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This study proposes an alternative approach to modeling the failure mechanisms of brickwork assemblages under combined shear

The Western Anatolia Region of Turkey is an important region of high seismic activity.The active dynamics of the region are shaped by a compression and expansion mechanism. This activemechanism is still ongoing and causes strong seismic activity in the region. The Frontinus Gate is amonument in the Roman city of Hierapolis of Phrygia located in southwestern Anatolia. The aim ofthis study is to investigate the seismic behavior of this stone masonry structure using discrete elementmodeling. For this purpose, nonlinear dynamic analyses were performed to simulate the structuralresponse of the gate under seismic excitation. Deformation, damage, and failure patterns induced inthe masonry gate for di erent levels of seismic action are evaluated and discussed. An earthquakewith a return period of 475 years is expected to cause some damage, but no collapse, while for areturn period of 2475 years, the models indicate collapse of the monument.

In this paper three historical masonry minarets in Istanbul, Turkey, are assessed for thedependency between the input harmonic motion and structural response parameters. Theirheights are 40, 73 and 74 m, while the slenderness is 12, 6 and 12, respectively. The discreteelement method is used in dynamic nonlinear analyses. Models were calibrated withmeasured natural frequencies. A series of sine-wave excitations is created for different frequency-amplitude pairs varying between 0.4 and 10 Hz, and between 0.1 and 1 m/s. Fromthe results of dynamic simulations, a general trend was observed for masonry minarets.Especially, slenderness and wall thickness play an important role on their dynamic responseand damage pattern. Dynamic behavior of these minarets cannot reliably be estimated bystatic non-linear analysis. Two engineering demand parameters (EDPs) are defined to characterizethe displacement of the minaret top and the inter-ring shear displacements alongthe minaret body. Damage performance criteria for minarets are proposed based on fourdamage states and tentative limit values are given. We were able to identify the occurrenceof those limit states as a function of frequency and amplitude of sinusoidal input motion.

This study presents a numerical investigation on the fracture mechanism of tension stiffening phenomenon in reinforced concrete members. A novel approach using the discrete element method (DEM) is proposed, where three-dimensional randomly generated distinct polyhedral blocks are used, representing concrete and one-dimensional truss elements are utilized, representing steel reinforcements. Thus, an explicit representation of reinforced concrete members is achieved, and the mechanical behavior of the system is solved by integrating the equations of motion for each block using the central difference algorithm. The inter-block interactions are taken into consideration at each contact point with springs and cohesive frictionalelements. Once the applied modeling strategy is validated, based on previously published experimental findings, a sensitivity analysis is performed for bond stiffness, cohesion strength, and the number of truss elements. Hence, valuable inferences are made regarding discontinuum analysis of reinforced concrete members, including concrete

Nowadays, the management and safety control of large dams is generally based on automatic monitoring, including the socalledseismic and structural health monitoring systems (SSHM), using the latest technology for automatic data measurement,acquisition and transmission. These systems should include software for automatic management and analysis of continuousmonitoring data and software for numerical simulation of the dam dynamic behavior using 3D finite element models. Thissoftware should be designed to provide useful and reliable information to meet the needs and expectations of stakeholders,and to support the studies of researchers and engineers responsible for structural health monitoring. This paper is focusedon the experience gathered from the SSHM system of Cabril dam, a 132 m high-arch dam, in Portugal, that has been undercontinuous dynamic monitoring since 2008. The importance of the software specifically developed for automatic modalidentification, automatic detection of seismic vibrations (distinct from vibrations due to the operation of discharge gates andpower groups), and automatic comparison between experimental data and computed results from a reference finite elementmodel of the dam-reservoir-foundation system, is highlighted. This software includes: (1) the generation of graphics withthe evolution of the identified natural frequencies over time and the comparison with calculated frequencies using differenthypothesis for concrete damage evolution; and (2) a service to automatically send emails summarizing key dynamic monitoringresults to stakeholders to provide the necessary support for informed management and engineering decision making.The main results from SSHM of Cabril dam are presented, namely regarding the evolution of modal parameter over time,considering the influence of water level variations, and the measured response during an earthquake event.

