Publications

A series of very shallowearthquakes occurred in the late afternoon ofMay 11, 2011 near the city ofLorca and 55 kmfromMurcia in Spain. The main shock (Mw5.2) occurred at 17:47 (UTC), causing9 deaths and over 250 injured with widespread damage and panic.The strong motion generated by the event was recorded in the town of Lorca near the epicenter.It was a short duration record with peak ground acceleration higher than 0.37 g. In the vicinity ofthe recorded motion (360 m), there is an obelisk composed of 11 frustums resting on a 1-m-highfoundation with a total height of 5.71 m. The general motion observed after the event was of theorder of 1 cm (translation) for most interfaces, while at the upper two, the motionwas of rotationof 2° to 4° in the counterclockwise direction seen from above.In order to understand the behavior of such a structure, numerical simulations of the obeliskwereperformed with the discrete element code 3DEC, employing a rigid block model. The deformationis assumed to be concentrated at the joints between the blocks, governed in the linear range by thejoint stiffness parameters, in the normal and shear directions. In the nonlinear range, a purelyfrictional behavior is adopted, without tensile strength. An elastic joint was introduced at thebase of the model, simulating the deformability of the foundation. The global model deformabilitywas calibrated by means of in situ dynamic characterization.Dynamic analyses were performed, taking into account the large displacement effects that governthe block rocking motion, applying the recorded seismic motion in the 3 directions. Parametricstudies were undertaken to assess the influence of the various input parameters. The modelresults are compared with the observed permanent displacements of the structure.

It is known that rigid circular particle models proposed in the literature do not properly reproduce therock friction angle and the rock tensile strength to compressive strength ratio. A 2D rigid particle model is herepresented which tries to overcome these issues while keeping the simplicity and the reduced computational costs characteristic of circular particle models. A particle generation algorithm is adopted which generates polygonal shape particles based on the Laguerre

The hydrodynamic interaction between a solid (dam and foundation) and a fluid(reservoir) should be considered whenever the reservoir is present. A fluid displacement-basedformulation is presented, and two fluid elements are proposed: an 8-node fluid cubic elementsub-integrated (F8N-1GP), and an 8-node mixed discretization cubic element formed by twoindependent 5 tetrahedra overlay (F8N-MDE). A forced vibration analysis, and a maximumdesign earthquake equivalent loading, are carried out in two different dams. The performanceof the proposed fluid displacement-based finite elements is compared with the performanceobtained with the degenerated solid (DS) concept, and with the simplified Westergaard addedmass approach. It is shown that the SD approach can lead to erroneous pressure values at thefluid domain, and that the penalty term which prevents circulation modes needs to be consideredwhen less regular meshes are adopted in the fluid discretization.

Apresenta-se a formulação explícita de um modelo hidromecânico em pequenos deslocamentos, baseado numa tecnologia de elementos finitos de junta. O modelo hidromecânico proposto requer um esquema de pré-processamento robusto, de modo a garantir que os contactos entre os diversos blocos que representam o maciço rochoso de fundação e a barragem são somente aresta/aresta. A parte mecânica do modelo, apesar de limitada a pequenos deslocamentos, tem a vantagem de permitir uma representação rigorosa da distribuição de tensões ao longo das juntas. A parte hidráulica do modelo é perfeitamente compatível com a parte mecânica. O modelo hidromecânico é validado recorrendo a uma situação hipotética de uma barragem gravidade fundada num maciço com fraturação regular e a uma situação real de uma barragem em serviço, comparando os resultados com os obtidos com um modelo discreto em grandes deslocamentos. São também comparados os resultados de análises de estabilidade, concluindo-se que é possível avaliar a segurança ao deslizamento de barragens gravidade em betão recorrendo a modelos de interação em pequenos deslocamentos.

A numerical model for analysis of masonry gravity dams based on the Discrete Element Method is presented.The dam and the rock foundation are represented as block assemblies, using elementary 3- and 4-node blocks. Complex block shapes are obtained by assembling the elementary blocks into macroblocks,allowing the model to be applied in various situations ranging from equivalent continuum to fully discontinuumanalysis. A contact formulation was developed, which represents the interaction between macroblocksin terms of contacts established between elementary blocks, based on an accurate edge

The work presents two new numerical techniques devised for modeling propagating material failure, i.e. cracks in fracture mechanics or slip-lines in soil mechanics. The first one is termed crack-path-field technique and is conceived for the identification of the path of those cracks, or slip-lines, represented by strain-localization based solutions of the material failure problem. The second one is termed strain-injection, and consists of a procedure to insert, during specific stages of the simulation and in selected areas of the domain of analysis, goal oriented specific strain fields via mixed finite element formulations. In the approach, a first injection, of elemental constant strain modes (CSM) in quadrilaterals, is used, in combination of the crack-path-field technique, for obtaining reliable information that anticipates the position of the crack-path. Based on this information, in a subsequent stage, a discontinuous displacement mode (DDM) is efficiently injected, ensuring the required continuity of the crack-path across sides of contiguous elements. Combination of both techniques results in an efficient and robust procedure based on the staggered resolution of the crack-path-field and the mechanical failure problems. It provides the classical advantages of the

