Publicações

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

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

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

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

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

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

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

Os romanos deixaram importantes contributos na área da Engenharia de Barragens, tanto nos aspectos relacionados com a concepção estrutural, como nos métodos construtivos e nos materiais utilizados. A barragem romana de contrafortes mais alta que se tem registo localiza-se em Belas, junto a Lisboa, e é conhecida como a Barragem de Olisipo. Apesar de se encontrar semidestruída e não desempenhar a função para a qual foi concebida, as suas ruínas constituem, ainda assim, um conjunto com interesse técnico e histórico. Este trabalho apresenta um estudo sobre as características geométricas e estruturais da Barragem de Olisipo. A análise estrutural foi realizada através do método do equilíbrio limite. Este estudo incidiu sobre duas secções transversais tipo da barragem, designadas por secção corrente e secção equivalente, esta última idealizada a partir da área de influência de um contraforte. Foram determinadas as linhas de pressões, as tensões verticais totais e efectivas na base da barragem e os factores de segurança em relação aos mecanismos globais de deslizamento e de derrubamento. O objectivo fundamental deste trabalho é divulgar e valorizar este importante património.

The evolution of numerical modelling in rock mechanics has made possible a more realistic representation of thebehaviour of rock masses, and a more reliable prediction of the response of rock engineering structures. Discontinuum modelling techniques, namely the discrete element method, based on the explicit representation of the rock mass discontinuous structure, have progressively acquired a broader role. In this lecture, the essential concepts and main features of these numerical techniques are discussed, with reference to their historical development. The use of these idealizations is exemplified by two areas in which they proved very effective. On one hand, the analysis of practical rock engineering problems, intended, for example, for safety assessment or monitoring interpretation. This type of application is illustrated herein by dam foundation analyses based on deformable block models.Asecond level of discontinuum modelling involves research aimed at the understanding of the fundamental behaviour of rock and rock masses. An example of this approach is the analysis of fracture phenomena with particle models, primarily of laboratory specimens, but being extended to larger scales. Critical issues identified in the effective application of these modelling tools are examined, as well as some foreseeable evolution trends.

A numerical model for the hydromechanicalanalysis of masonry dams based on the discrete elementmethod is presented. The dam and the rock foundation arerepresented as block assemblies, and a coupled flow-stressanalysis is performed in an integrated manner for the entiresystem. Complex block shapes may be obtained byassembling elementary blocks into macroblocks, allowingthe application of the model to situations ranging fromequivalent continuum to fully discontinuum analysis.A contact formulation was developed based on an accurateedge

In this work three constitutive contact models that include softening are adopted for particle model fracture studies in both rock and concrete. For a single local contact, the constitutive contact model performance is initially compared in tensile, pure shear and shear tests under constant axial. Additionally, compression, direct tensile, and confined triaxial tests of quasi-britlle material discretized with spherical particles are presented and the predicted macroscopic response is compared. For a single local contact, the three contact models predict a similar behaviour. As shown, it is possible to calibrate each contact model to reproduce complex macroscopic behaviour observed in rock and concrete, but each contact model requires different contact properties or particle generation procedures.

Asphalt mixture faces damage due to vehicle speed, repeated loads, and ultravioletradiation over time, regardless of being a self-healing material. Induced healing mechanismsare necessary to promote autonomous pavement recovery due to adverse in-service conditions,and the capsule-asphalt mixture system incorporating low-viscosity oils (rejuvenators) hasshown to be a possible solution in laboratory tests. This study aims to numerically investigatethe effect of rejuvenator-modified mastic (activated capsules) on the stiffness properties ofasphalt mixtures within the discrete element method. A three-dimensional model previouslyvalidated for rejuvenator-modified mastics with different rejuvenator-to-bitumen ratios (0, 2.5,and 10 wt%) is adopted. A generalised Kelvin contact model represents the time-dependentcontacts, and its contact parameters define the rejuvenator amount in the mastic phase. Theanalysis assesses the impact of the modified mastic amount and the rejuvenator-to-bitumenratio. Results show that the increasing modified mastic content progressively reduces themixture dynamic modulus. When the total mastic phase has rejuvenator-modified properties,the mixture stiffness modulus significantly reduces, and the phase angle performs differentlyfrom the expected (decrease with frequency) at a 10% rejuvenator-to-bitumen ratio due to theexcessively softened state, possibly compromising the pavement mechanical performance. Fora 0.30 wt% modified mastic ratio case adopting a local effect, the embedded elements do notsignificantly influence the mixture rheological properties, especially the stiffness modulus,which may be insufficient for self-healing purposes. Nevertheless, the negligible impact on thephase angle highlights the potential of the rejuvenator-modified asphalt mixture across differenttraffic and temperature conditions.

