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During the last decade, many vibration-based structural health monitoring systems have been successfully implemented in different structures such as bridges, towers, stadia and wind turbines, with the aim of studying the structure dynamics and its evolution over time, eventually detecting the occurrence of novel structural behaviour that may indicate the presence of damage.Such vibration-based monitoring systems generally rely on the identification of modal properties, which are then used as monitoring features. Therefore, from operational modal analysis to the tracking of those features and finally to data normalization, many processing steps occur that depend on the accuracy of the identified modal properties. Thus, the estimation of the uncertainties associated with the identified modal properties increases the robustness of this process.In this context, data obtained from the continuous dynamic monitoring of a concrete arch dam has been used to evaluate the gains of quantifying the uncertainties of modal properties, evaluating in particular the effect of taking these uncertainties into consideration when performing automated operational modal analysis, modal tracking and data normalization. Nevertheless, it is observed that the most significant gains of considering estimates uncertainties occur when these quantities are used for removing outliers during modal tracking.

Masonry arch bridges form a significant portion of the European transport infrastructure network. Manyof these bridges are relatively old but still in service. Increasing vehicle loads and speeds have highlightedthe need for reliable estimates of their service condition. Past research demonstrated that load-carryingcapacity of a masonry arch bridge is a function of the soil response. However, today, the approaches usedfor the simulation of soil in masonry arch bridges are over-simplistic and most of them do not take intoaccount the soil-structure interaction phenomena. This paper presents a novel modelling approach, basedon the discrete element method, for the simulation of backfill material in masonry arch bridges.According to the method, bricks in the barrel vault are simulated as an assembly of distinct blocks separatedby zero thickness interfaces at each mortar joint. Backfill is represented as an assemblage of denselypacked discrete irregular deformable particles, here called

Discrete element models are a powerful tool for the analysis of masonry, given theirability to represent the discontinuous nature of these structures, and to simulate the most commondeformation and failure modes. In particular, discrete elements allow the assessment of the seismicbehavior of masonry construction, using either pushover analysis or time domain dynamic analysis.The fundamental concepts of discrete elements are concisely presented, stressing the issues relatedto masonry modeling. Methods for generation of block models are discussed, with some examplesfor the case of irregular stone masonry walls. A discrete element analysis of a shaking table testperformed on a traditional stone masonry house is discussed, as a demonstration of the capabilitiesof these models. Practical application issues are examined, namely the computational requirementsfor dynamic analysis.

Earthquakes represent one of the major threats to cultural heritage monuments, such as classical ancient columns.Understanding the behaviour and dynamic response of such historic structures is useful for the assessmentof the conservation and rehabilitation techniques to be used for their preservation. The behaviour of ancientmulti-drum and monolithic columns subjected to dynamic loads is characterized by highly nonlinearity sinceboth rocking and sliding phenomena can occur. Analytical studies of multi-drum columns subjected to dynamicload is extremely complicated, if not impossible to perform. Nowadays, computational methods of analysis canbe used to represent their dynamic response. Using a software based on the Discrete Element Method (DEM) ofanalysis, a typical ancient multi-drum and an equivalent in dimensions monolithic columns subjected to horizontaland combined horizontal and vertical harmonic excitations were modelled to identify the main factorsaffecting their stability. Different acceleration amplitude and frequency input records were applied and their rolein the collapse/deformation mechanism was investigated. From the results analyses it was shown that novelstructural analysis tools that extend traditional methods of structural assessment could allow engineers to understandthe mechanisms that have allowed the surviving structures to avoid structural collapse and destructionduring strong earthquakes.

No 14º Encontro Internacional de Modelação Numérica em Barragens, organizado pela ICOLD, foi proposta a análise numérica de uma barragem de betão em arco localizada na Suécia sujeita a gradientes térmicos significativos ao longo do ano. Neste artigo apresentam-se os resultados numéricos obtidos com basenuma discretização mais refinada do corpo da barragem, quando comparada com o modelo adotado no encontro internacional. Os resultados da análise mecânica realizada com um modelo de fenda discreta são comparados com as observações in situ. Verifica--se que o modelo estrutural mais refinado permite obter resultados mais próximos dos observados, nomeadamente a distribuição de fendilhação no paramento de jusante e o campo de deslocamentos. Analisa-se ainda o efeito das armaduras distribuídas colocadas juntoao paramento de montante e ao paramento de jusante no controlo de deformação e fendilhação.

