Publications

A monumental tetrastyle canopy (four columns topped by a hollow cap overlaying a statue), built in1948 at the centre of Kathmandu, Nepal, has suffered full collapse during the April 25, 2015 Mw7.8earthquake. Two video camera recordings let us recover the most important movements of thestructure. At a distance of 2.9 km from the monument, an accelerometric station (KATNP) recordedthe motion which we used as input of a model structure made with DEM. Geometry and dimensionsof main elements were mostly obtained from satellite images. Concrete and steel in columns wereconsidered as the common practice at that time. We performed some sensitivity analyses varyingthe mechanical properties due to the possibility of aging alterations in concrete and steel and toincorporate uncertainties on the geometric characteristics. Albeit the response has a significantvariability, results show that it is possible to reproduce well the video images, attesting theimportance of video cameras to capture the dynamic performance of structures, providing insightinto their behaviour and data to support numerical investigations.

In this study, the in-plane structural behavior, capacity, and performance of dry-joint stone masonry walls (DJSMWs)and the effects of the vertical stress level on these factors are investigated via a stochastic discontinuumanalysis that considers the material uncertainty. A discontinuum type of analysis is performed based on thediscrete element method (DEM), where each stone masonry unit is explicitly represented in the computationalmodel. To better simulate the cracking and shear failure modes within the stone units, a coupled fracture energybasedcontact constitutive model is implemented into a commercial discrete element code, 3DEC. First, theproposed modeling approach is validated by comparing to experimental findings in literature. Then, theapproach is used to explore the failure mechanism and the force

The installation of vibration-based structural health-monitoring systems relying in the study of natural frequencies to assess the condition of civil engineering structures is becoming more and more common. The extraction of these monitoring features can be achieved through automated operational modal analysis, combining output-only identification methods with cluster analyses, and comparing the identified modal properties with references, in a process known as modal tracking. However, changing environmental and operational conditions affect the dynamic behaviour of structures, disturbing the process of modal tracking, which may lead to the loss of important information and to misidentifications. In this context, this paperproposes a new methodology for modal tracking within the scope of automated operational modal analysis, especially prepared for scenarios with strong external influence on modal properties. A concrete arch dam with large variations of some natural frequencies is used as case study, and the proposed methodology is compared to a standard procedure using a quite unique monitoring data set continuously collected for 3 years.

Neste artigo apresenta-se a formulação e resultados da aplicação de dois modelos descontínuos tridimensionais que simulam a interação hidromecânica. Nestes modelos o comportamento mecânico é simulado de forma idêntica mas o comportamento hidráulico é simulado com duas abordagens diferentes. O primeiro modelo baseia-se numa formulação que admite o escoamento através de elementos planos de interface. O segundo modelo, que se propõe neste artigo, baseia-se numa discretização unidimensional, ocorrendo o escoamento através de elementos de canais. Os modelos hidromecânicos implementados no módulo computacional Parmac3D Fflow são verificados e validados através de exemplos simples, e o modelo proposto é calibrado de modo a serem obtidos, com os dois modelos, os mesmos valores de pressão e de caudal. Foi desenvolvido um modelo hidromecânico de um conjunto barragem/fundação, tendo em consideração a existência de cortina de impermeabilização e de sistema de drenagem na fundação. Salientam-se as vantagens do modelo proposto no estudo do comportamento hidromecânico de fundações de barragens.

Earthquake damage in historic masonry buildings is generally caused by the collapse of individual portions thatbecome detached form the structure and fail by overturning. These mechanisms are mainly governed by thediscrete nature and geometry of the block units. Analyses based on explicit micro-modelling in which each blockis considered separately are therefore of increasing importance. This paper offers a robust tool for the seismicassessment of masonry structures under either, quasi-static or dynamic loading. Algorithms for performing dynamicpulses and pushover analyses through the Discrete Element Method are developed and described, takinginto account the actual discrete nature and geometry of masonry. A numerical procedure is proposed thatautomatically detects the collapse mode and follows the evolution of the analysis until collapse. The implementedmethod is able to give a reliable estimate of the expected failure mechanism, providing the seismicacceleration required to trigger the motion and the ultimate displacement beyond which the collapse occurs.Finally, the implemented algorithms are applied to two case studies and the results are compared with thetraditional analysis based on rigid-block kinematics to outline the features and potentialities of the proposedapproach.

