al., 2013), que también presenta un comportamiento inelástico, con diferente respuesta a tracción y compresión, endurecimiento, daño por fisuración y compresión, y rotura, y se usa en elementos finitos tipo lámina. El acero se representa de nuevo con un modelo constitutivo elastoplástico bilineal con rotura, usando elementos finitos tipo viga. Se modeliza una geometría equivalente del hormigón y del armado, y se tiene en cuenta la posición relativa del acero dentro de la masa de hormigón. Las mallas de ambos se unen mediante nodos comunes, produciendo una respuesta conjunta. En este trabajo se denominarán a estos modelos simplificadamente como modelos de EF estructurales. Con estos modelos de EF estructurales se simulan los mismos elementos constructivos que con los modelos de EF de continuo, y comparando sus respuestas estructurales frente a explosión se realiza la calibración de los primeros, de forma que se obtiene un comportamiento estructural similar con un coste computacional reducido. Se comprueba que estos mismos modelos, tanto los modelos de EF de continuo como los modelos de EF estructurales, son precisos también para el análisis del fenómeno de colapso progresivo en una estructura, y que se pueden utilizar para el estudio simultáneo de los daños de una explosión y el posterior colapso. Para ello se incluyen formulaciones que permiten considerar las fuerzas debidas al peso propio, sobrecargas y los contactos de unas partes de la estructura sobre otras. Se validan ambos modelos con un ensayo a escala real en el que un módulo con seis columnas y dos plantas colapsa al eliminar una de sus columnas. El coste computacional del modelo de EF de continuo para la simulación de este ensayo es mucho mayor que el del modelo de EF estructurales, lo cual hace inviable su aplicación en edificios completos, mientras que el modelo de EF estructurales presenta una respuesta global suficientemente precisa con un coste asumible. Por último se utilizan los modelos de EF estructurales para analizar explosiones sobre edificios de varias plantas, y se simulan dos escenarios con cargas explosivas para un edificio completo, con un coste computacional moderado. The frequency of explosions on buildings whether they are intended or accidental is small, but they can have catastrophic effects. Being able to predict in a accurate enough manner the consequences of these dynamic actions on civil buildings, among which frame-type reinforced concrete buildings are a frequent typology is desirable. In this doctoral thesis different practical options for the modeling and computer assisted numerical calculation of reinforced concrete structures submitted to explosions are explored. Numerical finite elements models with explicit time-based integration are employed, demonstrating their effective capacity in the simulation of the occurring fast dynamic and highly nonlinear physical and structural phenomena, allowing to predict the damage caused by the explosion itself as well as by the possible progressive collapse of the structure. The work has been carried out with the commercial finite elements code LS-DYNA (Hallquist, 2006), developing several types of calculation model classified in two main types: 1) Models based in continuum finite elements in which the continuous medium is discretized directly by means of nodal displacement degrees of freedom; 2) Models based on structural finite elements, with beams and shells, including kinematic hypothesis for linear and superficial elements. These models are developed and discussed at different levels: 1) material behaviour, 2) response of structural elements such as columns, beams and slabs, and 3) response of complete buildings or significative parts of them. Very detailed 3D continuum finite element models are developed, modeling mass concrete and reinforcement steel in a segregated manner. Concrete is represented with a constitutive concrete model CSCM (Murray et al., 2007), that has an inelastic behaviour, with different tension and compression response, hardening, cracking and compression damage and failure. The steel is represented with an elastic-plastic bilinear model with failure. The actual geometry of the concrete is modeled with 3D continuum finite elements and every and each of the reinforcing bars with beam-type finite elements, with their exact position in the concrete mass. The mesh of the model is generated by the superposition of the concrete continuum elements and the beam-type elements of the segregated reinforcement, which are made to follow the deformation of the solid in each point by means of a penalty algorithm, reproducing the behaviour of reinforced concrete. In this work these models will be called continuum FE models as a simplification. With these continuum FE models the response of construction elements (columns, slabs and frames) under explosive actions are analysed. They have also been compared with experimental results of tests on beams and slabs with various explosive charges, verifying an acceptable coincidence and allowing a calibration of the calculation parameters. These detailed models are however not advised for the analysis of complete buildings, as the high number of finite elements necessary raises its computational cost, making them unreliable for the current calculation resources. In addition to that, structural finite elements (beams and shells) models are developed, which, while having a reduced computational cost, are able to reproduce the global behaviour of the structure with a similar accuracy. Mass concrete and reinforcing steel are also modeled segregated. Concrete is represented with the concrete constitutive model EC2 (Hallquist et al., 2013), which also presents an inelastic behaviour, with a different tension and compression response, hardening, compression and cracking damage and failure, and is used in shell-type finite elements. Steel is represented once again with an elastic-plastic bilineal with failure constitutive model, using beam-type finite elements. An equivalent geometry of the concrete and the steel is modeled, considering the relative position of the steel inside the concrete mass. The meshes of both sets of elements are bound with common nodes, therefore producing a joint response. These models will be called structural FE models as a simplification. With these structural FE models the same construction elements as with the continuum FE models are simulated, and by comparing their response under explosive actions a calibration of the former is carried out, resulting in a similar response with a reduced computational cost. It is verified that both the continuum FE models and the structural FE models are also accurate for the analysis of the phenomenon of progressive collapse of a structure, and that they can be employed for the simultaneous study of an explosion damage and the resulting collapse. Both models are validated with an experimental full-scale test in which a six column, two floors module collapses after the removal of one of its columns. The computational cost of the continuum FE model for the simulation of this test is a lot higher than that of the structural FE model, making it non-viable for its application to full buildings, while the structural FE model presents a global response accurate enough with an admissible cost. Finally, structural FE models are used to analyze explosions on several story buildings, and two scenarios are simulated with explosive charges for a full building, with a moderate computational cost.

