Publicações

This study highlights the continued need for numerical simulation methods to predict the earthquakeresponse and damage of masonry mosques, despite recent advances in research. TheKamanl

Circular/spherical rigid particle models that were initially applied to rock fracture studieswere not able to match the ratio of the compressive strength to tensile strength that occurs in rock.In addition, the predicted macroscopic friction angle was much lower than the known hard rockexperimental values. Several enhancements have been proposed to address these issues, namelythe use of a clumped particle logic or the adoption of polygonal/polyhedral grain structures, eitherrigid or flexible. In this work, a flexible 2D DEM based particle model (PM) that allows deformableparticles to interact in a simplified way is presented. The proposed flexible PM model keeps thecontact interaction simplicity and the reduced computational costs characteristic of circular rigidparticle models. The PM model is tested using biaxial tests and Brazilian tests. A discussion re-garding the influence of the grain deformability on the macroscopic elastic and strength response ispresented. It is shown that, when compared with a rigid model, the proposed flexible PM modelpredicts more reasonable indirect tensile strength to direct tensile strength ratio and requires asmaller value of contact fracture energy to give a good agreement with known experimental data.It is also shown that the proposed flexible PM model can predict a behaviour similar to that ob-tained using a flexible PM model through inner particle discretization that is more computationallydemanding.

Circular and spherical particle models are a class of discrete elements (DEM) that have been in-creasingly applied to fracture studies of quasi-brittle materials, such as rock and concrete, due to their proven ability to simulate fracture processes through random particle assemblies repre-senting quasi-brittle materials at the grain scale. More recently, DEM models have been applied to old stone masonry fracture studies. In order to extend its applicability to structures of larger di-mensions, an enhanced hybrid particle model is here proposed that allows finite elements with a given surface roughness, provided by the discretization of the element boundary with particles, to interact with the particulate media in which they are embedded. The performance of the hybrid model is compared with that of a traditional all-particle model under uniaxial testing. It is shown that similar results are obtained, namely in the elastic phase, figures of rupture, pre-peak and post-peak behaviour, while the hybrid model allows a significant computational run time re-duction of 20% to 25% in the coarse particle assemblies. Finally, the proposed hybrid model is applied in the simulation of shear tests of stone masonry walls, dry and mortared joints, providing a reasonably good agreement with both experimental results and predictions. For the rubble masonry tests, the hybrid model allows a computation run time reduction of around 40%, when compared with an all-particle model.

Discrete element models are widely used in the analysis of masonrystructures, as they provide an effective approximation of the observedbehaviour, namely for modelling collapse modes governed by thediscontinuities. Assessment of the response under earthquakes is an importantapplication of these models, which perform time domain dynamic analysisusing explicit algorithms. Rayleigh damping is generally used, but itsmass-proportional component has potential adverse effects, and the small stepsrequired by explicit solutions lead to large computational costs. An alternativedamping formulation employing Maxwell elements in parallel with the jointstiffness is proposed and tested. Problems involving linear elastic analysis ofcolumn bending, rocking of rigid blocks, and out-of-plane failure of masonrywalls under seismic loading are examined. The proposed damping approachdisplayed a sound mechanical performance and is computationally efficient.These early results justify further investigation of the technique for a broaderapplication in masonry structural dynamics.

This research explores the mechanical behavior of dry-joint masonry subjected to combined shear

Concrete gravity dams are mass concrete structures, often built on rock mass foundations, conceived to rely upon their weight for stability. To prevent sliding, these structures are usually keyed/embedded into the foundation, a good construction practice particularly relevant in medium to high intensity seismic zones. In stability analysis, the extra strength obtained by keying the dam into the foundation is usually either neglected or taken as a passive resistance, which, such as explored in this paper, do not reflect the real structural response in pre-collapse situations. Limit state philosophy requires the ultimate equilibrium conditions to be expressed as accurately as possible. In this paper, the rigid-body equilibrium of a wedgy model representing the dam and a downstream rock wedge is analyzed according to the large displacement regime. Failure mechanisms were identified, analytically described and numerically validated. Application to two Portuguese large concrete gravity dams led to safety factors considerably larger than those computed assuming the usual practice. The proposed approach is intended to support probabilistic and/or semi-probabilistic methodologies for safety assessment of concrete gravity dams, in the design and feasibility phases, in which the limit state approach is inherently followed.