In this study, a novel computational modeling strategy is proposed to estimate the lateral load capacity andbehavior of unreinforced masonry (URM) structures. All commonly noted failure mechanisms are captured viathe proposed modeling strategy using the discrete element method (DEM) in three-dimensions (3D). Masonrywalls are represented as a system of elastic discrete blocks, where the nodal velocities are evaluated by integrating the equations of motion using the central difference method. Then, the mechanical interactions among adjacent blocks are examined utilizing the relative contact displacements and employed in the contact stress calculation. Through this research, a new stress-displacement contact constitutive model is considered and implemented in the commercial software 3DEC, which includes softening stress-displacement behavior for tension, shear, and compression along with the fracture energy concept. The results of the discontinuum models are validated on small- and large-scale experimental studies available in the literature with good agreement. Furthermore, important inferences are made regarding the effect of block size, the number of contact points, and contact stiffness values for robust and accurate simulations of masonry walls.

De acordo com a legislação portuguesa e tendo em consideração o risco sísmico da zona de construção das barragens é obrigatório a implementação de um Sistema de Observação Sísmica (SOS), incorporando instrumentação para caracterizar a ação sísmica induzida nas obras e a respetiva resposta estrutural. Em complemento, têm sido instalados Sistema de Monitoramento Dinâmico Contínuo (SMDC). O SOS permite não apenas a caracterização da ação sísmica, mas também a sua propagação ao longo do maciço rochoso, bem como a resposta estrutural da barragem. O SMDC visa identificar as características dinâmicas da barragem e sua evolução ao longo do tempo, considerando a variação das condições ambientais e operacionais, bem como a possível evolução das propriedades mecânicas dos materiais. Os processamentos são efetuados automaticamente incluindo a caracterização do nível de aceleração e a identificação dos parâmetros modais da barragem. Os valores obtidos pelo processamento automático são armazenados em base de dados, sendo enviados alertas quando são atingidos os patamares de alarme previamente definidos.Os resultados provenientes destes sistemas são comparados com os resultados de modelos numéricos sofisticados, calibrados com o recurso a ensaios experimentais de caraterização dinâmica realizados na obra durante a fase de primeiro enchimento.A combinação da monitorização dinâmica com os modelos numéricos é uma ferramenta fundamental no controlo de segurança estrutural e gestão de risco das barragens.

Today, there are several computational models to predict the mechanical behaviour of masonry structures subjected to external loading. Such models require the input of material parameters to describe the mechanical behaviour and strength of masonry constructions. Although such masonry materialparameters are characterised by stochastic

Nonhomogeneous material characteristics of masonry lead to complex fracture mechanisms,which require substantial analysis regarding the influence of masonry constituents. In this context, thisstudy presents a discontinuum modeling strategy, based on the discrete element method, developed toinvestigate the tensile fracture mechanism of masonry wallettes parallel to the bed joints consideringthe inherent variation in the material properties. The applied numerical approach utilizes polyhedralblocks to represent masonry and integrate the equations of motion explicitly to compute nodalvelocities for each block in the system. The mechanical interaction between the adjacent blocks iscomputed at the active contact points, where the contact stresses are calculated and updated basedon the implemented contact constitutive models. In this research, di erent fracture mechanisms ofmasonry wallettes under tension are explored developing at the unit

During the last decade, many vibration-based structural health monitoring systems have been successfully implementedin different structures such as bridges, towers, stadia and wind turbines, with the aim of studying thestructure dynamics and its evolution over time, eventually detecting the occurrence of novel structural behaviourthat may indicate the presence of damage.Such vibration-based monitoring systems generally rely on the identification of modal properties, which arethen used as monitoring features. Therefore, from operational modal analysis to the tracking of those featuresand finally to data normalization, many processing steps occur that depend on the accuracy of the identifiedmodal properties. Thus, the estimation of the uncertainties associated with the identified modal properties increasesthe robustness of this process.In this context, data obtained from the continuous dynamic monitoring of a concrete arch dam has been usedto evaluate the gains of quantifying the uncertainties of modal properties, evaluating in particular the effect oftaking these uncertainties into consideration when performing automated operational modal analysis, modaltracking and data normalization. Nevertheless, it is observed that the most significant gains of consideringestimates uncertainties occur when these quantities are used for removing outliers during modal tracking.

This paper presents a study, which describes the influence of the dynamic behaviour of the intake tower on the experimental results obtained from operational modal analysis of Cabril dam. A 3D finite element model, for the intake tower of Cabril dam, was developed in order to study the dynamic behaviour of this neighbour structure of the dam. The main dynamic parameters computed and evaluated experimentally for this structure are summarized and discussed, to understand how they can interfere in the modal identification of Cabril dam.