Conservation of the European-built heritage is nowadays closely related to interventions in masonry construction. Since a significant part of these structures are located in earthquake prone zones, designing protective measures that ensure their preservation requires the assessment of the associated seismic vulnerability and the understanding of their degradation mechanisms. However, due to the presence of discontinuities between its constituent elements, the numerical simulation of the non-linear response of masonry structures subjected to strong earthquakes is a cumbersome task, especially when performed using the traditional finite element method. As an alternative, the discrete element method is particularly suitable for the numerical analysis of such structures under large, damaging loads. By allowing discrete displacements/rotations of individual bodies, and by automatically recognising new contacts between bodies, while eliminating obsolete ones, this numerical approach can simulate the complete detachment of discrete bodies initially in contact.The present paper illustrates the use of the discrete element method to assess the seismic vulnerability of stone arches. A probabilistic approach allows to consider the variability of theseismic action and the uncertainties in the definition of the material properties. First, an unreinforced masonry arch is considered. Based on non-linear multi-directional incremental dynamic analyses, five damage states are proposed and the respective fragility curves are elaborated. Toimprove the arch

A seismic assessment study of two historical masonry arch bridges, with different geometries and spans, ispresented. The seismicity of the two locations was analyzed in order to define the seismic action to be applied.Artificial ground motion records were generated accordingly, and real ground motions were also used. The twonumerical models were created with a 3D discrete element code. The accuracy of the deformability of the blockmodels was verified by comparison with a finite element model. In situ measurements of the natural frequencieswere available for one of the bridges, providing further means for model calibration. Time domain dynamicanalyses were performed with each set of ground motions, allowing an evaluation of damage and failure modesunder seismic action. The shorter span bridge was found to withstand the regulatory records with minimumdamage. In contrast, the longer span bridge displayed a significant vulnerability to earthquake action. The studyshows that rigid block models have the ability to represent effectively the dynamic elastic response of the bridgesand can be calibrated by ambient vibration measurements. Furthermore, the discrete element models provide apowerful tool to investigate the nonlinear dynamic response and failure of these structures, which has to be basedon a comprehensive set of dynamic records.

Stability analyses of geotechnical structures in rock are traditionally performed using deterministic methods. In Europe, Eurocode7, introduced in the beginning of the 21st century, adopts limit state design and semi-probabilistic methods, using partial factors for the design of geotechnical structures. Meanwhile, reliability-based design, using probabilistic methods, is becoming more common in practical cases. The paper considers an intentionally simple case study?the analysis of a slope in a rock mass with one discontinuity, considered in a discrete way, forming a rock block to be stabilised by anchors?to compare the results obtained with the different methods. The objective is to calculate the force applied by the anchors so that the ultimate limit states of sliding of the rock block is verified. Deterministic-based design optimization considering both the traditional global safety factor approach and the partial factor approach following the Eurocode 7 are first applied. A reliability-based design optimization procedure?which takes geometrical and mechanical properties of the discontinuities as random variables?is then used, and the results are compared to the former ones. A discussion is presented concerning the consistency of the obtained results.

Civil engineering structures are generally supposed to have long operation life spans during which they aresubmitted to many factors, both environmentally and human-induced, that degrade their condition and performance,gradually leading to the occurrence of damages and malfunctions. Therefore, systems capable ofmonitoring and assessing structural performance automatically are highly desirable.In this context, this paper describes the vibration-based structural health monitoring of Baixo Sabor arch dam,in Portugal, detailing results from the several processing stages needed to achieve the ability to detect damage.Automated operational modal analysis is applied to the data obtained during the first three years of monitoring,after which environmental and operational conditions affecting modal properties are studied and their effectsminimised through the combined application of weighted regression models and principal components analysis.Finally, damages are simulated in a numerical model of the dam, and the results are used to test the ability ofdamage detection tools to find these anomalies.The present paper uses a quite unique set of experimental data to test for the first time the ability of avibration-based SHM system to identify realistic damages in an arch dam.