Concrete gravity dams are mass concrete structures, often built on rock mass foundations, conceived to rely upon their weight for stability. To prevent sliding, these structures are usually keyed/embedded into the foundation, a good construction practice particularly relevant in medium to high intensity seismic zones. In stability analysis, the extra strength obtained by keying the dam into the foundation is usually either neglected or taken as a passive resistance, which, such as explored in this paper, do not reflect the real structural response in pre-collapse situations. Limit state philosophy requires the ultimate equilibrium conditions to be expressed as accurately as possible. In this paper, the rigid-body equilibrium of a wedgy model representing the dam and a downstream rock wedge is analyzed according to the large displacement regime. Failure mechanisms were identified, analytically described and numerically validated. Application to two Portuguese large concrete gravity dams led to safety factors considerably larger than those computed assuming the usual practice. The proposed approach is intended to support probabilistic and/or semi-probabilistic methodologies for safety assessment of concrete gravity dams, in the design and feasibility phases, in which the limit state approach is inherently followed.

A detailed modelling approach to represent masonry at the meso-scale is proposed, basedon the discrete element method, considering the nonlinear behavior of the joints and the units. Thefracture of units is represented by the bonded-block concept, in which a random network of potentialcracks is created, allowing the progressive development of failure mechanisms. For simplicity, onlythe 2D case is presented, but the extension to 3D is straightforward. A key component of the proposedmodel is a framework for a joint or interface constitutive model, including the post-peak softeningrange, taking into account the experimental fracture energies. In this model, the softening curves intension or shear are defined by piecewise linear segments, calibrated to reproduce the most commonmasonry constitutive models. The essential issues involved in the application of bonded-blockmodels to masonry are examined, namely the block shape, either Voronoi polygons or triangles; size;deformability; and the influence of the main constitutive parameters. Uniaxial compression tests areanalyzed in detail. The simulation of a well-known experiment of a brick panel under shear showsthe good performance of the proposed approach. The investigation results demonstrate the model

To predict the structural behaviour of ancient stone masonry walls is still a challenging taskdue to their strong heterogeneity. A rubble-stone masonry modeling methodology using a 2D particlemodel (2D-PM), based on the discrete element method is proposed given its ability to predict crackpropagation by taking directly into account the material structure at the grain scale. Rubble-stone(ancient) masonry walls tested experimentally under uniaxial compression loading conditions arenumerically evaluated. The stone masonry numerical models are generated from a close mappingprocess of the stone units and of the mortar surfaces. A calibration procedure for the stone-stoneand mortar-mortar contacts based on experimental data is presented. The numerical studies showthat the 2D-PM wall models can predict the formation and propagation of cracks, the initial stiffnessand the maximum load obtained experimentally in traditional stone masonry walls. To reducethe simulation times, it is shown that the wall lateral numerical model adopting a coarser mortardiscretization is a viable option for these walls. The mortar behaviour under compression with lateralconfinement is identified as an important micro-parameter, that influences the peak strength and theductility of rubble-masonry walls under uniaxial loading.

This paper is focused on the study of the dynamic behaviour of two large arch dams, and it presents some innovations for the improvement of Seismic and Structural Health Monitoring (SSHM) systems for dams. The work describes a methodology based on the integrated use of software for automatic monitoring data analysis and of computational 3D finite element (3DFE) models for dam dynamic behaviour simulation. The monitoring data analysis software was developed for automatic modal identification, in order to obtain natural frequencies and mode shapes, for automatic detection of vibrations induced by seismic events, to be distinguished from those caused by other operational sources, and for comparison between results retrieved from measured vibrations and numerical results from 3DFE modelling. The numerical simulations are carried out using a 3DFE program developed for dynamic analysis of dam-reservoir-foundation systems, based on a solid–fluid coupled formulation and considering the dam-water dynamic interaction, including calculation modules for complex modal analysis and for linear and non-linear seismic analysis. The case studies are two large arch dams that have been under continuous dynamic monitoring over the last ten years: Cabril dam (132 m high), the highest dam in Portugal, and Cahora Bassa dam (170 m high), in Mozambique, one of the highest dams in Africa. The SSHM systems installed in both dams have similar schemes and were designed to continuously record accelerations in several locations at the upper part of the dam body and near the dam-foundation interface, using uniaxial and triaxial accelerometers. The most significant experimental results from continuous dynamic monitoring are presented and compared with numerical results for both dams, with emphasis on the evolution of natural frequencies over time, including the vibration mode shapes for various water levels, and on the measured accelerations during low-intensity seismic events. Furthermore, the main results of non-linear seismic response simulations are provided, considering the effects due to joint movements and tensile and compressive concrete damage, aiming to assess the seismic performance of both dams based on the Endurance Time Analysis method.