The paper aims at presenting some achievements of joint statistics. The different statistical distributions used for the description of the main parameters of the joint sets (attitude, intensity, area, and aperture) are introduced. For the attitude, a comparison of the existing distribution functions is made. For the intensity, the formulas for its determination are given, the applicable statistical models are presented, and the Poisson model for the occurrence of the discontinuities in rocks is discussed in depth. The statistical models for the distribution of the volume of the blocks of a rock mass are introduced. For the area, again, the formulas for its determination are given, and the applicable statistical models presented. Finally, the distribution function for the aperture is referred to, as well as a note on the roughness and waviness.

A libertação do estado de tensão inicial nos maciços rochosos é a principal acção a considerar em escavações subterrâneas. Como o estado de tensão é muito influenciado pela topografia e por condições geológicas particulares de cada local, a sua determinação a partir de ensaios de campo necessita de uma abordagem particular que, tendo em conta a natureza pontual dos ensaios e a sua variabilidade, permita estimar o estado de tensão global no maciço. Apresentam-se os ensaios realizados para o projecto de uma central subterrânea, com destaque para a modelação numérica que permitiu integrar os resultados dos ensaios e determinar o estado de tensão global mais provável. Os modelos usados permitiram considerar no estado de tensão inicial o efeito erosivo do rio ao escavar o vale e da abertura das galerias onde os ensaios foram executados.

This paper deals with issues related to the evaluation of design parameters from some types of in situ and laboratory tests performed, during the geotechnical investigations, to characterize the most relevant geotechnical properties of the rock mass and also the actions. Some considerations regarding safety evaluation and limit state design are presented. Several types of Rock Mechanics tests are introduced in some detail, and a few application examples covering different Rock Engineering projects are presented to show how test results can be analysed to determine their values to be used in the design. The following examples are shown: triaxial tests to determine the strength of the intact rock, a joint network study for a dam foundation, laboratory shear tests to assess the shear strength of rock joints, flat jack and overcoring tests to estimate the in situ state of stress for an underground cavern, and borehole dilatometer and large flat jack tests to evaluate the deformability of a concrete dam foundation.

The paper presents a description of the Picote II site, the objectives of the study that was carried out to assess the in situ state of stress in the rock mass, details of the testing programme and the methodology used for its interpretation. An overcoring testing programme was performed at the design stage, and a specific methodology was developed for the global interpretation of the test results, making use of a numerical model and considering the effect of the existing canyon on the stress field. This enabled to make recommendations regarding the initial stress field to consider in the design of the powerhouse cavern.Owing to the scarce information obtained at the design stage and to the high values of the calculated horizontal stresses, it was decided to perform additional stress measurement tests, using small flat jacks, once construction started and excavation of the adits reached the proximity of the underground powerhouse. Numerical simulations were also done for its interpretation and they confirmed the stress levels obtained at the design stage. The monitoring scheme implemented in the powerhouse cavern includes instrumentation to measure stress changes, which will occur during the excavation. Finally, the significance of the state of stress assessment to the powerhouse design and to the interpretation of monitoring data collected during construction is discussed.

O Aqueduto das Águas Livres, localizado em Lisboa, hoje desactivado, entrou em funcionamento em 1748. Construído em alvenaria de pedra e tendo uma extensão de 14 km desde a nascente principal, é ainda constituído por diversos aquedutos subsidiários e de distribuição,com um total de 58 km de extensão.Num dos muitos canais subterrâneos existentes está localizada uma abóbada que permite a intersecção de dois alinhamento de túneis. Esta abóbada encontra-se sobre uma importante artéria da cidade de Lisboa com um trânsito automóvel bastante intenso.O estado de conservação da abóbada tem suscitado interrogações quanto à sua capacidade resistente, verificando-se recentemente o desprendimento de um bloco de alvenaria e o deslizamento parcial de outros, o que motivou uma medida de segurança imediata que passou pelo total escoramento da estrutura.Procedeu-se a análise estrutural da abóbada de alvenaria através do 3DEC. Esta aplicação baseia-se no Método dos Elementos Discretos (MED) e tem vindo a ser utilizada, com crescente interesse, no estudo das estruturas de alvenaria.O presente artigo aborda alguns aspectos relacionados com o MED, descreve os procedimentos adoptados para execução do modelo e apresenta resultados quanto a capacidade resistente. A parte final é dedicada avaliação dos resultados e apresentação de soluções para a sua reabilitação e reforço.

