Publications

Modelos detalhados de partículas têm sido adotados na modelação da fratura em materiais quase-frágeis. Neste artigo é adotado um modelo de partículas 2D que tem sido desenvolvido tendo em vista o estudo da fratura em rocha. Os sistemas de partículas são gerados com base num algoritmo de geração de partículas poligonais baseado nos Voronois de Laguerre da triangulação de Delaunay dos centros de gravidade das partículas circulares. O modelo de partículas poligonais, aproximado através de partículas circulares que interagem entre si através de um esquema de contacto múltiplo, é validado em ensaios biaxiais, e em ensaios do tipo Brasileiro, em rocha. São apresentados vários estudos paramétricos que permitem identificar a influência dos parâmetros micromecânicos nas propriedades macroscópicas, elásticas e resistentes. É por fim analisada a relevância de um modelo de contacto com leis de enfraquecimento bilinear em tração e corte de modo a obter valores coerentes de tração última nos ensaios diretos e nos ensaios Brasileiros.

A convenient approach to performing stability analysis of concrete gravity dams is the so-called twodimensional

A relevant parameter for estimating discontinuity shear strength is the basic friction angle, usually derived from different types of tilt tests. However, the tilt tests described in the literature produce varying basic friction angle values. From a large number of different types of tilt tests on different kinds of rocks, it was possible to conclude that the mechanisms of sliding along cylinder generatrixes and planar surfaces are quite different, andthat tests based on sliding along generatrixes are not appropriate for determining reliable basic friction anglevalues for discontinuity planes. Tests on small specimens are also not recommended, for geometry reasons and because ensuring reliable stress conditions is difficult. Toquantify the natural variability in tilt testing, large specimens of the same granite were tested. The results revealed coefficients of variation for the basic friction angle in the range of 5

The significant advances in masonry dam design that took place in the second half of the19th century are analyzed and discussed within the context of the historical developmentof dam construction. Particular reference is made to the gravity dam profiles proposed bySazilly, Delocre, and Rankine, who pioneered the application of engineering concepts to damdesign, basing the dam profile on the allowable stresses for the conditions of empty and fullreservoir. These historical profiles are analyzed taking into consideration the present safetyassessment procedures, by means of a numerical application developed for this purpose,based on limit analysis equilibrium methods, which considers the sliding failure mechanisms,the most critical for these structures. The study underlines the key role of upliftpressures, that was only addressed by Lévy after the accident of Bouzey Dam, and providesa critical understanding of the original design concepts, which is essential for therehabilitation of these historical structures.

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The work focuses on the connections of strain localization modeling of material failure and discrete fracture mechanics. It is an attempt to give an answer to the old question of whether the finite element solutions of material failure problems based on strain localization techniques, using standard continuum stress

In concrete arch dam foundations, potential failure mechanisms are typically defined by natural rock discontinuities or the concrete-rock interface. Discrete element models are particularly adequate for the safety assessment of these failure scenarios, given their ability to represent the geologic structure of the rock mass, as well as the concrete cantilevers. Application of these procedures to 2 large dams presently under construction in Portugal, Baixo Sabor and Alto Ceira arch dams, is presented. The numerical models represent the foundation rock mass as a system of deformable blocks defined by the main faults and joint sets identified at the site. The safety analysis is performed by progressive reduction of strength along the discontinuities until the failure condition is reached.

The goal of this paper is to simulate the interaction of stress waves and rock fractures in a particle micromechanical model. Stress waves travelling in fractured rock masses are slowed down and attenuated by natural heterogeneities, voids, microcracks and, above all, by faults and fractures. Considerable laboratory and theoretical investigation have uncovered the major aspects of this phenomenon, but models that cover the core mechanisms of the wave propagation in rock masses are necessary to investigate aspects of wave

O método dos elementos discretos adoptando partículas para discretização dodomínio tem sido utilizado no estudo do fenómeno da fractura em meios nãohomogéneos, como o betão e a rocha. Neste artigo, é proposto um modelo de análisepara o betão armado no qual as armaduras são modeladas com elementos rígidosunidimensionais ligados por molas. Os elementos rígidos interagem com o betão,modelado por partículas circulares, através de uma interface de contacto. O modelo évalidado com base em ensaios de flexão em viga a três pontos e a quatro pontos,sem armaduras de esforço transverso. No ensaio de flexão a 3 pontos o modelo dáuma boa aproximação do comportamento real em termos do processo de evolução dafractura e da relação carga-deslocamento. No ensaio de flexão a 4 pontos, verifica-seuma boa correlação com os resultados experimentais, nomeadamente o valor dacarga última, o efeito de escala e a evolução do processo de fractura.