The paper investigates the effectiveness of two-dimensional Discrete Element Method as a tool forstructural analysis of arches provided with buttresses and backfill and strengthened with externallybonded reinforcement. Masonry vault and buttresses are modelled as an assembly of 2Drigid blocks interacting through non-linear contact joints, the backfill is discretized into deformableelastic-plastic triangular elements, while the reinforcement is modelled by means of trusselements bonded to the substrate through non-linear springs. A parametric analysis on theinfluence of material parameters and the effect of the discretization of the backfill is carriedout, and the outcome of different reinforcement systems, consisting of Steel Reinforced Groutapplied either at the intrados or at the extrados, are analysed. The comparison with experimentalfull-scale tests proved the ability of the numerical approach to capture hinges position, loadbearing capability, as well as the increase in deflection and load capacity provided by thereinforcement.

A análise estrutural de pavimentos para cargas verticais pode ser realizada com base em vários modelos numéricos: método dos elementos finitos, método dos elementos discretos, método da espessura equivalente, e métodos baseados na análise elástica de multi-camada. Neste trabalho édescrita a formulação de um modelo de análise multi-camada com base na equação decompatibilidade de um corpo elástico linear em coordenadas cilíndricas. Vários tipos de solução de pavimentos são analisados, sendo os resultados obtidos com o modelo de multi-camada proposto comparados com os obtidos com um programa de elementos finitos 3D que apresenta uma maior robustez numérica, e com um programa multi-camada equivalente, BISAR.

A aplicação de modelos de identificação modal no domínio da frequência à análise dos resultados de ensaios de vibração ambiental efectuados no corpo da barragem do Cabril mostrou que, para além dos esperados picos espectrais correspondentes aos modos de vibração da barragem também surgem nos espectros da resposta medida outros picos importantes cuja frequência não corresponde a nenhuma das conhecidas frequências naturais da obra. Colocou-se então a hipótese desses picos espectrais estarem relacionados com o comportamento dinâmico da torre das tomadas de água que é uma estrutura auxiliar, porticada, em betão armado, com altura idêntica à da barragem (132 m). Trata-se de uma estrutura que se encontra imersa na albufeira junto ao paramento de montante da obra, e que suporta os órgãos de manobra das comportas das tomadas de água dos dois grupos de produção de energia e da descarga de fundo. Assim, com vista a analisar a referida hipótese de ocorrência de fenómenos de interacção dinâmica entre a torre e a própria barragem, foi desenvolvido neste trabalho um modelo de elementos finitos 3D para analisar o comportamento dinâmico da torre, o qual foi calibrado com base em resultados experimentais obtidos a partir: i) de ensaios de vibração ambiental efectuados no corpo da barragem e na torre, e; ii) de um sistema de observação em contínuo do comportamento dinâmico instalado recentemente no corpo da barragem. Neste artigo apresenta-se também um estudo de previsão do comportamento dinâmico da torre sob acções sísmicas, efectuando a análise no domínio do tempo e pelo método do espectro de resposta.

As barragens são estruturas que representam risco potencial elevado pois em caso de rotura podem causar perdas humanas e materiais importantes. Através da sua observação criteriosa e com recurso a modelos numéricos faz-se a avaliação de cenários de rotura, obtendo-se factores de segurança que servirão como critérios de decisão para acções de reforço e reabilitação.Neste contexto apresenta-se o caso de uma barragem localizada no Canadá cuja análise do cenário de rotura por deslizamento, sugere a aplicação de cabos de ancoragem de modo a serem alcançadas as condições de segurança pretendidas. Previamente é feita uma breve revisão das técnicas de reforço e reabilitação associadas aos principais cenários de deterioração relativos às barragens gravidade de betão e alvenaria.