Neste trabalho apresenta-se um modelo tridimensional de elementos discretos paraanálise do comportamento dinâmico da barragem do Cabril tendo em conta o efeito das juntas decontracção. Os resultados são comparados com os de um modelo de elementos finitostridimensionais na hipótese de continuidade. O estudo da barragem é efectuado para diferentescotas de água na albufeira, simulando-se o efeito das pressões hidrodinâmicas com base nahipótese de massas de água associadas, proposta por Westergaard. A influência do nível da águana resposta dinâmica do conjunto é estudada com base na análise das variações das frequênciaspróprias comparando-se resultados numéricos e experimentais.

Apresentam-se os resultados do estudo, em modelo numérico, do comportamento sísmico da barragem da Chicamba, em Moçambique. Foram realizados cálculos em regime elástico e cálculos não lineares tendo em consideração o comportamento das juntas verticais de contracção das abóbadas. Os resultados da análise permitiram avaliar as condições de segurança da obra para acções sísmicas.

Masonry is a combination of units such as stones, bricks or blocks usually laid in a cementitious or limemortar. It is probably the oldest material used in construction and has proven to be both simple to buildand durable. Over the years, existing masonry constructions have inevitably suffered damage with time.Earthquakes, soil settlements, material degradation and lack of maintenance are the main reasons forthat. Careful and periodic assessment of such structures is necessary in order to evaluate their structuralcapacity and safety levels. However, performing the structural analysis of masonry construction is notan easy task. A review is presented of the main models based on the discrete element method and the available related numerical techniques that have been proposed for the analysis of masonry. The essential assumptions adopted by these models and numerical implementation issues are discussed. Differences between available models are illustrated by applications to various masonry problems including static and dynamic analysis of masonry arch bridges, walls, vaults, domes and ancient colonnades.This book is composed of 17 chapters authored/co-authored by 25 outstanding researchers from 11countries (Canada, France, Greece, Hungary, Iran,Italy, Mexico, Norway, Portugal, UK, USA), whichwere reviewed by 60 referees.

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This chapter consists of two parts. First a general overview is given: the exact definition of the Discrete Element Method is provided, and the main types of existing models are introduced; then the theoretical fundaments of the most important approaches available today for masonry analysis are given. The second part of the chapter focuses on 3DEC, the most widespread commercial DEM code for masonry analysis. This second part begins with a theoretical overview. Application issues for masonry structures are then considered (block material behaviour, contact representation, structural elements like cables or bars etc.). Among the practical examples arches, barrel vaults, walls, coloumns and complete structures (like houses) are presented, including the issues of quasi-static versus dynamic analysis and of block fracture as well. The readers can find helpful advice on how to simulate their own problems most effectively.

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Discrete element models have become a major tool for masonry analysis, allowing a suitable representation of its discontinuous nature and marked nonlinear behaviour. The chapter reviews the fundamental assumptions of the main DEM formulations available. It focuses more specifically on the widely used UDEC and 3DEC codes, explaining their relation with the other approaches, and the most relevant issues arising in their application to masonry. Applications to the main types of structures are reviewed, considering both static and dynamic analyses. Recent research providing comparisons of the numerical models with experimental and field data is particularly covered. The discussion of the different examples is aimed at clarifying the key capabilities of DEM and demonstrating the most effective ways of using it in a variety of masonry analysis situations.

This chapter is focused on the Portuguese experience on the developmentand exploration of systems for continuously monitoring dam vibrations, usingaccelerometers. The pioneer system for seismic and structural health monitoring(SSHM) installed in Cabril dam (the highest Portuguese arch dam: 132 m high) isdescribed in detail. The design of this system was the result of a long-term LNECresearch program, still ongoing. These monitoring systems should include softwaredeveloped to automatically perform the analysis of collected data, including theautomatic comparison with numerical results from 3DFE models. In view of thegood results obtained with the system in operation in Cabril dam since 2008, similarsystems have been installed in other large dams in Portugal, particularly in recentlybuilt dams. Finally, Baixo Sabor dam is presented as an example of a new Portuguesedam with a complete SSHM system, in operation since 2015. Themain experimentalresults obtained for both dams are shown, namely the evolution of natural frequenciesover time, mode shapes and the measured seismic response to earthquake events.