The overcoring method for measuring in situ stresses is frequently used in rock engineering projects. Most models for its interpretation assume that the rock is homogeneous, linear elastic and isotropic. The elastic constants are determined by various methods, namely by biaxial tests on the recovered core.A three-dimensional finite element model was developed, which allows to compute the stress state from the strain measurements obtained during overcoring, assuming a transversely-isotropic behaviour of the rock mass. Different testing methodologies for elastic constants determination of anisotropic rocks are introduced and discussed. Several numerical tests were performed to analyse the influence of the weakness planes that sometimes occur in the rock core owing to the tensile strains that are generated during the biaxial test. To avoid the tensile strains in the biaxial test, a new triaxial testing procedure of the overcored rock sample with the cell was developed. The effect of the degree of rock anisotropy on in situ stress determination and the error involved in neglecting rock anisotropy are analysed. Differences on the principal stresses and principal directions calculated considering the usual isotropic model and the developed numerical model for a real case of anisotropic rock are presented.

A determinação da resposta dinâmica das obras e o acompanhamento da evolução do seu comportamento durante as várias fases da vida é muito importante, estando inserido nas atividades do controle de segurança estrutural. A realização de ensaios de vibração forçada em barragens de betão para a determinação do comportamento dinâmico continua a ser uma das técnicas mais fiáveis nesta área. Nesta comunicação descreve-se a metodologia de ensaio, e apresentam-se os resultados relativos a um caso de estudo, referente à caraterização do comportamento dinâmico da barragem do Baixo Sabor. Foi desenvolvido um modelo numérico, com representação do sistema barragem-albufeira-fundação, para apoio na preparação do ensaio e interpretação dos resultados experimentais.

Os trabalhos de escavação para a implantação de grandes obras, (barragens, centrais subterrâneas, tuneis, etc.) utilizam frequentemente metodologias de desmonte da rocha com recurso a explosivos. Esta técnica sendo rápida e eficientemente produtiva, obriga ao controle da propagação de vibrações no meio circundante com ênfase ao parque edificado e respetivas infraestruturas.Recentemente foram efetuadas obras de aumento da capacidade de descarga de uma barragem de betão, nas quais, foi necessário efetuar desmonte de rocha com o recurso a explosivos nas imediações da barragem existente.Estes pressupostos impulsionaram ao desenvolvido de um modelo numérico híbrido descontínuo de elementos discretos e elementos finitos recorrendo ao 3DEC, representando os blocos da abóbada, as juntas de contração e o maciço de fundação. O objetivo deste modelo é estudar o efeito das vibrações provocadas pelas explosões no comportamento da barragem de betão e respetiva fundação, avaliando a sua segurança estrutural. A correta modelação do comportamento da fundação é fundamental para uma avaliação estrutural adequada.No presente trabalho apresentam-se os resultados do modelo numérico comparando com as medições de velocidades efetuadas em vários pontos da fundação e da estrutura no decorrer das obras, sendo posteriormente analisado os efeitos na barragem. O presente trabalho, deu início ao desenvolvimento de um modelo numérico capaz de representar a resposta da estrutura às vibrações, minimizando a subjetividade da classificação do seu grau de resistência.A elaboração deste modelo numérico permitiu desenvolver novas abordagens para a simulação das explosões, da propagação ao longo do maciço e respetivos efeitos na estrutura. Estas abordagens, devidamente adaptadas, são passiveis de serem implementadas em estudos futuros.

. The nowadays-available dynamic monitoring equipment integrating very sensitive low noise sensors creates an opportunity to implement continuously operating dynamic monitoring systems in dams and validate the suitability of these systems to monitor such massive structures with the goal of detecting damage. The detection of abnormal structural behaviour, that may indicate the occurrence of damage, can be based on control charts and is associated with shifts in the modal parameters values that are not explained by other physical phenomena but a change in the structure

In this paper the seismic response of a large arch dam (290 m high), located in a high seismicity region, is analysed. The goal is to study the influence of the reservoir water level in the dam

A determinação da resposta dinâmica das obras e o acompanhamento da evolução do seu comportamento durante as várias fases da vida é muito importante, estando inserido nas atividades do controle de segurança estrutural. A realização de ensaios de vibração forçada em barragens de betão para a determinação do comportamento dinâmico continua a ser uma das técnicas mais fiáveis nesta área. Nesta comunicação descreve-se a metodologia de ensaio, e apresentam-se os resultados relativos a um caso de estudo, referente à caraterização do comportamento dinâmico da barragem do Baixo Sabor. Foi desenvolvido um modelo numérico, com representação do sistema barragem-albufeira-fundação, para apoio na preparação do ensaio e interpretação dos resultados experimentais.