Micromechanical modelling based on the Discrete Element Method (DEM) has been widely used to investigate asphalt behaviour due to its ability to represent an irregular microstructure with variable-sized aggregates, bitumen and voids. The 3D rigid particle models with randomly distributed spherical particles and adopting elastic and/or simple viscoelastic models at the contacts are the standard approach, however, in recent years, a significant research effort is noted to incorporate real particle morphologies in the numerical models.In this study, a previously developed 3D DEM model of asphalt employing a generalised Kelvin contact model formulation for the viscoelastic contacts is further improved with realistic particle shapes representing the coarse aggregates. A digital library of aggregate shapes was created from the X-ray computed tomography (CT) scan of an asphalt specimen, using an adaptive image-processing method to separate the aggregates in the CT images and the Delaunay triangulation method to define the aggregate 3D surface model. Several virtual aggregates with different sizes were selected from the library to represent the coarse aggregate gradation of the modelled 3D DEM asphalt specimen. Each virtual aggregate is discretized with smaller spherical particles and its deformability is taken into account through the inner particle contacts. The numerical asphalt specimens with realistic particle shapes were submitted to uniaxial tension-compression cyclic tests to determine the stiffness properties, and the results were compared with those of the numerical specimens with all constituents represented by single spherical rigid particles. As shown, the proposed methodology greatly enhances the 3D DEM model's ability to simulate the asphalt behaviour.

O artigo considera um caso de estudo intencionalmente simples

Uma das técnicas de reforço usadas na reabilitação e reforço estrutural de paredes deedifícios antigos em alvenaria de pedra é o confinamento transversal simples através deelementos de aço fixados perpendicularmente à parede. Neste estudo apresenta-se osresultados numéricos da simulação de ensaios de compressão simples de paredes reforçadoscom esta técnica, utilizando um modelo de partículas 2D (MP-2D). Os estudos numéricosapresentados demonstram que os modelos do tipo MP-2D apresentam uma boa concordânciacom ensaios experimentais, nomeadamente no acréscimo do valor máximo em compressãosimples. Demonstra-se assim, que os modelos MP-2D podem ser adotados nodesenvolvimento de soluções de reforço deste tipo, nomeadamente na definição dascaracterísticas das barras, posicionamento e quantificação.

análise de cenários de rotura associados à fendilhação do betão requer a utilização deferramentas computacionais que sejam capazes de lidar com o comportamento resultante damicro-fendilhação generalizada e/ou de macro-fendas. Nesta comunicação é proposto ummodelo de partículas (MP) híbrido, de elementos discretos e elementos finitos, para a análisetridimensional da fratura em barragens de betão. Após a validação dos parâmetros do modeloem ensaios uniaxiais os resultados obtidos com este modelo são comparados com osresultados obtidos com um modelo de dano e com os resultados obtidos com um modelo MPhíbrido adotado na totalidade do corpo da barragem. Verifica-se que é possível analisarcenários de rotura estáticos em barragens de betão com modelos do tipo MP,preferencialmente híbridos, tendo em vista a redução dos custos computacionais.

This paper presents the development of a three-dimensional micromechanicalmodel based on the Laguerre-Voronoi diagrams of the grain structure to study the viscoelasticbehaviour of asphalt mastic with the use of the discrete element method (DEM).Usually, the DEM models of asphalt mastics adopt a Burger's contact model to reproducethe known viscoelastic behaviour. A generalized Kelvin chain model (GK) was developedwithin a particle model (PM) framework in order to obtain a better agreement in thedetermination of dynamic properties of mastics. Numerical cyclic tests under a frequencyrange varying from 10 to 0.10 Hz were implemented to analyse the dynamic response.The parameters of the DEM model are determined from macroscale material properties,which are obtained by fitting lab-based dynamic modulus and phase angle results. Theinfluence of the parameters defining the contact models on the dynamic response wasinvestigated. An iterative procedure was derived to convert the macroscale propertiesinto calibrated contact parameters of the proposed model. Simulation tests show a goodcorrelation between the numerical results obtained with the GK contact model and theexperimental data when compared with the agreement obtained with the Burger's model.

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The safety of concrete arch dams depends to a large extent on the soundness of thefoundation rock mass. The large arch dams presently under design and construction apply verysignificant loads to their abutments and foundations. The assessment of the foundation stabilityrequires the analysis of the potential failure mechanisms defined by the major rock massdiscontinuities and joint sets. For dams located in areas of intense seismic activity, the analysisneeds to take into account the potential effects of earthquakes, not only on the concrete arch,but also in the nearby rock discontinuities. The discrete element method is a major numericaltools for discontinuum modelling, allowing the analysis of block systems defined by multiplejoint planes. In the paper, the key issues involved in its application to arch dam foundations arereviewed. In particular, the representation of the discontinuities in models intended for failureanalysis is discussed. The evaluation of safety factors under static loading is addressed. Theframework for seismic analysis of arch dams is also examined, namely the dynamic boundaryconditions. Options to analyse the dynamic dam-water interaction and model calibration issuesare discussed, based on practical examples.

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.