Behaviour of FRP confined concrete in square columns

A significant amount of research has been conducted on FRP-confined circular columns, but much less is known about rectangular/square columns in which the effectiveness of confinement is much reduced. This paper presents the results of experimental investigations on low strength square concrete columns confined with FRP. Axial compression tests were performed on ten intermediate size columns. The tests results indicate that FRP composites can significantly improve the bearing capacity and ductility of square section reinforced concrete columns with rounded corners. The strength enhancement ratio is greater the lower the concrete strength and also increases with the stiffness of the jacket. The confined concrete behaviour was predicted according to the more accepted theoretical models and compared with experimental results. There are two key parameters which critically influence the fitting of the models: the strain efficiency factor and the effect of confinement in non-circular sections.

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.

Radiological impact of cement, concrete and admixtures in Spain

It has been analyzed samples of portland cement (PC) with and without admixtures, samples of calcium aluminate cement (CAC) with different content of Al2O3 and specimens of concrete made with PC and CAC using High Resolution Gamma Spectrometry. The activity concentration index (I) is much less than 0.5 mSv y-1 for all the concrete specimens according to the Radiation protection document 112 of the European Commission. The PC without admixtures (CEM I 52,5 R) and the PC with addition of limestone (CEM II/BL 32,5 N) also have an I value much lower than 0.5 and the PC with the addition of fly ash and blast furnace slag (CEM IV/B (V) 32,5 N and III/A 42.5 N/SR) have an I value close to 0.6. The I value of the CAC used in the manufacture of structural precast concrete is of the order of 1 mSv y-1. Some of the CAC used in refractory concrete reaches a value close to 2 mSv y-1.