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

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

This work presents a numerical application for stability analysis of masonry gravity dams. From the geometrical dimensions, the material characteristics, hydrostatic loads and seismic loads, the application automatically determines the following results: thrust line for the dead weight load and the dead weight together with the other loads; stress diagram and safety factors for the failure of the dam-foundation contact as part of an overall analysis; safety factors for the failure of horizontal planes along the body of the dam; parametric properties analysis (volumetric mass) and the resistant characteristics (friction angle) on the base of the dam.The analyses of three historical masonry dams located in Algeria were made. This work highlights the capacity of the numerical application as it can work with different section geometry, including curved and discontinuous sections, and the importance of assessing several scenarios in the scope of a preliminary and expedite safety evaluation.

A análise de cenários de ruptura, estático e dinâmicos, associados à fendilhação do betão requer ferramentas computacionais que sejam capazes de lidar com o comportamento resultante da micro-fendilhação generalizada e/ou de macro-fendas. É reconhecida a dificuldade de caracterizar tal problema com base numa formulação contínua local. Assim, neste trabalho optou-se por um modelo detalhado de partículas, inicialmente desenvolvidos para estudo do comportamento micro-mecânico de meios granulares, que têm em consideração a interacção física entre as partículas e a influência da meso-estrutura do material. Dada a escala em análise, o modelo de análise detalhada só é aplicado na zona em que se espera que ocorra fendilhação para os cenários estudados, barragem. Na zona de fundação é utilizado um modelo de elementos finitos. Dado os recursos computacionais existentes é necessário adoptar para as partículas esféricas dimensões superiores às dimensões do agregado adoptado. O modelo é validado com base em ensaios experimentais realizados em modelos no núcleo de modelação matemática e fisica do departamento de barragens do Laboratório Nacional de Engenharia Civil.

Abordam-se, neste trabalho, os aspectos gerais da modelação numérica do comportamento de maciços rochosos, com particular incidência na sua aplicação ao estudo de grandes obras subterrâneas. Apresentam-se sucintamente os principais métodos e a sua evolução, com referência a alguns trabalhos realizados no país. Discutem-se as potencialidades actuais dos modelos numéricos, e algumas das questões que se colocam na sua aplicação prática, recorrendo a diversos exemplos recentes no domínio das obras subterrâneas.

O método de sobrecarotagem é frequentemente utilizado para a determinação do estado de tensão em maciços rochosos. Nesta técnica de ensaio, a determinação do estado de tensão é feita partir das extensões medidas durante a sobrecarotagem e das constantes elásticas do tarolo que são determinadas, em regra, a partir dos resultados de um ensaio biaxial. Foi desenvolvido um modelo tridimensional de elementos finitos que permite considerar um comportamento tanto isotrópico como transverso isotrópico para a determinação do estado de tensão. Foram realizadas diversas simulações numéricas do ensaio biaxial para avaliar a influência de microfissuras normais ao eixo dos tarolos na determinação das constantes elásticas. O modelo foi também utilizado para analisar a influência da consideração da anisotropia na determinação do estado de tensão em maciços rochosos.

O comportamento resultante da micro-fendilhação generalizada e/ou da presença de macro-fendas é dificilmente caracterizado a partir de uma formulação contínua. Por este motivo, na modelação da fractura em geo-materiais têm sido propostos modelos detalhados de partículas, inicialmente desenvolvidos para estudo do comportamento micro-mecânico de meios granulares, que têm em consideração a interacção física entre as partículas e a influência da estrutura granular do material. Neste trabalho, é apresentado um modelo de partículas rígidas esféricas que tem sido desenvolvido tendo em vista o estudo da fractura no betão e em rocha. O modelo é validado em ensaios triaxiais, e em ensaios de compressão diametral, em rocha, sendo estudada a influência do modelo constitutivo do contacto.

