Publicações

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

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

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

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

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

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

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

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

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

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

Nesta comunicação apresenta-se a modelação de paredes de alvenaria de pedra tradicionalrecorrendo a um modelo de partículas (MP) 2D, baseado no método dos elementos discretos, quetem sido adotado na modelação da fratura em materiais quase-frágeis. Nesta abordagem numérica,os elementos constituintes da estrutura de alvenaria, pedras e a argamassa, são entendidos comosendo formados por um esqueleto de agregados de várias dimensões em contacto direto, comligações do tipo coesivo, que permitem ao esqueleto de agregados suportar forças de tração. Odesenvolvimento dos modelos numéricos apresentados teve por base os modelos experimentaisdesenvolvidos e ensaiados pelo segundo autor [1].Após uma descrição sucinta do modelo numérico, apresenta-se os ensaios experimentais adotadoscomo referência dos estudos numéricos realizados. Descreve-se a metodologia de geração dosmodelos numéricos representativos da estrutura de alvenaria de pedra e apresenta-se o processo decalibração das propriedades dos contactos pedra-pedra e argamassa-argamassa, de modo a se obteruma resposta elástica e resistente próxima da pedra e da argamassa, alcançada nos ensaiosexperimentais.Em seguida são simulados ensaios de compressão simples com base nos parâmetros de contactodefinidos no processo de calibração. Dos ensaios numéricos, verifica-se que, com base nosparâmetros calibrados, os valores de rigidez e de resistência máxima obtida numericamente são daordem de grandeza dos valores obtidos experimentalmente. Os estudos apresentados demonstramque, após calibração dos parâmetros de contacto, os modelos MP permitem representar, com baseem modelos de interação simples, o processo de formação e propagação de fendas em paredes dealvenaria de pedra tradicional, a rigidez, a ductilidade e o valor da carga máxima.

têm sido adotados no estudo da fratura e propriedades viscoelásticas do mastique e dasmisturas betuminosas a partir da representação de uma microestrutura irregular e doscontactos partícula-partícula. Nesse sentido, este trabalho apresenta um modelo departículas tridimensional baseado nos diagramas de Laguerre-Voronoi da estruturagranular para o estudo da viscoelasticidade dos mastiques betuminosos. Dos modelosde contacto existentes, o modelo de Burger é o mais utilizado na análise dos materiaisbetuminosos. Contudo, este modelo apresenta limitações na previsão de propriedadesdinâmicas numa ampla variedade de frequências. Para isso, um modelo de contacto dotipo generalizado de Kelvin (GK) foi desenvolvido para a representação dos contactosviscoelásticos. Este modelo, composto por uma parcela elástica, uma parcelaviscoelástica e uma parcela visco-plástica, é baseado numa formulação incremental, emque o incremento de deslocamento resulta num incremento de força. A conversão daspropriedades macroscópicas, obtidas a partir do ajuste de resultados experimentais emmastiques, em parâmetros de contacto e a respetiva calibração são apresentados. Osmastiques foram submetidos a ensaios cíclicos com carregamento sinusoidal paravalidar o modelo em diferentes temperaturas e frequências. Verificou-se que ocomportamento reológico obtido com o modelo de contacto foi bem previsto. Por fim, osresultados reológicos obtidos com o modelo GK e o modelo de Burger foramcomparados. Como esperado, o modelo de contacto GK apresentou uma melhorresposta quando comparado aos resultados obtidos experimentalmente. Estudos docomportamento dinâmico em misturas betuminosas estão em andamento.

Modelos híbridos de separação de efeitos do tipo HSCT-FE para estudo do comportamento de barragens abóbada

N/A

Use of SSHM data for dynamic behaviour analysis and damage detection on large dams. The cases of Cabril dam and Cahora Bassa dam

Nesta comunicação é apresentado um modelo de partículas 3D (MP), baseado nométodo dos elementos discretos, que inclui de forma aproximada a deformabilidade dapartícula e a geometria poliédrica. Neste modelo MP, o interior de cada partícula édiscretizado com uma malha de elementos finitos do tipo tetraédrico. Por razõescomputacionais procurou-se manter o modelo de contacto o mais simples possível,deste modo as partículas poliédricas são aproximadas por partículas esféricas, queinteragem entre si com base num modelo de contacto múltiplo em que a superfície decontacto é definida com base na faceta comum aos diagramas de Laguerre-Voronoique representam as partículas em contacto. Apresentam-se os resultados numéricosobtidos em ensaios triaxiais em rocha com o modelo de partículas flexivel (VGM3D-F)e comparam-se com os obtidos com um modelo de partículas rígidos. O estudoapresentado permite concluir que a inclusão da deformabilidade da partícula aumentao desempenho dos modelos do tipo MP.

As barragens de Ferradosa e Olgas, localizadas no Alto Douro, nos concelhos de Freixo de Espada à Cinta e Moncorvo, respetivamente, foram construídas entre 2007 e 2009. São estruturas gravidade de betão com cerca de 30 m de altura. A água das respetivas albufeiras destina-se ao abastecimento público, sendo exploradas pela empresa Águas do Norte, do grupo Águas de Portugal, com o apoio do LNEC nos aspetos relacionados com a segurança estrutural.Na comunicação apresentam-se os aspetos relevantes da análise e interpretação do comportamento observado das barragens durante o primeiro enchimento da albufeira e os primeiros 10 anos de exploração.Na análise estrutural consideraram-se modelos planos de elementos finitos das barragens e respetivas fundações, o comportamento viscoelástico dos materiais, a variação das ações da água e as variações térmicas no betão das obras.Os resultados numéricos são comparados com os resultados da observação contínua das obras, apresentando uma boa concordância.