Small concrete gravity dams are sometimes built using passive steel anchors to enhance their stability for the applied loads. It is important to assess the amount of internal tensile and shear forces resisted by the anchors to verify their structural adequacy. This paper presents the application of the distinct element method to study the magnitude and distribution of internal anchor forces. Comprehensive parametric analyses considering the anchor shear stiffness and the friction angle of the dam-foundation interface have been performed on a small dam 3 m high. The case of several anchors along the section was also investigated. It is shown that (a) the required displacements to induce anchor loads are very small (of the order of 10x10-3 mm of crack opening), (b) that the anchor shear stiffness has small impact in the load share between anchor and concrete, and finally (c) that strength properties of rock-concrete interface play a key role in the structure behavior.

Release of the in situ stresses is often the most relevant action in underground projects. 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. The paper presents a global methodology for evaluation of the most likely natural stress field from in situ test results. Some case histories are presented as examples of application. One 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 during the initial testing programme in different locations. 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.

Neste trabalho apresenta-se um processo iterativo de cálculo, com base na análise limite, para determinação do comprimento de fissuras nos planos horizontais de barragens gravidade sujeitos a esforços de tracção e, em consequência, alteração das condições de aplicação da subpressão. Esta ferramenta baseia-se num modelo de dados proveniente de uma aplicação mais vasta que, a partir da geometria da barragem, características do material, nível da água a jusante e montante, condições de drenagem e solicitação sísmica, permite a determinação das condições de estabilidade da estrutura. Faz-se a análise dos dois acidentes ocorridos na barragem de Bouzey, um por deslizamento pela base e o outro por derrubamento parcial da secção, em que a ocorrência de fissuração e o efeito da subpressão tiveram papel determinante.

As barragens são estruturas que apresentam um risco potencial elevado, pelo que a sua fiabilidade deve ser avaliada continuamente através de um programa de observação. Com base nos dados recolhidos podem ser estudados possíveis cenários de rotura através de modelos numéricos. Descreve-se neste trabalho os principais cenários de rotura a serem considerados quando da avaliação de segurança de uma barragem gravidade e apresenta-se o caso de uma pequena barragem descarregadora, localizada no Canadá, para qual foi elaborado um estudo de estabilidade, inicialmente através de um modelo de equilíbrio limite e posteriormente por meio de um modelo em elementos discretos, no qual foi avaliada uma solução de reforço constituída pela aplicação de ancoragens passivas.

Large flat jack tests are used to assess rock mass deformability in the design stages of large projects. The paper introduces a methodology for interpretation of the tests, with which it is also possible to obtain the in situ normal and shear stress components on the flat jack plane. The main problem regarding interpretation of large flat jack tests has to do with the effect of the tension crack that may develop in the rock mass, depending on the loading pattern, the rock mass tensile strength and the in situ stress normal to the jack. The three-dimensional numerical model that was developed simulates the test with the actually applied loading and accounts for the development of the tension crack. Model results show that the extent of the tension crack is irrelevant for the determination of the in situ stresses. Therefore, the in situ stress values can be used as an important parameter for interpretation of the test results, and furthermore constitute one more output of this reliable in situ test.

O dimensionamento de barragens, de acordo com a regulamentação portuguesa, engloba averificação da segurança da obra para diversos cenários de rotura. Nesta comunicação,apresenta-se o estudo experimental do comportamento dinâmico até à rotura de um modelode uma barragem abóbada com representação da albufeira. Os resultados experimentaisserão comparados com os obtidos a partir de modelações matemáticas devidamente calibradas.

The structural safety control of large dams is based on the continuous observation of its behavior under static and dynamic actions and on the use of mathematical models for the simulation of the real dam behavior. These mathematical models should be calibrated taking into account the real behavior of the system dam-reservoir-foundation (mainly influenced by the reservoir water level). For the safety control of old dams, usually with cracking, the mathematical models should include some features for crack simulation.

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.

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.

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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.

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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.