Multifunctional cement composites strain and damage sensors applied on reinforced concrete (RC) structural elements

In this research, strain-sensing and damage-sensing functional properties of cement composites have been studied on a conventional reinforced concrete (RC) beam. Carbon nanofiber (CNFCC) and fiber (CFCC) cement composites were used as sensors on a 4 m long RC beam. Different casting conditions (in situ or attached), service location (under tension or compression) and electrical contacts (embedded or superficial) were compared. Both CNFCC and CFCC were suitable as strain sensors in reversible (elastic) sensing condition testing. CNFCC showed higher sensitivities (gage factor up to 191.8), while CFCC only reached gage factors values of 178.9 (tension) or 49.5 (compression). Furthermore, damage-sensing tests were run, increasing the applied load progressively up to the RC beam failure. In these conditions, CNFCC sensors were also strain sensitive, but no damage sensing mechanism was detected for the strain levels achieved during the tests. Hence, these cement composites could act as strain sensors, even for severe damaged structures near to their collapse.

An improved procedure for obtaining and maintaining well characterized partial water saturation states on concrete samples to be used for mass transport tests

A conditioning procedure is proposed allowing to install into the concrete specimens any selected value of water saturation degree with homogeneous moisture distribution. This is achieved within the least time and the minimum alteration of the concrete specimens. The protocol has the following steps: obtaining basic drying data at 50 °C (water absorption capacity and drying curves); unidirectional drying of the specimens at 50 °C until reaching the target saturation degree values; redistribution phase in closed containers at 50 °C (with measurement of the quasi-equilibrium relative humidities); storage into controlled environment chambers until and during mass transport tests, if necessary. A water transport model is used to derive transport parameters of the tested materials from the drying data, i.e., relative permeabilities and apparent water diffusion coefficients. The model also allows calculating moisture profiles during isothermal drying and redistribution phases, thus allowing optimization of the redistribution times for obtaining homogeneous moisture distributions.

Recommendation of RILEM TC 178-TMC: Testing and modelling chloride penetration in concrete

This RILEM Technical Recommendation intends to give a general description of methods of sampling for obtaining chloride concentration profiles in concrete, applicable both for laboratory cast concrete specimens, for concrete cores taken from structures and for testing on site. These sampling procedures may be applied for obtaining concentration profiles of any other chemical species present in concrete.

Feasibility of electrochemical chloride extraction from structural reinforced concrete using a sprayed conductive graphite powder–cement paste as anode

This article summarizes research on the application of a conductive cement paste as an anode in the now classical technique of electrochemical extraction of chlorides applied to a concrete structural element by spraying the paste on the surface of a concrete structural element, a pillar. Sprayed conductive cement paste, by adding graphite powder, is particularly useful to treat sizable vertical surfaces such are structural supports. Outcomes indicate that this kind of anode not only provides electrochemical chloride removal with similar efficiency, but also is able to retain moisture even without the use of a continuous dampening system.

Moisture Distribution in Partially Saturated Concrete Studied by Impedance Spectroscopy

The moisture content and its spatial distribution has a great influence on the durability properties of concrete structures. Several non-destructive techniques have been used for the determination of the total water content, but moisture distribution is difficult to determine. In this paper impedance spectroscopy is used to study the water distribution in concrete samples with controlled and homogeneously distributed moisture contents. The technique is suitable for the determination of water distribution inside the sample, using the appropriate equivalent circuits. It is shown that using the selected drying procedures there is no change in the solid phase of the samples, although the technique can only be used for the qualitative study of variations in the solid phase when samples are too thick. The results of this work show that for a wide range of concrete percentages of saturation, from full to 18 % saturation, practically all the pores keep at least a thin layer of electrolyte covering their walls, since the capacitance measurement results are practically independent of the saturation degree.

Chloride Penetration Prediction in Concrete through an Empirical Model Based on Constant Flux Diffusion

An empirical model based on constant flux is presented for chloride transport through concrete in atmospherical exposure conditions. A continuous supply of chlorides is assumed as a constant mass flux at the exposed concrete surface. The model is applied to experimental chloride profiles obtained from a real marine structure, and results are compared with the classical error-function model. The proposed model shows some advantages. It yields a better predictive capacity than the classical error-function model. The previously observed chloride surface concentration increases are compatible with the proposed model. Nevertheless, the predictive capacity of the model can fail if the concrete microstructure changes with time. The model seems to be appropriate for well-maturated concretes exposed to a marine environment in atmospherical conditions.