The safety control of large dams under static and dynamic loads, involving observation data and numerical modeling, is now one of the challenges of structural engineering. The complexity of the dam-reservoir-foundation geometry, the presence of different types of discontinuities, the water-structure interaction, the influence of thermal and water level variations, the development of deterioration processes over time and the occurrence of exceptional events such as major floods or earthquakes, makes the structural safety control of large dams an activity that requires a continuous updating, both in terms of the equipment for measuring, transmission, and storage of the observation data, and in terms of computer applications to support the automation process of collecting, processing, analysis and management of all information required to the safety control. The recent LNEC and EDP experience on the revision of the monitoring system of Cabril dam, the highest portuguese arch dam, is presented as a case study in this paper. After a brief presentation of the main dam characteristics

Esta comunicação descreve um trabalho de monitorização e estudo da geração e propagação das vibrações produzidas por uma operação subaquática de desmonte de rocha que teve lugar no Porto de Leixões em 2006. Terminada a monitorização, que exigiu um acompanhamento cuidado dos impactos dos rebentamentos na malha urbana circundante, definiram-se leis empíricas de atenuação e um modelo de inteligência artificial (redes neuronais perceptrão multicamada) que forneceram estimativas da velocidade máxima de vibração em função da carga e da distância. Estes métodos tornaram possível a definição de distribuições espaciais de vibração para todo o desenrolar da obra. Finalmente, desenvolveu-se um modelo dinâmico de diferenças-finitas tridimensional de parte da obra, no qual foram estudados diversos cenários de geração e propagação. Este modelo permitiu, por uma lado extrair conclusões qualitativas interessantes sobre a propagação da vibração deste caso, e por outro comprovar a aplicabilidade da modelação numérica nesta classe de problemas, tanto em obras superficiais como em obras subterrâneas, tais como a escavação de túneis e cavernas em rocha.

A aplicação de modelos de identificação modal na análise de resultados de ensaios de vibração ambiental efectuados na barragem do Cabril (a maior barragem portuguesa - abóbada simples com 132 m de altura) mostrou a ocorrência de picos espectrais importantes, cuja frequência não correspondia às conhecidas frequências naturais da obra, tendo-se colocado a hipótese desses picos estarem relacionados com o comportamento dinâmico da torre das tomadas de água

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.

N/A

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.

N/A

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.

A brief description of the phenomena and problems associated with underground structures in hydraulic projects is presented, namely in what concerns the powerhouses, surge chambers and pressure tunnels and shafts. An analysis of the calculation methodologies followed in the structural design of this works is presented, as well as of the numerical models usually adopted, namely finite and boundary element models. Finally, some applications of computational mechanics are presented. First, a parameter study for underground powerhouses, with special emphasis in the definition of shapes, existence of several caverns,and in the tridimensional equilibria is described. Afterwards, examples of application to some hydraulic projects are illustrated: a large underground powerhouse in Mozambique, the Alto Lindoso hydroelectric power scheme in construction in the north of Portugal, and the Castelo do Bode tunnel, in operation, integrated in the water supply system to Lisbon.

O presente trabalho aborda a origem do estado de tensão interna dos maciços rochosos e apresenta os factores que o influenciam. Apresentam-se as técnicas e a aparelhagem correntemente utiiizada na determinação do estado de tensão, bem como a interpretação dos ensaios mais comuns, dando-se maior relevo aos ensaios com macacos planos pequenos (S F J) e com o extensómetro tridimensional (S T T),efectuados correntemente pelo LNEC.

Descreve-se sucintamente uma técnica para amostragem linear de descontinuidades em faces expostas de maciços rochosos e referem-se métodos para tratamento dos dados de campo com vista à definição defamílias de descontinuidades e caracterização de uma forma estatística da sua orientação, espaçamento e extensão. Apresentam-se os resultados obtidos para o caso de uma galeria subterrânea no aproveitamentohidroeléctrico do Alto Lindoso. Para as famílias de descontinuidade identificadas apresenta-se um estudo dos blocos tetraédricos que se poderão formar nas diferentes faces de rocha e analisam-se as suas condições de estabilidade.

N/A

Apresentam-se, neste relatório, modelos numéricos baseados no método dos elementos da fronteira, desenvolvidos no LNEC para análise de estruturas subterrâneas. Tecem-se algumas considerações sobre o método dos elementos de fronteira, descrevem-se os modelos desenvolvidos para equilíbrios planos e tridimensionais e apresentam-se alguns exemplos de aplicação.

N/A

N/A

N/A

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.