Para verificação do cumprimento das exigências de segurança das barragens,tanto relativamente à funcionalidade (cenários correntes), como em relação àsegurança ao colapso (cenários de rotura), é essencial utilizar modelos de simulação oude interpretação (no caso de obras existentes) do seu comportamento. Estes modelossão idealizações (simplificações) da realidade, tanto no que diz respeito às acções(modelos das acções), como no que respeita à componente estrutural (modelos estruturais).A solução destes modelos, através de adequados métodos de análise, quantificaparâmetros da resposta das estruturas que permitem avaliar a sua segurança, utilizandocritérios de segurança previamente definidos.A validação destes modelos pode ser feita, no caso de cenários correntes,através da sua comparação com os resultados da observação do comportamento debarragens. No caso de cenários de rotura, não existe muita experiência de comparaçãodestes resultados com situações reais: é pequeno o número de acidentes ocorrido e,mesmo nestes, o volume de informação é reduzido. Desta forma, o recurso a métodosexperimentais, para o estudo de cenários de rotura, tem uma importância acrescida.Assim o principal objectivo deste trabalho é contribuir para melhorar a capacidade deavaliação da segurança de barragens de betão envolvendo cenários de rotura pela fundação.Neste trabalho desenvolveram-se dois ensaios experimentais em modelosfísicos: um primeiro envolvendo uma barragem abóbada, para o estudo de cenários derotura da fundação para acções estáticas; e um segundo de uma barragem gravidadeensaiado em mesa sísmica, com vista a estudar a rotura pela fundação para acçõesdinâmicas.A previsão e interpretação dos ensaios foram efectuadas com modelosmatemáticos adequados, que permitiram a sua validação e posterior utilização no estudode outros cenários.

Neste trabalho apresenta-se o sistema para monitorização em contínuo do comportamento dinâmico da barragem do Cabril que foi instalado em 2008, pelo LNEC e pela EDP, referindo alguns dos principais resultados que têm sido obtidos a partir da análise dos dados recolhidos, quer sob excitação ambiente/operacional, quer sob ações sísmicas. Salienta-se a importância do desenvolvimento do software para tratamento, análise e gestão automática dos dados e apresentam-se os programas que têm vindo a ser desenvolvidos no LNEC, em MATLAB, para apoio a este tipo de sistemas, nomeadamente programas de identificação modal (Modal_ID2.0 e Modal_ID_Auto2.0) e programas de elementos finitos tridimensionais para análise do comportamento dinâmico de sistemas barragem-fundação-albufeira (DamDySSA2.0).

This document presents the research plan for the doctoral thesis of LNEC's Junior Research Fellow Margarida Espada. This work, to be submitted to the Faculty of Engineering of the University of Porto (FEUP), will be developed in the Modelling and Rock Mechanics Unit of the Concrete Dams Department, and it is part of the on-going P2I research project DEMRock6m. This work aims at developing more efficient methodologies to perform safety studies and seismic analysis of rock engineering structures, based on discrete element models and in the integrated use of probabilistic models for the geometric and shear strength parameters and for the water pressures in rock discontinuities. This will allow a more realistic definition of the rock mass in discrete element models and an adequate identification of the potential failure mechanisms.

Neste relatório é apresentado o método de Euler para calcular as órbitas do sistema n-corpos,por exemplo, o dos planetas do sistema Solar, tendo em conta a propagação das forçasgravíticas entre o Sol e os planetas e entre os planetas entre si. Apenas requer como dadosiniciais uma observação anterior das órbitas em termos de posição e velocidade. A correcçãoda interacção entre planetas não é suavizada, o que se justifica pelos seus valores. A correcçãorelativista é importante.

As equações de Navier-Stokes são equações de derivadas parciais. As incógnitas nocaso de incompressibilidade consistem no campo de velocidades. As pressões numa 1ªaproximação resultam de um equilíbrio estático.A principal causa de problemas relacionados com a solução destas equações é devida àparcela das acelerações convectivas que está na origem da turbulência.Pesando estas equações e integrando duas vezes por partes obtém-se uma forma fracadestas equações.Em problemas 3D as variáveis independentes são 3 espaciais e 1 temporal. Admite-seque o campo de velocidades pode ser desenvolvido em série de distribuições de Delta deDirac espaciais e suas derivadas com coeficientes funções do tempo. Com funções deteste polinomiais obtém-se a formulação distribucional proposta das equações deNavier-Stokes.

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O objectivo deste relatório é o estudo da matemática aplicada à solução de problemasfísicos de propagação de ondas esféricas com operador espacial biharmónico,consideradas quânticas.As técnicas matemáticas usadas incluem a transformada de Laplace da função de ondaf e o cálculo de sua inversa tal como sugerida por Pipes e Harvill.O método matemático usado para descrever as ondas esféricas quânticas é compequenas adaptações o método causal não-linear descrito por Croca.