This paper focuses on studying the dynamic behaviour of large dams over time, including identification of modal parameters (naturalfrequencies, modal damping ratios and mode shapes) and seismic response analysis, based on measured acceleration time histories.A comparison between experimental results obtained from continuous vibration monitoring data and numerical modelling results from 3DFE models is presented. The aim is to emphasize the interest of combining the use of recorded data from continuous dynamic monitoringsystems and of numerical modelling software for seismic and structural health monitoring of dams.

The seismic response of a 290 m high arch dam, located in ahigh seismicity zone in China, is studied in this paper. The goal isto evaluate the influence of the reservoir water level on the dam

Over the last 50 years, a significant amount of effort has been taken to develop numerical approaches andtools for the structural analysis of masonry. These range from considering masonry as an anisotropic continuum(macro-models) to the more detailed ones considering masonry as an assemblage of units andjoints (micro-models). In this paper, a detailed micro-modelling approach for the analysis of masonrycouplets and prisms is proposed. The approach represents masonry units and mortar joints as an assemblageof densely packed discrete irregular deformable particles bonded together by zero thickness interfacelaws. The mechanical properties (here referred to as micro-properties) of irregular particles andcontacts are responsible for the mechanical behaviour of masonry. In addition, the approach allows failureto occur either at the brick, mortar and/or brick/mortar interface. A series of computational modelswere developed and their results are compared against small-scale experimental findings. A good agreementbetween the experimental and the numerical results was obtained which demonstrates the hugepotential of the modelling approach proposed. The significant advantage of this approach is to modelcracking as a real discontinuity among particles and not as a modification in the material properties.In addition, reliable prediction of masonry strength can allow one to reduce the costly and timely experimentaltesting and avoid the reliance on conservative empirical formulas.

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

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

The objective of this work is to reconstruct and analyze the seismic response of a pre Doric temple from the Panhellenic sanctuary at Nemea, Greece. Archaeological and historical evidence suggests that this temple, previously posited to have been damaged or destroyed in a battle, may have been damaged by an earthquake. Using Itasca

Given the results of triaxial tests, regressions are commonly used to evaluate the parameters of failure criteria that model intact rock strength, and to perform statistical inferences used to evaluate characteristic values defined in EC7. These inferences are only possible if the basic hypothesis underlying regression are followed, namely homoscedasticity (constant variance of the errors). This paper presents analyses of 23 sets of triaxial tests, starting by the evaluation of the regression parameters of the Mohr-Coulomb linear criterion and of the Hoek-Brown non-linear criterion, followed by carrying several statistical tests to check the homoscedasticity null hypothesis of independence between the variance of intact rock strength and the confining stress.

Rigid particle models taking directly into consideration the physical mechanisms and the influence of the material grain structure have been developed for fracture studies of quasi-brittle material such as rock. A 2D rigid particle generalized contact model (VGCM2D) has been recently proposed which properly reproduces the rock friction angle and the rock tensile strength to compressive strength ratio, while keeping the simplicity and the reduced computational costs characteristic of circular particle models. In this work the VGCM2D contact model is extended in order to include the particle deformability by considering in each particle an inner finite element mesh triangular discretization. The VGCM2D flexible contact model is tested against known experimental data on a granite rock, namely uniaxial and biaxial tests and Brazilian tests. The study carried out shows the importance of considering the particle deformability in order to obtain results closer to the experimental data.