Preliminary interpretation of shaking-table response of a full-scale 3-storey building composed of thin reinforced concrete sandwich walls

In the last few decades, the use of cast in situ reinforced concrete sandwich panels for the construction of low- to mid-rise buildings has become more and more widespread due to several interesting properties of this construction technique, such as fast construction and high thermal and acoustic performances. Nonetheless the level of knowledge of the structural behavior of systems made of squat reinforced concrete sandwich panels is still not so consolidated, especially with reference to the seismic response, due to the lack of experimental studies. In recent years, while various experimental tests have been conducted on single panels aimed at assessing their seismic capacity, only few tests have been carried out on more complex structural systems. In this paper, the experimental results of a series of shaking-table tests performed on a full-scale 3-storey building are presented in detail. The main goal is to give to the scientific community the possibility of develop independent interpretation of these experimental results. An in-depth interpretation of the discrepancies between the analytical predictions and the experimental results is beyond the objective of this paper and is still under development. Nonetheless, preliminary interpretations indicate that both the stiffness and the strength of the building under dynamic excitation appear quite superior with respect to those expected from the results of previous pseudo-static cyclic tests conducted on simple specimens.

Efficiency of a conductive cement-based anodic system for the application of cathodic protection, cathodic prevention and electrochemical chloride extraction to control corrosion in reinforced concrete structures

This article describes the research carried out regarding the application of cathodic protection (CP) and cathodic prevention (CPrev), in some cases with a pre-treatment of electrochemical chloride extraction (ECE), on representative specimens of reinforced concrete structures, using an anodic system consisting of a graphite-cement paste applied as a coating on the surface. The aim of this research is to find out the competence of this anode for the aforementioned electrochemical treatments. The efficiency of this anode has been clearly demonstrated, as well as its capability to apply a combined process of ECE and after CP.

Procedure for calculating the chloride diffusion coefficient and surface concentration from a profile having a maximum beyond the concrete surface

Chlorides induce local corrosion in the steel reinforcements when reaching the bar surface. The measurement of the rate of ingress of these ions, is made by mathematically fitting the so called “error function equation” into the chloride concentration profile, obtaining so the diffusion coefficient and the chloride concentration at the concrete surface. However, the chloride profiles do not always follow Fick’s law by having the maximum concentration at the concrete surface, but often the profile shows a maximum concentration more in the interior, which indicates a different composition and performance of the most external concrete layer with respect to the internal zones. The paper presents a procedure prepared during the time of the RILEM TC 178-TMC: “Testing and modeling chloride penetration in concrete”, which suggests neglecting the external layer where the chloride concentration increases and using the maximum as an “apparent” surface concentration, called C max and to fit the error function equation into the decreasing concentration profile towards the interior. The prediction of evolution should be made also from the maximum.

Shape Effect of Electrochemical Chloride Extraction in Structural Reinforced Concrete Elements Using a New Cement-Based Anodic System

This article shows the research carried out by the authors focused on how the shape of structural reinforced concrete elements treated with electrochemical chloride extraction can affect the efficiency of this process. Assuming the current use of different anode systems, the present study considers the comparison of results between conventional anodes based on Ti-RuO2 wire mesh and a cement-based anodic system such as a paste of graphite-cement. Reinforced concrete elements of a meter length were molded to serve as laboratory specimens, to closely represent authentic structural supports, with circular and rectangular sections. Results confirm almost equal performances for both types of anode systems when electrochemical chloride extraction is applied to isotropic structural elements. In the case of anisotropic ones, such as rectangular sections with no uniformly distributed rebar, differences in electrical flow density were detected during the treatment. Those differences were more extreme for Ti-RuO2 mesh anode system. This particular shape effect is evidenced by obtaining the efficiencies of electrochemical chloride extraction in different points of specimens.