Publicações

The Baixo Sabor hydroelectric power plant, located in the northeast of Portugal, includes a reservoir with a storage capacity of 630 million m3 of water created by a concrete double-curvature arch dam, 100 m high, which was equipped with a 20-channel vibration based structural health monitoring system.This paper, apart from describing the dam, presents the main characteristics of the monitoring system and the results obtained during the first 6 months of operation and the first filling of the reservoir. These results include in particular the characterization of the accelerations amplitude and the evolution of the dam modal parameters (natural frequencies, modal damping ratios and mode shapes). It is particular interesting to observe the influence of the water level on the modal parameters and the development of statistical models to mitigate this effect.

Earthquakes cause severe damage to masonry structures due to inertial forces acting in the normaldirection to the plane of the walls. The out-of-plane behavior of masonry walls is complex anddepends on several parameters, such as material and geometric properties of walls, connectionsbetween structural elements, the characteristics of the input motions, among others. Differentanalytical methods and advanced numerical modeling are usually used for evaluating the out-ofplanebehavior of masonry structures. Furthermore, different types of structural analysis can beadopted for this complex behavior, such as limit analysis, pushover, or nonlinear dynamic analysis.Aiming to evaluate the capabilities of different approaches to similar problems, blind predictionswere made using different approaches. For this purpose, two idealized structures were tested on ashaking table and several experts on masonry structures were invited to present blind predictions on theresponse of the structures, aiming at evaluating the available tools for the out-of-plane assessment ofmasonry structures. This article presents the results of the blind test predictions and the comparisonwith the experimental results, namely in terms of formed collapsed mechanisms and control outputs(PGA or maximum displacements), taking into account the selected tools to perform the analysis.

The analysis of the shaking table test of a 3-wall stone masonry structure performed with a discreteelement model is presented. The numerical model, created with the code 3DEC, employed a rigidblock representation and a Mohr-Coulomb joint model. Joint stiffness calibration to match theexperimental natural frequencies is discussed, as well as the boundary conditions to simulate theshake table. Comparisons are made with themeasured displacements at key locations, and themodesof deformation and fracture of the walls. The DEM model was able to reproduce important features ofthe shaking table tests. The experimental deformation and near collapse patterns were clearlyidentifiable in the numerical simulations, which produced displacements within the observed ordersof magnitude, for the various levels of excitation.

This paper 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

The 1:10 scale model of the 15th century Mustafa Pasha Mosque in Skopje, that underwent a comprehensiveshake table program, is modeled by the discrete elements approach. A rigid block model withnonlinear behavior concentrated at the joints was developed and calibrated by comparison with theobserved response. Time domain analyses of the discrete model were performed under the various levelsof dynamic excitation used in the shake table test. Under the lower levels of input, the time and frequencydomain characteristics of the shake table experimental response were fairly well simulated by thenumerical model. This model also predicted well the zones and the level of damages. For the higher inputlevels, the comparison was less satisfactory. Overall, the discrete element approach showed the capabilityto handle the dynamic nonlinear modeling of relatively complex masonry structures.

This work investigates tensile crack propagation in concrete gravity dams by using some recently developed numerical techniques (crack-path field and strain injection techniques). The work carefully addresses aspects related to mesh independence, robustness and computational cost, which are the main issues in fracture modeling. The novel technique consists of a procedure to insert, in the selected domain areas, specific strain fields for enhancing the performance of the underlying finite elements in modeling fracture. Representative numerical simulations of concrete dams show the accuracy and robustness of the methodology.

Block models have been shown to provide a realistic representation of the behavior of many types of masonry structures under static and dynamic loads. When the strength of the units is such that movements along the joints govern the behavior, it is acceptable to make the simplifying assumption that blocks act as rigid bodies. This assumption is particularly useful when dealing with seismic problems, for which the computational times for time domain analysis may be substantial. In this paper, the application of discrete element models for dynamic analysis of masonry structures is addressed. The emphasis is on the seismic behavior of block stone masonry, but the treatment is general to cover other types of masonry. First, the assumptions involved in the choice of a block representation are discussed, stressing in particular the case of rigid block models. Numerical issues are examined, including contact models, calculation of natural frequencies, time stepping algorithms, damping and boundary conditions. A review is presented of modeling examples published in the literature for various types of masonry structures. The choice of numerical representation and its main features are discussed for each case.

Much research in recent years has focused on the seismic analysis of concrete and earthfill dams,and few works have addressed the case of masonry dams. The structural behavior of masonrydams is controlled essentially by its discontinuous nature, which may induce significant nonlinearresponse during an intense earthquake. In this article, a numerical tool based on the Discrete ElementMethod is presented, aimed at the static, dynamic, and hydromechanical analysis of masonry gravitydams. The use of discontinuous models is mandatory for the study of failure mechanisms involvingthe masonry discontinuities, the dam-rock interface or the rock mass joints. The Discrete ElementMethod is able to assemble continuous and discontinuous meshes simultaneously in the same model,providing a versatile tool to consider various assumptions and levels of analysis, ranging from simplifiedto detailed structural representations. A comprehensive study of the seismic behavior of LagoaComprida Dam, located in Portugal, is presented. Both continuous and discontinuous models weredeveloped to assess the main failure mechanisms, including overstress, partial and global sliding,and overturning.

