Publications

The out-of-plane flexural bending capacity of masonry is a fundamental property for understanding the behavior of masonry structures. This study investigates the behavior of unreinforced masonry wallettes subjected to combined compression-flexural loading using the discrete element method (DEM), and provides a novel framework to estimate the masonry strength. A simplified micro-modeling strategy is utilized to analyze a masonry wallette, including the variation of the mechanical properties in masonry units and joints. Stochastic DEM analyses are performed to simulate brickwork assemblages, assuming a strong unit-weak joint material model typical of most masonry buildings, including historical ones. Once the proposed computational approach is validated against the experimental findings, the effect of spatial and non-spatial variation of mechanical properties is explored. Two failure types are identified: joint failure and brick failure. For each failure mechanism, the variability of the response and the effects of the modeling parameters on the load-carrying capacity is quantified. Afterward, Lasso regression is employed to determine predictive equations in terms of the material properties and vertical pressure on the wallette. The results show that the most important parameters changing the response are the joint tensile strength and the amount of vertical stress for joint failure, whereas the unit tensile strength dominates the response for brick failure. Overall, this research proposes a novel framework adopting validated advanced computational models that feed on simple test results to generate data that is further utilized for training response prediction models for complex structures.

Discrete element models are being increasingly applied to model rock failure processes.Bonded-particle models, based on circular or spherical particle systems, have been successfully usedfor two decades. More recently, bonded-block models, using polygonal or polyhedral elements, have proven to be a powerful alternative. This paper describes the basis of the application of these models in the numerical simulation of failure in rock materials. The critical governing parameters are identified, and their influence is discussed. The model calibration procedure based on the analysis of laboratory tests is discussed. An application example of an underground excavation problem is presented using a simple bonded-block model employing rigid blocks and a bilinear softening contact model. The results show the capability of this approach to reproduce observed failure modes involving block fractures.

Masonry arches are a fundamental component of historical structures. The assessment of the vulnerability ofthese heritage constructions to seismic loading requires reliable and efficient numerical models. Discrete element models are an alternative to finite element models, being particularly effective in modelling collapse mechanisms created by shearing and separation of the units along the joints. Discrete element codes typically rely on explicit methods of integration of the equations of motion for dynamic analysis, which may require large run times when the recommended stiffness-proportional component of Rayleigh damping is applied. A novel approach is proposed using an alternative damping model, Maxwell damping, which involves placing multiple spring-dashpot elements in the joints, in parallel with the standard stiffness springs. This damping model is tested in the dynamic analysis of masonry arches, under pulse and earthquake loading. The results obtained in this early investigation show a good performance in the simulation of collapse under dynamic loads, in general agreement with the analyses conducted with classical stiffness-proportional damping, but reducing significantly the computational effort.

Rigid particle models based on the discrete element method (DEM) have been adopted to model creep, fracture, and the viscoelastic behaviour of asphalt mixtures considering an irregular micro-structure and particle contacts. Within a DEM framework, the Burgers contact model, which is known to have a narrow frequency and temperature range, is usually adopted to model viscoelastic properties. In this study, a new explicit three-dimensional generalised Kelvin (GK) contact model formulation for the DEM model is proposed for asphalt materials. The model is implemented following two different methodologies (GK and GK). The models are validated in uniaxial tension-compression sinusoidal tests for predicting the dynamic modulus () and phase angle (

Encapsulated rejuvenators embedded in asphalt mixtures are a promising technology toextend the service life of asphalt pavements. However, their effects on the asphalt mixture

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This paper describes the study of the metrological quality of the excitation force inthe context of force vibration test of concrete dams. For this purpose, a measurementuncertainty evaluation was performed, based on available probabilistic information about theinput quantities

A conjugação entre os modelos numéricos e os resultados observadosdo comportamento das obras é uma ferramenta fundamentalno apoio ao controle de segurança de grandes obras. A barragemdo Baixo Sabor possui um sistema de monitorização dinâmicaem continuo, e foram realizados dois ensaios de vibração forçadapara duas cotas de albufeira. Neste contexto foram desenvolvidosmodelos numéricos da barragem do Baixo Sabor incorporando oconjunto barragem-fundação-albufeira. Neste artigo, apresentamseos resultados dos modelos numéricos desenvolvidos para váriosníveis da albufeira comparando com os resultados experimentais.

The structural rehabilitation of historic/traditional rubble masonry wall constructionsrequires consolidation and retrofitting solutions to be employed in order to withstand dynamic loads,high vertical loads, and differential settlements. One of these strengthening techniques is basedon the use of steel bar connectors perpendicular to the wall, considered individually or integratedinto more complex strengthening techniques. The aim of this study is to evaluate numerically thestrengthening effect of transverse steel connectors on rubble masonry walls. With this purpose, a 2Dparticle-reinforced model (2D-PMR) was devised and applied to model uniaxial compression tests.The results presented show that predictions calculated using the proposed 2D-PMR model are veryclose to known experimental results, particularly in the corresponding failure modes, the increase ofthe maximum uniaxial compression value, and ductility. Parametric studies are also conducted byvarying the diameter of the steel bars and the level of strengthening to assess the influence of thebar-bond effect and lateral plates. The presented parametric numerical studies show that (i) a two-level strengthening solution guarantees a similar response to the three-level strengthening solutionadopted in the experiments; (ii) it is not relevant to apply a grout injection during the applicationprocess of the steel connectors if lateral plates are adopted; and (iii) the 2D-PMR model can be usedin the definition of the steel bar diameter and properties; as shown, a smaller (8 mm) bar diameterpredicts a similar strengthening effect to the (12 mm) bar size adopted in the experiments. Given theperformance of the proposed 2D-PMR model, further work is underway that will allow the 2D-PMRmodel to numerically assess other reinforcement techniques, namely, reinforced micro-concrete layersand textile reinforced mortar.

he current first generation of Eurocodes is a suite of ten Euro-pean standards for the design of buildings and civil engineeringworks, whose implementation started in 2010. EN 1990 sets thebasis of structural design, with the other Eurocodes dealingwith different materials and specific aspects of design. Geo-technical aspects of design are covered by EN 1997

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

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

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

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

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

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

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

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

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

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

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

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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.