Minarets are important elements of mosques that constitute the essence of Islamic art. They aretall and slender structures. Old ones are mostly made of cut-stone-block masonry andoccasionally of brick masonry, while the new ones are generally of reinforced concrete. Theyhave suffered significant damage during past earthquakes, the most recent event being the 23October 2011 Van, Turkey earthquake, underlining the need for their maintenance, preservationand protection. Istanbul, the largest city of Turkey, is home to many historical and modernminarets. Assessment of their dynamic behavior is significant due to the expectation of a largeevent in the near future. This study shows the results of the dynamic nonlinear analysis of twomasonry minarets of different heights to better understand their structural behavior under seismicconditions. The numerical models are created using 3DEC by discrete element method. Thenumerical analyses are performed using a series of sine-wave excitations by gradually changingthe frequency and amplitude of input velocity. Displacement magnitudes, maximum shear andnormal stresses, maximum shear and normal displacements, relative displacements and residualdisplacements are recorded. The results are evaluated and compared with those previouslyobtained from the analyses carried out under real and synthetic earthquake inputs.

A barragem da Cahora-Bassa localiza-se na zona norte de Moçambique inserida numa zona sísmica de risco elevado devido à influência do

The paper presents contributions to the statistical study of the parameters of the Mohr-Coulomb and Hoek-Brown strength criteria, in order to assess the characteristic failure envelopes for intact rock, based on the results of several sets of triaxial tests performed by LNEC.

O ensaio de vibração forçada consiste na aplicação a uma estrutura de uma força com uma variação no tempo sinusoidal perfeitamente conhecida, materializada através de um vibrador de massa excêntrica. Tirando partido do facto de se verificar um significativo aumento da amplitude da resposta da estrutura quando a frequência da ação se encontra na vizinhança das frequências naturais da estrutura, a medição da resposta da estrutura sob a ação 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 respetivo amortecimento e as configurações modais. Nesta comunicação descreve-se a metodologia de ensaio e apresentam-se os resultados de caracterização do comportamento dinâmico da barragem de Cahora Bassa com base na realização de um ensaio de vibração forçada e o desenvolvimento de um modelo matemático calibrado com os resultados experimentais.

A determinação do comportamento dinâmico das obras e o acompanhamento da sua evolução durante as várias fases da vida é muito importante, e está inserido nas atividades do controle de segurança estrutural. A realização dos ensaios de vibração forçada em barragens para a determinação do comportamento dinâmico continua a ser uma das técnicas mais fiáveis nesta área. Nesta comunicação descreve-se a metodologia de ensaio, incluindo os desenvolvimentos recentemente efetuados, e como exemplo de aplicação, apresentam-se os resultados relativos a um ensaio realizado para caraterização do comportamento dinâmico da barragem de Cahora Bassa, incluindo o modelo matemático desenvolvido para a sua interpretação.

The paper introduces and presents instances of application of methodologies foranalysis of the stress field obtained from the results of in situ stress measurements using the overcoring, hydraulic fracturing and flat jacks methods. These methodologies integrate all stress measurements, and use numerical models of the rock mass that represent the ground topographyand the underground excavations, so that the most likely stress field in the zone of interest for the design of several large underground structures is obtained.

Os processos de fratura, que penetram de forma profunda no corpo de uma barragem debetão, podem afetar seriamente a sua segurança estrutural. Devido ao potencial catastróficoassociado à rotura de grandes barragens, é fundamental dispor de modelos numéricoscapazes de prever realisticamente o eventual desenvolvimento de fissuras bem como aresistência estrutural última associada aos mecanismos de colapso estrutural.Neste trabalho estuda-se o problema de propagação de fraturas (por tração) em barragensde betão do tipo gravidade usando algumas técnicas numéricas desenvolvidas e propostasrecentemente:

Masonry is a combination of units such as stones, bricks or blocks usually laid in a cementitious or limemortar. It is probably the oldest material used in construction and has proven to be both simple to buildand durable. Over the years, existing masonry constructions have inevitably suffered damage with time.Earthquakes, soil settlements, material degradation and lack of maintenance are the main reasons forthat. Careful and periodic assessment of such structures is necessary in order to evaluate their structuralcapacity and safety levels. However, performing the structural analysis of masonry construction is notan easy task. A review is presented of the main models based on the discrete element method and the available related numerical techniques that have been proposed for the analysis of masonry. The essential assumptions adopted by these models and numerical implementation issues are discussed. Differences between available models are illustrated by applications to various masonry problems including static and dynamic analysis of masonry arch bridges, walls, vaults, domes and ancient colonnades.This book is composed of 17 chapters authored/co-authored by 25 outstanding researchers from 11countries (Canada, France, Greece, Hungary, Iran,Italy, Mexico, Norway, Portugal, UK, USA), whichwere reviewed by 60 referees.

