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The research here presented has employed the newly evolved finite-discrete element method in the development of novel numerical solutions for the analysis of failure and collapse of reinforced concrete structures under hazardous blast loads. The first step to achieving this was to study the structural response, failure and collapse of individual structural elements. Thus the research in this area is taken further by using numerical solutions to study the behaviour of reinforced concrete beams to the point of failure. The results are implemented into the combined finite-discrete element method through a novel computationally efficient two noded beam element. Numerical integration across the cross section of the beam element is applied to facilitate the application of nonlinear constitutive laws for both steel and concrete for the case of multi-axial bending coupled with axial force. The accuracy of this new element is tested and validated under both static and dynamic loading situations using analytical solutions together with experiments undertaken at the University of Alberta and The Swiss Federal Institute of Technology. The proposed element has the advantage of reducing the size of the problem by fifty percent through the elimination of the rotational degrees of freedom using static condensationT. he new element,w hen coupledw ith NBS contactd etection, enables the same finite element mesh to be used for the discretised contact solutions, thus further reducing the CPU time required. When implemented into the finite-discrete element method, the proposed numerical solution also takes into account contact-impact and inertia effects. It is therefore both an accurate and CPU efficient solution to the combined finite-discrete element analysis of structural response, failure and collapse of real life structuresw hen subjectedt o hazardouslo ads as demonstratedin the thesis. T Bangash

Les structures en voûte sont présentes dans la plupart des anciens ouvrages maçonnés : tunnels, ponts, palais, cathédrales ou autres. Arches et voutes sont avec les murs les structures porteuses utilisées en maçonnerie. Leur bon état est alors la clef du bon fonctionnement d’un ouvrage. Les ouvrages maçonnés constituent à présent une proportion importante du patrimoine culturel. Toutefois, la plupart de ces ouvrages sont centenaires et le processus de dégradation s’est déjà enclenché depuis des décennies. Aujourd’hui, leur maintenance et réparation présentent des problèmes importants à leurs gestionnaires. Parfois des réparations ont été entreprises sans pour autant assurer la durabilité souhaitée. La fréquence des interventions se trouve augmentée et les coûts induits deviennent rapidement insupportables. Une situation qui a poussé certains gestionnaires à abandonner complètement leurs ouvrages, malgré leur valeur et leur importance patrimoniales. En effet, l’une des causes majeures d’abandon d’ouvrage est le coût excessif des inspections et des réparations. La question qui se pose dans de telles circonstances est de savoir comment mettre au point une stratégie à la fois efficace et surtout économique de maintenance de ces ouvrages, capable de prolonger leurs durées de vie ? Deux problèmes particuliers d’inspection sous incertitude sont traités : La présence localisée de perte de matière et la perte de matière généralisée. Pour traiter ces deux cas un programme a été développé. Le modèle, sur lequel il s’appuie, permet l’analyse globale de la voûte tout en minimisant au maximum le temps de calcul. Ce modèle constitue un compromis intéressant entre précision et temps de calcul. Les simulations de Monte Carlo ont été couplées à la méthode des éléments finis et implémentées dans un nouvel outil numérique, baptisé ArcProg_Z, afin de proposer une méthodologie cohérente pour l’évaluation probabiliste de la capacité portante des voûtes et de prévision de son mécanisme de ruine.Enfin, une étude de fiabilité de la voûte étudiée précédemment a été menée. La performance de la voûte a été évaluée à travers le calcul de sa probabilité de défaillance « instantanée et dépendante du temps » en fonction du coefficient de variation du module d’Young des différents segments. Les résultats obtenus pour chaque cas sont présentés et discutés. / The vault structures are present in most of the old masonry structures: tunnels, bridges, palaces, cathedrals or other civil infrastructures. Arches and vaults as well as walls are the supporting structures used in masonry. Their condition is then the key of the proper functioning of a structure. Masonry construction works are now a significant proportion of the cultural heritage. Most of them are century old and the degradation process is already running since several decades. Actually, the maintenance and repair continue to represent serious issues for their managers. Sometimes repairs have been undertaken without ensuring the aimed durability. The frequency of interventions is increased and the resulting costs are rapidly becoming unbearable. A situation has led some managers to completely abandon their buildings, despite their heritage value and national significance. Indeed, one of the major reasons for building abandonment is the excessive cost of inspections and repairs. The question that arises in such circumstances is how to develop a maintenance strategy that is both effective and most economical of these structures, capable to prolong their lifespan?Two particular inspection issues under uncertainty are discussed: The localized presence of material loss and generalized loss of material. To deal both cases, a program was developed. The model on which it is based, provides the overall analysis of the vault while minimizing the computation time. This model presents an interesting compromise between accuracy and computation time. Monte Carlo simulations are coupled with the finite element method and implemented in a software package named ArcProg_Z, in order to propose a consistent methodology for probabilistic assessment of the load bearing capacity of the vaults and predicting its failure mechanism.Finally, reliability study of the vault is carried out. The performance of the vault is assessed by calculating the probability of failure “instantaneous and time-dependent” according to the coefficient of variation of the Young's modulus of several segments.The obtained results for each case are presented and discussed.

Real-time substructure is a novel hybrid method for the dynamic testing of structures. During an experiment, the structure of interest is divided into two entities. The crucial parts for the project undertaken are physically replicated and loaded dynamically through powerful actuators while the rest is numerically modelled and solved via real-time software. The dynamics of both substructures must be accurately reproduced, as well as their mutual interaction. The applications are multiple but that of earthquake engineering is primarily considered in this research. Beyond the accurate modelling of both substructures, three main issues are crucial to the validity of a real-time hybrid simulation. Firstly, the loading equipment must be capable of imposing large loads and accurate displacements on the laboratory specimen. The behaviour of this loading system must be consistent and predictable over a wide range of frequencies and velocities. Secondly, the computational solver employed to emulate the numerical model dynamics requires stability, computational efficiency and accuracy. It must be able to deal with non-linear multi-degree of freedom systems. Thirdly, the interaction between the two substructures must be reliably emulated by a set of communication devices. The reciprocal boundary conditions must be imposed on the interface of each substructure. This notably implies quasi-instantaneous measurement and application of physical forces and displacements. The two substructures have to be solved simultaneously and in real-time. The three areas mentioned above have been investigated in this research. Initially, the laboratory installations of the hardware and software were focussed on. The servo-controlled hydraulic actuation system was optimised and a development rig was designed and constructed. It was found that hardware settings could greatly improve the general actuator performance, even though some particular situations could compromise it. This work was then complemented by an extensive study of the necessary actuation compensation. Numerous algorithms – either previously published or developed in the course of this research – were implemented and formally compared through a set of real-time experiments. Particularly, some challenging multi-axis experiments with a high level of actuator coupling were conducted. Direct extrapolation coupled with adaptive delay estimation was found to be the most effective approach to ensure synchronisation of the substructures. Attention was then given to the integration algorithms used to solve the numerical substructure problem and output the actuator demand on a real-time basis. Both explicit and implicit schemes were considered, even though an explicit formulation is required for this hybrid application. Computationally simple schemes are more suitable and several were shown to satisfy the necessary accuracy and stability requirements. Successful realtime hybrid tests were carried out with fifty degrees of freedom in the numerical substructure, including non-linear force/displacement relationships and using integration time-steps proving unconditional stability of the algorithms used. Finally, a realistic earthquake engineering application of the real-time substructure method was conducted. A steel column was tested physically as part of 20-storey building structure subject to the 1940 El Centro earthquake. To further display the usefulness of the method, an energy dissipative device was also integrated in the numerical model and its effect on the building response was shown.