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A análise do comportamento de barragens de betão com base em modelos de elementos finitos tridimensionais exige a definição da discretização a adoptar para o conjunto barragem-fundação, ou barragem-fundação-albufeira. A realização desta tarefa sem o recurso a programas de geração automática é muito dispendiosa pelo que tem vindo a ser desenvolvido no NMMF um módulo computacional para geração automática de malhas de elementos finitos tridimensionais especialmente adaptado para a geração de malhas tridimensionais de barragens abóbada. Inicialmente desenvolvido em FORTRAN, o referido módulo computacional para geração de malhas de elementos finitos tridimensionais tem vindo a ser objecto de diversos melhoramentos, os mais recentes centrados ao nível da interface com o utilizador. Assim, apresenta-se neste relatório o módulo computacional

This document presents a back analysis procedure for identification of the elastic parameters of transversely isotropic rock cores, containing an overcoring triaxial strain probe, from the strains measured during a biaxial test. A three-dimensional finite element model was developed to simulate the biaxial test on the overcored rock specimen and to compute the strains at the location of the strain gauges. Different optimisation algorithms were tested and the most suitable one was selected. The back analysis procedure was tested for identification of the five elastic parameters and the two orientation angles that characterise a transversely isotropic rock core. In spite that, with the developed methodology, convergence was reached and all those parameters could be identified, sensitivity analyses demonstrated that the results obtained were not stable and therefore they were not reliable. By introducing constrains based on common practice and previous experience, a stable and robust methodology was achieved: the three elastic parameters, E1, E2 and ?2, are reliably identified using the value of G2 calculated with Saint-Venant’s expression and a fixed value of ?1, while the orientation parameters are obtained from observation of overcored rock. Analysis of the results shows that application of this methodology represents an enormous step forward when compared with the traditional use of isotropy. Besides, the methodology is general and can also be used with other types of overcoring equipment. The five elastic parameters and the two orientation angles obtained can then be used, together with the overcoring strains, to compute the complete in situ state of stress.

This document presents the work developed by the PhD student Margarida Espada in the scope of the course unit Risk Analysis in Geotechnical Works of the Doctoral Program in Civil Engineering of the Faculty of Engineering of the University of Porto (FEUP). This work presents a reliability analysis, using the response surface method (RSM), for the case study of the left bank excavation slopes of the Baihetan arch dam foundation, which is one of the case studies of Margarida Espada's PhD thesis. The aim was to approximate an implicit limit state function by computing safety factors, using a discrete element model of the Baihetan left bank developed in 3DEC software, where the shear strength parameters of two important rock discontinuities were considered as random variables. The probability of failure was then obtained through an iterative process, using approximation methods. This work presents the 3DEC model developed to analyse the stability conditions in the Baihetan left bank and the results of the reliability analysis.

O problema da solução das equações de Navier Stokes é abordado neste trabalhopropondo-se uma técnica de representação das incógnitas deslocamentos e pressõesvariáveis no espaço e no tempo em série de Delta de Dirac e suas derivadas no tempocujos coeficientes se determinam com base na solução de sistemas de equaçõesdiferenciais definidos no espaço (problema com três variáveis espaciais independentesque pode ser estudado pelo método de Monge).

Neste relatório apresentam-se as equações básicas da elastodinâmica linear, as soluçõesfundamentais e o teorema da representação no domínio de tempo e de frequência.Para movimentos finitos de casca formula-se o teorema dos trabalhos virtuais e a suaimplementação pelo método dos elementos finitos.

Neste relatório apresentam-se os principais aspectos da modelação sísmica de barragensabóbada. Assim propõe-se: modelos numéricos de geração de sismos por uma falha; aforma como o sismo actua na barragem; modelos para estudar a influência da albufeirana vibração do conjunto; métodos para solução das equações do movimento; e novasformulações de elementos finitos para o problema estrutural.

In pressure tunnels and shafts, in addition to the mechanical effect that excavation has on the rock mass and the disturbance that it introduces in the water flow, also the contained water can interact from the mechanical and hydraulic points of view with the rock mass. Seepage in fractured rock masses is dominated by the flow that takes place through the joints, and this is highly d(;pendent on their properties, namely aperture and roughness. Joint aperture, in tum, i::; very sensitive to stress changes. Special attention must therefore be paid to the joints in hydromechanical analyses. In this report are presented some studies that were carried out for the hydromechanical characterization of joints of the Alto Lindoso rock mass and numerical simulations of the hydromechanical behaviour of two selected sections of the high pressure circuit.