This paper presents the application of a fluid displacement based formulation for the modelling of dynamic dam-reservoir interactions. This approach requires the introduction of a constraint penalty term multiplier that should be as high as necessary to enforce rotational constraint, but small enough to avoid numerical ill-conditioning and overly stiff responses. A maximum design earthquake and a forced vibration numericalanalyses of an arch dam are carried out. The performance of two different displacement based finite elements are compared against each other and against known forced vibration experimental results on an arch dam, for a given reservoir level. The influence of the penalty term, of the free surface motion and of the type of finite element are assessed.

The 166 m high Cahora Bassa arch dam, built in the Zambezi River in Mozambique more than 40 years ago, is undergoing a process of swelling reactions of the concrete, which has been accompanied since it was detected in its early stages. Several measures were imple-mented, namely the upgrade of the monitoring system and the use of numerical models for analysis of the dam

The safety evaluation of concrete arch dams requires validated numerical procedures capable of representing the dynamic interaction between the dam and the reservoir during a seismic event. The proposed numerical model employs a discrete element formulation, which is ulti-mately intended to represent the potential dynamic slip of discontinuities in the rock mass foun-dation. The present paper focuses on the dam-water interaction modelling, which is a key com-ponent of the dynamic response of concrete arch dams. A fluid element discretization of the res-ervoir domain was adopted, based on Cundall's mixed discretization technique, which provides a displacement formulation for time domain analysis. Simple validation tests confirmed the ac-curacy of the solution. The model was also applied to a case study involving a recently built arch dam in Northern Portugal. In situ measurements of the dam dynamic response were made by two methods: forced vibration tests, performed before and after filling the reservoir, and a continuous monitoring systems installed in the structure. These measurements provided exten-sive data that allowed the dynamic characterization of the concrete arch structure and the vali-dation of the numerical model.

The safety control of dams under operation is based on the comparison between observed data, from monitoring systems, and numerical data from mathematical models developed to simulate/predict the dam behaviour over time. For the direct analysis of observed data semi-statistical models for effects separation are usually adopted, namely of the type HST or HSCT. For dam behaviour simulation/prediction Finite Element Method (FEM) models, based on the fundamental equations of structural mechanics, are mostly used.In order to detect the abnormal behaviour derived from the pathological effects, e.g. concrete swelling effects, it is necessary to use a robust HSCT model capable of distinguishing normal time effects, related with viscoelasticity, from other time effects, e.g., related with concrete swelling. In this paper, a hybrid HSCT-FEM model is proposed, and it is applied to the case of Aguieira dam.

The concrete gravity dam proposed for the 15th International Benchmark Workshop on Numerical Analysis of dams (Theme A) was numerically studied using computational finite element modules developed by the authors for dam analysis. The computational models allow non-reflecting boundary conditions, free-field boundary conditions, fluid structure interaction following a Lagrangian displacement based formulation for the fluid and nonlinear material behaviour, both continuum damage and discrete crack approaches. The seismic analysis is carried out using a central difference method, a Newmark implicit integration scheme can be adopted for other types of loading. The computational modules have been used in the assessment of the behaviour of several operating dams. The natural frequencies and force vibration analysis (Case A), the seismic analysis for various reservoir levels following a linear elastic model (Case D) and non-linear seismic type analysis including nonlinear behaviour (Case E) are assessed and discussed using both 2D and 3D modules.

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 relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto DEMRock6m do P2I/LNEC 2013-2020. Os resultados da atividade desenvolvida são analisados e avaliados em face dos objetivos inicialmente previstos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto MEBAD do P2I/LNEC 2013-2020, no período 2016-2023. Os resultados da atividade são analisados e avaliados, em face dos objetivos previstos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto RockGeoStat do P2I/LNEC 2013-2020. Os resultados da atividade desenvolvida são analisados e avaliados em face dos objetivos inicialmente previstos.