The underground structures of the Venda NovaII reversible hydroelectric power scheme present features that make it an interesting case study. Worthy of mention are the inclination and length of the unlined pressure tunnel, the high water head and the great depth of the powerhouse cavern. In projects of this type, the main effect ofthe internal water pressure in the pressure tunnel is the establishment of seepage from the tunnel into the rock mass, which can reach the adits and the powerhouse cavern.This seepage is influenced by several factors, such as the geometry of the underground openings, the rock massproperties

Ground vibration is the most important environmental effect of blasting, and tools for its understanding and control are a prime necessity for the excavation of tunnels and caverns in hard ground. This paper contributes to an improved understanding of the way waves travel in the ground, particularly when there are excavations in the path of propagation, while also enhancing existing numerical models to better simulate that behaviour and thus provide better means to address underground vibration impacts. To this purpose, twenty low intensity blast between neighbour tunnels of an underground complex were performed, followed by a numerical study of the test. The test and simulation showed that, contrary to what is implied in semi-empirical attenuation laws, factors like the propagation path or local amplification can be more important than instant explosive weight and distance to blast.

tThis paper presents the development of a three dimensional computational model, based on the DiscreteElement Method (DEM), which was used to investigate the effect of the angle of skew on the load carryingcapacity of twenty-eight different in geometry single span stone masonry arches. Each stone of the archwas represented as a distinct block. Mortar joints were modelled as zero thickness interfaces which canopen and close depending on the magnitude and direction of the stresses applied to them. The variablesinvestigated were the arch span, the span: rise ratio and the skew angle. At each arch, a full width verticalline load was applied incrementally to the extrados at quarter span until collapse. At each load increment,the crack development and vertical deflection profile was recorded. The results compared with similar

Purpose - The rigid spherical particle models proposed in the literature for modeling fracture in rock have some difficulties in reproducing both the observed macroscopic hard rock triaxial failure enveloped and compressive to tensile strength ratio. With the purpose of obtaining a better agreement with the experimental behaviour, a 3D generalized rigid particle contact model based on a multiple contact point formulation is presented which allows moment transmission and includes in a straightforward manner the effect of friction at the contact level.Design/methodology/approach

Ao longo dos últimos anos, têm sido desenvolvidos no LNEC técnicas para a realização deensaios de vibração em barragens de betão inseridos em metodologias de determinação daspropriedades dinâmicas destas obras. Inicialmente o objectivo destes ensaios era apenascontribuir para a avaliação da segurança das barragens de betão relativamente a acçõessísmicas. Mais recentemente, estes ensaios são também encarados como ensaios de carga derealização fácil e económica. De facto, as frequências naturais de cada estrutura dependemdas suas características, em particular, da sua deformabilidade, pelo que a realização destetipo de ensaio, em épocas distintas da vida útil das obras, permite determinar a evolução notempo da sua deformabilidade média e, eventualmente, detectar e quantificar a evolução deum processo de deterioração dos materiais.O ensaio de vibração forçada consiste na aplicação a uma estrutura de uma força com umavariação no tempo sinusoidal perfeitamente conhecida, materializada através de um vibradorde massa excêntrica. Esta acção provoca nas estruturas, em regra, um movimentovibratório forçado com a mesma frequência de variação no tempo da força aplicada (emboradesfasada) e com amplitudes que, para além da intensidade da força, dependem da suafrequência de aplicação e das frequências naturais da estrutura. Tirando partido do facto de severificar um significativo aumento da amplitude da resposta da estrutura quando a frequênciada acção se encontra na vizinhança das frequências naturais da estrutura, a medição daresposta da estrutura sob a acção de uma força com uma variação sinusoidal no tempo,aplicada com diversas frequências, permite identificar as frequências naturais da estrutura(aquelas para as quais se verificarão os picos de amplitude), bem como o respectivoamortecimento.

In this work the finite element implementation of thermal analysis of concrete dams is described. The different temperature boundary conditions are properly represented. For the exposed face of the dam both convection/radiation heat transfer and solar radiation are implemented. The model is validated by calculating the response of a concrete arch dam and comparing the results of the monitoring system values.

Mechanical properties of soft rocks such as marls are strongly affected by suction, directly connected with wetting and dryingcycles resulting from climate actions. An extensive experimental programme was carried out in order to characterize the physicaland mechanical properties of Abadia marls, used in the A10 motorway near Arruda dos Vinhos (Portugal). The experimentalprogramme consisted of laboratory unconfined compression and Brazilian splitting tests, oedometric tests and triaxial tests, all ofthem performed under controlled suction.