The analysis of the shaking table test of a 3-wall stone masonry structure performed with a discreteelement model is presented. The numerical model, created with the code 3DEC, employed a rigidblock representation and a Mohr-Coulomb joint model. Joint stiffness calibration to match theexperimental natural frequencies is discussed, as well as the boundary conditions to simulate theshake table. Comparisons are made with themeasured displacements at key locations, and themodesof deformation and fracture of the walls. The DEM model was able to reproduce important features ofthe shaking table tests. The experimental deformation and near collapse patterns were clearlyidentifiable in the numerical simulations, which produced displacements within the observed ordersof magnitude, for the various levels of excitation.

A computationally affordable modeling of dynamic fracture phenomena is performed in this study by using strain injectiontechniques and Finite Elements with Embedded strong discontinuities (E-FEM). In the present research, classical strain localizationand strong discontinuity approaches are considered by injecting discontinuous strain and displacement modes in the finite elementformulation without an increase of the total number of degrees of freedom. Following the Continuum Strong DiscontinuityApproach (CSDA), stress

During the last decade, many vibration-based structural health monitoring systems have been successfully implemented in different structures such as bridges, towers, stadia roofs and wind turbines, with the aim of studying the structures dynamics and its evolution over time and even-tually detect the occurrence of novel structural behaviour that may indicate the presence of damage.Such vibration-based monitoring systems generally rely on the identification of modal proper-ties, which are then used as monitoring features. Therefore, from operational modal analysis to the tracking of the said features, many processing steps occur that depend on the accuracy of the identified modal properties in order to produce good results. Thus, the calculation of the uncertainties associated with the identified modal properties may act as an important tool in this process.In this context, data obtained from the continuous dynamic monitoring of a concrete arch dam has been used to test the effect of taking the uncertainties of identified modal properties into consideration when performing operational modal analysis and modal tracking.

A barragem de Pretarouca, no rio Balsemão (serra de Montemuro, concelho de Lamego), tem 29,70 m de altura e 305 m de desenvolvimento. A albufeira tem 3,2 hm3, destinando-se a água a abastecimento público. A obra, construída entre 2007 e 2009, é explorada pela empresa Águas do Norte, do grupo Águas de Portugal, com o apoio do LNEC nos aspetos relacionados com a segurança estrutural.Na comunicação apresentam-se os aspetos relevantes da análise e interpretação do comportamento observado da barragem durante o primeiro enchimento da albufeira, ocorrido em 2009, e o período de exploração subsequente. Na análise estrutural considerou-se um modelo plano do conjunto barragem-fundação, o comportamento viscoelástico dos materiais, a variação das ações da água e as variações térmicas que ocorreram no betão da obra.Os resultados numéricos são comparados com os resultados da observação contínua da obra, apresentando uma boa concordância.

This paper presents the relevant monitoring data and the main results of the analysis and interpretation of the structural behaviour of Bouçoais-Sonim dam, a medium-size gravity concrete dam of 42.5 m high, during the first filling of the reservoir, in March 2005, and the subsequent 10 years of operation.As usual, the dam safety control is performed by considering the data provided by the monitoring system, which is analysed and interpreted with the support of numerical models. These activities are particularly relevant during the first filling of the reservoir, which is a real load testing, and during the first years of operation, when the dam

O Laboratório Nacional de Engenharia Civil (LNEC), desde a sua criação, em 1946, tem dado um apoio significativo ao projeto, à construção e à exploração de barragens de betão e obras subterrâneas associadas, tanto em Portugal como no estrangeiro. Esta atividade tem sido muito diversificada e abrange todas as fases de vida das obras, podendo salientar-se os estudos e atividades relacionados com a caracterização dos maciços rochosos, a definição de formas estruturais e hidráulicas, utilizando modelação física e matemática, a análise estrutural por métodos experimentais e numéricos, a observação do comportamento e o controlo da segurança. No sentido de reduzir a dependência energética de Portugal, nos últimos anos tem vindo a ser aumentada a capacidade de produção hidroelétrica, com o reforço de potência de aproveitamentos existentes e com a construção de novos aproveitamentos. O presente trabalho apresenta os aspetos principais de algumas obras em que o LNEC tem estado envolvido, colaborando com a autoridade nacional, os donos de obra, os projetistas e os construtores. As atividades descritas têm vindo a ser desenvolvidas por uma vasta equipa de especialistas do LNEC, entre os quais se incluem os autores do presente trabalho.