The main goal of this report is to present DamDamage3D1.0, a 3D finite element-based program for non-linear static analysis of arch dams, developed using MATLAB. The non-linear simulations are performed using a damage law and an iterative numerical method based on the stress-transfer technique, considering the redistribution of unbalanced forces in each iteration due to material damage. The concrete

The main goal of this report is to present DamDamage3D1.0, a 3D finite element-based program for non-linear static analysis of arch dams, developed using MATLAB. The non-linear simulations are performed using a damage law and an iterative numerical method based on the stress-transfer technique, considering the redistribution of unbalanced forces in each iteration due to material damage. The concrete

In this work we present the version 1.0 of the GDams2D 1.0 program developed for 2D analysis of gravity dams using the finite element method. This initial version of the program is prepared to analyze the structural behavior of gravity dams for static loads, considering linear-elastic behavior, and using Lagrange finite elements of 4 sides, with 9 nodal points. The GDams2D 1.0 program, developed in MATLAB, includes a module for automatic generation of meshes with a great level of refinement (generated from coarse meshes of quadrilaterals, with 4 nodal points at the vertices) and is designed for easy adaptation to non-linear analyzes, using stress-transfer modules such as those recently developed for the DamSlide3D and DamDamage3D programs. After a brief reference to the fundamentals of solid mechanics and to the simplified hypotheses of plane elasticity, the Fundamentals of the Finite Element Method (FEM) are presented, referring in particular the formulation of the four-node, linear and isoparametric, finite element (FE4nos), with two translation d.o.f per node, and the quadrangular FEs of 9 nodes (FE9nos) used in GDams2D 1.0. Based on some examples of application to simple 2D structures whose response is knownanalytically, the advantages of FEs are emphasized in relation to FE4nos and the verification and operability of GDams2D 1.0 is made using various discretizations. Finally, the case of a gravity dam (25 m high) is presented. The dam

The main objective of this work is the development and presentation of a three-dimensional finite element program, DamSlide3D, to study the behavior of gravity dams for scenarios of sliding through the dam-foundation interface. The DamSlide3D, developed using MATLAB, includes cube-type finite elements with 20 nodal points ("serendipity") and finite interface elements with 16 nodal points (joint elements). Initially, we present the fundamental equations of Solid Mechanics, referring to the main simplified hypotheses considered in the computationally implemented formulation, which is presented mathematically as a problem of boundary values using a displacement formulation. For the structure body and for the foundation, the hypothesis of isotropic materials with linear elastic behavior is assumed and for the interfaces the hypothesis of non-linear behavior is considered using the Mohr- Coulomb criterion. The DamSlide3D input data is provided in an excel file and includes structure geometry data, material properties, support conditions and load parameters. As output, the program graphically displays the stress field (principal stresses) and the displacement field (deformed structure). The program was verified throughout three numerical tests with known theoretical solutions. In these tests a simple structure was used, composed by a column discretized in 3DFE. At the contact surface between the column and the base (horizontal surface) it was considered an interface discretized using joint finite elements. A plane surface that crosses the column with a given slope is also considered, discretized using the same type of joint finite elements. In the first test, the field of elastic stresses at the base, due to self-weight (SW) and hydrostatic pressure (HP), was compared with the theoretical results. In the second test the nonlinear column response was studied for different values of thefriction angle at the inclined interface (in this test the structure is only submitted to SW). In the third test, for the main SW + HP loads, the stability of the column is studied for a variation of the friction angle, and for a variation of the water level. In these three numerical tests the results were always consistent with the theoretical solutions. Finally, as an example of application, a gravity dam structural behavior was analyzed considering the non-linear behavior in the dam-foundation interface. The dam was subjected to self-weight and hydrostatic pressure. A parametric study was developed in order to study the dam stability for differentvalues of water level and friction angle.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto CoMatFail até ao final de 2017. É feita a apreciação da atividade desenvolvida, nomeadamente quanto ao grau de cumprimento do plano de trabalhos, bem como dos objetivos específicos e dos indicadores de desempenho propostos na ficha de projeto. São ainda referidas as aplicações dos resultados da investigação em trabalhos contratados ao LNEC e as candidaturas a financiamento externo desenvolvidas no âmbito do projeto. Inclui-se em anexo a ficha do projeto atualizada, que contempla a revisão do plano de trabalhos.

Neste relatório apresenta-se de forma sucinta a descrição da atividade de investigação realizada no âmbito do projeto DEMRock6m no período 2016-2017. Os resultados da atividade são analisados e avaliados em face dos objetivos inicialmente previstos, sendo proposta uma revisão do plano de atividades para os próximos três anos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto RockGeoStat no período 2016-2017. Os resultados da atividade são analisados e avaliados em face dos objetivos inicialmente previstos, sendo proposto um prolongamento do projeto até ao final de 2018.

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.