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This chapter consists of two parts. First a general overview is given: the exact definition of the Discrete Element Method is provided, and the main types of existing models are introduced; then the theoretical fundaments of the most important approaches available today for masonry analysis are given. The second part of the chapter focuses on 3DEC, the most widespread commercial DEM code for masonry analysis. This second part begins with a theoretical overview. Application issues for masonry structures are then considered (block material behaviour, contact representation, structural elements like cables or bars etc.). Among the practical examples arches, barrel vaults, walls, coloumns and complete structures (like houses) are presented, including the issues of quasi-static versus dynamic analysis and of block fracture as well. The readers can find helpful advice on how to simulate their own problems most effectively.

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Discrete element models have become a major tool for masonry analysis, allowing a suitable representation of its discontinuous nature and marked nonlinear behaviour. The chapter reviews the fundamental assumptions of the main DEM formulations available. It focuses more specifically on the widely used UDEC and 3DEC codes, explaining their relation with the other approaches, and the most relevant issues arising in their application to masonry. Applications to the main types of structures are reviewed, considering both static and dynamic analyses. Recent research providing comparisons of the numerical models with experimental and field data is particularly covered. The discussion of the different examples is aimed at clarifying the key capabilities of DEM and demonstrating the most effective ways of using it in a variety of masonry analysis situations.

This chapter is focused on the Portuguese experience on the developmentand exploration of systems for continuously monitoring dam vibrations, usingaccelerometers. The pioneer system for seismic and structural health monitoring(SSHM) installed in Cabril dam (the highest Portuguese arch dam: 132 m high) isdescribed in detail. The design of this system was the result of a long-term LNECresearch program, still ongoing. These monitoring systems should include softwaredeveloped to automatically perform the analysis of collected data, including theautomatic comparison with numerical results from 3DFE models. In view of thegood results obtained with the system in operation in Cabril dam since 2008, similarsystems have been installed in other large dams in Portugal, particularly in recentlybuilt dams. Finally, Baixo Sabor dam is presented as an example of a new Portuguesedam with a complete SSHM system, in operation since 2015. Themain experimentalresults obtained for both dams are shown, namely the evolution of natural frequenciesover time, mode shapes and the measured seismic response to earthquake events.

Para verificação do cumprimento das exigências de segurança das barragens,tanto relativamente à funcionalidade (cenários correntes), como em relação àsegurança ao colapso (cenários de rotura), é essencial utilizar modelos de simulação oude interpretação (no caso de obras existentes) do seu comportamento. Estes modelossão idealizações (simplificações) da realidade, tanto no que diz respeito às acções(modelos das acções), como no que respeita à componente estrutural (modelos estruturais).A solução destes modelos, através de adequados métodos de análise, quantificaparâmetros da resposta das estruturas que permitem avaliar a sua segurança, utilizandocritérios de segurança previamente definidos.A validação destes modelos pode ser feita, no caso de cenários correntes,através da sua comparação com os resultados da observação do comportamento debarragens. No caso de cenários de rotura, não existe muita experiência de comparaçãodestes resultados com situações reais: é pequeno o número de acidentes ocorrido e,mesmo nestes, o volume de informação é reduzido. Desta forma, o recurso a métodosexperimentais, para o estudo de cenários de rotura, tem uma importância acrescida.Assim o principal objectivo deste trabalho é contribuir para melhorar a capacidade deavaliação da segurança de barragens de betão envolvendo cenários de rotura pela fundação.Neste trabalho desenvolveram-se dois ensaios experimentais em modelosfísicos: um primeiro envolvendo uma barragem abóbada, para o estudo de cenários derotura da fundação para acções estáticas; e um segundo de uma barragem gravidadeensaiado em mesa sísmica, com vista a estudar a rotura pela fundação para acçõesdinâmicas.A previsão e interpretação dos ensaios foram efectuadas com modelosmatemáticos adequados, que permitiram a sua validação e posterior utilização no estudode outros cenários.