Large flat jack tests are used to assess rock mass deformability in the design stages of large projects. This testconsists in cutting a thin slot in the rock mass in which a flat jack with large dimensions is inserted; oil pressure inside thejack loads the slot walls while the rock mass deformation is measured by displacement gauges located inside the jack and atthe surface. The main difficulty regarding interpretation of large flat jack tests has to do with the effect of the tension crackthat may develop in the rock mass during the tests. A three-dimensional numerical model was developed for theinterpretation of large flat jack test results. The model was used to establish the relations between the in situ stressperpendicular to the slots, the rock mass tensile strength, the applied pressures and the crack depth.

Large flat jack tests are one of the field techniques used to assess rock mass deformability. The paper introduces a methodology for interpretation of these tests. A three-dimensional numerical model was developed, which simulates the test with the actually applied loading and allows assessing the evolution of the displacements in the location of the transducers. The depth of the tension crack that may develop in the rock mass during the test is assessed at each test stage. The paper presents the calculations that were performed for simulation of an actual large flat jack test protocol with four loading and unloading cycles.

ABSTRACT: The Distinct Element Method was proposed by Cundall in 1971 as a numerical technique to study rock mechanics problems, based on the representation of a rock mass as a system of blocks or particles. In recent years, the concepts underlying such

A segurança de barragens continua a ser uma preocupação actual da comunidade científica,designadamente pelo elevado risco potencial que em regra é inerente a estas obras e pelanecessidade constante do prolongamento da sua vida útil. Para verificação do cumprimentodas exigências de segurança das barragens, tanto relativamente à funcionalidade (cenárioscorrentes), como em relação à segurança ao colapso (cenários de rotura), é essencial utilizarmodelos de simulação ou de interpretação (no caso de obras existentes) do seucomportamento. Estes modelos são idealizações (simplificações) da realidade, tanto no quediz 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,quantifica parâmetros da resposta das estruturas que permitem avaliar a sua segurança,utilizando critérios de segurança previamente definidos. A validação destes modelos pode serfeita, no caso de cenários correntes, através da sua comparação com os resultados daobservação do comportamento de barragens.Com este objectivo, foi implementado pela primeira vez, um sistema de observação sísmica(SOS), numa grande barragem portuguesa. O SOS tem o duplo objectivo da localização deeventos sísmicos e registo da reposta estrutural da barragem a este tipo de solicitação. Para acaracterização da acção sísmica foram implantadas três estações remotas a formarem umtriângulo com cerca de 15km de lado a montante da barragem, adicionalmente foi instaladauma quarta estação a jusante da barragem (fig. 1). O comportamento estrutural é observadoatravés de cinco sismómetros localizados no corpo da barragem (fig. 2). Todos ossismómetros são compostos por acelerómetros tridimensionais, com digitalizadores de 18 bitsligados em rede, e geridos a partir de uma unidade central. As estações remotas comunicamcom a central de comando por transmissão via wireless. Os sismómetros colocados nabarragem estão ligados por cabo de fibra óptica a uma unidade que concentra os dados paradepois os enviar por wireless para a unidade central.Este sistema está em fase experimental de funcionamento, estando a iniciar-se a exploraçãodos registos gerados pelo sistema.Nesta comunicação será descrito o sistema de observação instalado, a sua exploração e análisedos resultados. Os valores observados provenientes deste sistema serão comparados commodelos matemáticos adequados. O modelo matemático da barragem será desenvolvido comelementos finitos representando a abóbada e as juntas de contracção existentes no protótipo,podendo considerar-se o comportamento não linear do material e das juntas.

The most relevant action in the design of underground projects is often the release of the in situ stresses that occurs during the construction stage. Several different field methods are available to measure the in situ state of stress. Some allow the evaluation of the complete state of stress at a given point, while others only supply a single stress component. Interpretation of test results is seldom straightforward. The paper presents a global methodology for the evaluation of the most likely natural stress field given a set of in situ test results. Some case histories are presented as application examples. The first example deals with the case of an underground powerhouse where high horizontal stresses were determined by overcoring tests, which were later confirmed by flat jack tests performed during the construction of access adits. A second one considers the analysis of a testing programme where overcoring and flat jack tests were both performed at different locations during the initial testing programme. The last one refers to the results of overcoring tests in the vicinity of existing underground caverns, which have to be adequately considered in order to estimate the natural state of stress. Global interpretation models are required to transform a set of point wise test results into a comprehensive stress field to be used in design analysis.

Abstract. Portugal is presently facing a new hydroelectricity era, with theimplementation of a large development program including not only the power upgrade ofexisting large hydro schemes, but also the construction of several new ones, almost all ofthem considered in the

Hard soils/ soft rocks (HSSR) are natural materials where the bonds between particles have important contributionto their strength and stiffness. Progressive rupture of these bonds affects irreversibly the hydro-mechanical behaviorof these materials. Most of the existing models follow the idea that bond degradation depends on accumulatedplastic strains. Such is the case of the model used to describe the mechanical behavior observed in oedometer andisotropic compression tests performed on marls.

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.