The Baixo Sabor dam, whose construction ended in 2014, is a double curvature concrete arch dam 123 m high, built and owned by EDP Produção (a company of EDP-Energias de Portugal Group) in Sabor river, one of the right side tributaries of the river Douro in the North of Portugal. This structure creates a large reservoir whose first filling took place between 2015 and 2016. The estimate of the modal properties of this structure has been developed on the basis of two alternative procedures: (1) the performance of forced vibration tests based on the use of an eccentric mass vibrator and (2) the implementation of a vibration based structural health monitoring system, involving 20 uniaxial accelerometers, used to observe the dam behaviour during the first filling of the reservoir and the two first years of operation. This paper, apart from making a brief description of the dynamic tests performed, as well as, of the main characteristics of the monitoring system and results obtained during the first months of operation, presents a comparative analysis between the modal estimates achieved by the input-output and output-only modal identification techniques employed using the data associated to the performance of the forced vibration tests.

The Baixo Sabor hydroelectric power plant, located in the northeast of Portugal, includes a reservoir with a storage capacity of 630 million m3 of water created by a concrete double-curvature arch dam, 100 m high, which was equipped with a vibration based structural health monitoring system. This system involves 20 uni-axial accelerometers, 12 of them radially disposed in a gallery close to the dam crest, and the other 8 radially placed along two other galleries. The accelerometers are connected to a set of digitizers distributed in the three instrumented galleries and synchronized by GPS. This paper presents the main characteristics of the monitoring system and the results obtained during the first 18 months of operation, which include the first filling of the reservoir. These results include in particular the characterization of the accelerations amplitude and the evolution of the dam modal parameters (natural frequencies, modal damping ratios and mode shapes), as well as of the influence of the water level and tem-perature on the modal parameters. Suitable statistical models are applied to mitigate those effects in order to obtain time series of natural frequencies suitable for detection of structural changes.

No 14º encontro internacional de modelação numérica em barragens, organizado pela ICOLD, foi proposta a análise numérica de uma barragem de betão em arco localizada na Suécia sujeita a gradientes térmicos significativos ao longo do ano. Nesta comunicação apresentam-se os resultados numéricos obtidos com base numa discretização mais refinada do corpo da barragem, quando comparada com o modelo adotado no encontro internacional.A análise térmica transiente é realizada com um modelo de elementos finitos com condições de fronteira de Dirichlet (betão/água e fundação/água) e condições de fronteira de Robin (betão/ar e fundação/ar). A análise mecânica não linear é realizada numa primeira fase com elementos finitos do tipo cubo de 8 nós tendo por base os gradientes de temperatura obtidos na análise térmica. A armadura existente no paramento de montante e no paramento de jusante é modelada com elementos planos quadrangulares cujos pontos nodais se encontram rigidamente ligados aos elementos de volume tipo cubo. De modo a simular adequadamente o comportamento da ligação da barragem à fundação considerou-se de forma explícita a interface barragem/fundação mediante elementos de junta.Os resultados da análise mecânica realizada com um modelo de fenda discreta, em que se admite que cada elemento finito do tipo cubo adotado na discretização da barragem interage com os elementos vizinhos através de elementos de junta com comportamento não linear em tração e corte, são comparados com as observações in situ. Verifica-se que o modelo estrutural mais refinado permite obter resultados mais próximos dos observados, nomeadamente a distribuição de fendilhação no paramento de jusante e o campo de deslocamentos. Analisa-se ainda o efeito das armaduras distribuídas colocadas junto ao paramento de montante e ao paramento de jusante no controlo de deformação e fendilhação.

Pretende-se com este trabalho estudar o efeito das vibrações provocadas pelas explosões devidas a desmontes no comportamento da barragem de betão e respetiva fundação, avaliando a sua seguran-ça estrutural através de um modelo numérico híbrido descontínuo de elementos discretos e elemen-tos finitos recorrendo ao 3DEC.Apresentam-se os resultados do modelo numérico comparando-o com as medições de velocidades efetuadas no decorrer das obras envolvendo desmontes a fogo, sendo posteriormente analisado os efeitos na barragem. O presente trabalho deu origem ao desenvolvimento de um modelo numérico capaz de representar a resposta da estrutura às vibrações, minimizando a subjetividade da classifica-ção do seu grau de resistência.

O dimensionamento de barragens, de acordo com a regulamentação portuguesa, engloba a verifica-ção da segurança da obra para diversos cenários de rotura. Nesta comunicação, apresenta-se um exemplo de aplicação conjunta de métodos experimentais e numéricos para: i) determinação do coe-ficiente de segurança de uma barragem abóbada num cenário de rotura por deslizamento de parte do maciço de fundação para ações estáticas, ii) o estudo do comportamento dinâmico até à rotura uma barragem de gravidade por deslizamento ao longo da fundação. Os resultados experimentais foram comparados com os obtidos a partir de modelações matemáticas devidamente calibradas.

This paper presents the Hydropower Scheme of Baixo Sabor, a brief description of the tectonic framework scheme area, the studies to predict the seismic actions envisaging the dam

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.