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

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

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

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

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

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

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

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

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

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

This document presents a back analysis procedure for identification of the elastic parameters of transversely isotropic rock cores, containing an overcoring triaxial strain probe, from the strains measured during a biaxial test. A three-dimensional finite element model was developed to simulate the biaxial test on the overcored rock specimen and to compute the strains at the location of the strain gauges. Different optimisation algorithms were tested and the most suitable one was selected. The back analysis procedure was tested for identification of the five elastic parameters and the two orientation angles that characterise a transversely isotropic rock core. In spite that, with the developed methodology, convergence was reached and all those parameters could be identified, sensitivity analyses demonstrated that the results obtained were not stable and therefore they were not reliable. By introducing constrains based on common practice and previous experience, a stable and robust methodology was achieved: the three elastic parameters, E1, E2 and ?2, are reliably identified using the value of G2 calculated with Saint-Venant’s expression and a fixed value of ?1, while the orientation parameters are obtained from observation of overcored rock. Analysis of the results shows that application of this methodology represents an enormous step forward when compared with the traditional use of isotropy. Besides, the methodology is general and can also be used with other types of overcoring equipment. The five elastic parameters and the two orientation angles obtained can then be used, together with the overcoring strains, to compute the complete in situ state of stress.

This document presents the work developed by the PhD student Margarida Espada in the scope of the course unit Risk Analysis in Geotechnical Works of the Doctoral Program in Civil Engineering of the Faculty of Engineering of the University of Porto (FEUP). This work presents a reliability analysis, using the response surface method (RSM), for the case study of the left bank excavation slopes of the Baihetan arch dam foundation, which is one of the case studies of Margarida Espada's PhD thesis. The aim was to approximate an implicit limit state function by computing safety factors, using a discrete element model of the Baihetan left bank developed in 3DEC software, where the shear strength parameters of two important rock discontinuities were considered as random variables. The probability of failure was then obtained through an iterative process, using approximation methods. This work presents the 3DEC model developed to analyse the stability conditions in the Baihetan left bank and the results of the reliability analysis.

O problema da solução das equações de Navier Stokes é abordado neste trabalhopropondo-se uma técnica de representação das incógnitas deslocamentos e pressõesvariáveis no espaço e no tempo em série de Delta de Dirac e suas derivadas no tempocujos coeficientes se determinam com base na solução de sistemas de equaçõesdiferenciais definidos no espaço (problema com três variáveis espaciais independentesque pode ser estudado pelo método de Monge).

Neste relatório apresentam-se as equações básicas da elastodinâmica linear, as soluçõesfundamentais e o teorema da representação no domínio de tempo e de frequência.Para movimentos finitos de casca formula-se o teorema dos trabalhos virtuais e a suaimplementação pelo método dos elementos finitos.

Neste relatório apresentam-se os principais aspectos da modelação sísmica de barragensabóbada. Assim propõe-se: modelos numéricos de geração de sismos por uma falha; aforma como o sismo actua na barragem; modelos para estudar a influência da albufeirana vibração do conjunto; métodos para solução das equações do movimento; e novasformulações de elementos finitos para o problema estrutural.

In pressure tunnels and shafts, in addition to the mechanical effect that excavation has on the rock mass and the disturbance that it introduces in the water flow, also the contained water can interact from the mechanical and hydraulic points of view with the rock mass. Seepage in fractured rock masses is dominated by the flow that takes place through the joints, and this is highly d(;pendent on their properties, namely aperture and roughness. Joint aperture, in tum, i::; very sensitive to stress changes. Special attention must therefore be paid to the joints in hydromechanical analyses. In this report are presented some studies that were carried out for the hydromechanical characterization of joints of the Alto Lindoso rock mass and numerical simulations of the hydromechanical behaviour of two selected sections of the high pressure circuit.