Concrete gravity dams are mass concrete structures which resist to external loads mainly by their dead weight. The geometrical solution currently considered, which evolved from the reasoned application of mathematical theory to structural engineering, are characterized by right-angled triangular profiles with downstream face slopes of 0.7 to 0.8. In medium to high seismic intensity zones, such as Portugal, other constructive dispositions may be necessary. Under seismic loadings, it is generally accepted that the gravity profile keyed into the foundation at a depth corresponding to 10% of the dam height is a crucial contribution to ensure structural stability conditions. However, this detail is often not considered in stability analyses, which is generally understood as a conservative strategy. In this work, the benefits from considering the keyed depth in stability analyses are evaluated. For that, 100-meter-high hypothetical gravity profiles, keyed at a depth of 10 meters, are considered. To allow the development of rigid-body failure mechanisms, a downstream rock wedge, inclined at a critical angle, is assumed. At first, the analytical expressions that describe the failure mechanisms identified, considering the dam-foundation interface as a dominant failure surface, are deduced and validated through numerical modelling. Afterwards, the frictional properties of the interface, for several loading conditions which result in different total net forces and the corresponding application points, are computed. Lastly, the stability benefit is evaluated by comparing the safety factor obtained with the correspondent of an unkeyed profile. When explicitly considering the keyed depth in stability analyses, higher safety levels are obtained which can be crucial to ensure stability conditions. It was proved that, under the same load conditions, the consideration of unkeyed profiles would demand higher values of the friction angle, up to 12º more than considering the correspondent keyed profile. Moreover, this also ensures stability conditions for more inclined resultant net forces.

The Foz Tua hydroelectric development is located in the north of Portugal at the mouth of the Tua river, a tributary of the Douro river, and is equipped with 270 MW of power capacity, making it a very important asset in the country

The continuous displacement monitoring is essential for the safety control of large dams. It shouldbe based on the comparison between numerical model results and monitoring data, e.g. observeddisplacements using plumb lines, geodetic methods or, more recently, with GNSS (GlobalNavigation Satellite System). For Cabril dam, the case study presented in this paper, no plumblines were installed in the central section. Thus, the displacement monitoring in this section iscarried out by classical geodetic methods that do not allow continuous monitoring (only twoobservation campaigns per year). So, in this case, the use of GNSS was considered particularlyuseful, as it allows continuous monitoring of displacements at the top of the central section. AsCabril dam presents cracking problems since the first filling, it is important to continuously monitorseveral notable points, which includes the point at the top of the central section. The present workfocuses on the validation of the displacements obtained by GNSS, at Cabril dam, using a 3D finiteelement model, developed in MATLAB, in which the horizontal cracking at the upper zone issimulated through joint elements. The 3DFE model was calibrated based on the displacementsobserved by plumb lines (in two non-central sections) and by classical geodetic methods,considering variations in hydrostatic pressure and annual temperature variations. Thedisplacement evolution observed by plumb lines and geodetic methods were analyzed usingHSCT (Hydrostatic, Seasonal, Creep and other Time effects) separation of effects models, tofacilitate the comparison process between the observed displacements and the numerical results.In this way, the 3DFE model was firstly calibrated using plumb lines results and then it was usedto validate GNSS measurements.

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

N/A

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

N/A

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

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

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

Neste trabalho apresenta-se o sistema para monitorização em contínuo do comportamento dinâmico da barragem do Cabril que foi instalado em 2008, pelo LNEC e pela EDP, referindo alguns dos principais resultados que têm sido obtidos a partir da análise dos dados recolhidos, quer sob excitação ambiente/operacional, quer sob ações sísmicas. Salienta-se a importância do desenvolvimento do software para tratamento, análise e gestão automática dos dados e apresentam-se os programas que têm vindo a ser desenvolvidos no LNEC, em MATLAB, para apoio a este tipo de sistemas, nomeadamente programas de identificação modal (Modal_ID2.0 e Modal_ID_Auto2.0) e programas de elementos finitos tridimensionais para análise do comportamento dinâmico de sistemas barragem-fundação-albufeira (DamDySSA2.0).

This document presents the research plan for the doctoral thesis of LNEC's Junior Research Fellow Margarida Espada. This work, to be submitted to the Faculty of Engineering of the University of Porto (FEUP), will be developed in the Modelling and Rock Mechanics Unit of the Concrete Dams Department, and it is part of the on-going P2I research project DEMRock6m. This work aims at developing more efficient methodologies to perform safety studies and seismic analysis of rock engineering structures, based on discrete element models and in the integrated use of probabilistic models for the geometric and shear strength parameters and for the water pressures in rock discontinuities. This will allow a more realistic definition of the rock mass in discrete element models and an adequate identification of the potential failure mechanisms.

Neste relatório é apresentado o método de Euler para calcular as órbitas do sistema n-corpos,por exemplo, o dos planetas do sistema Solar, tendo em conta a propagação das forçasgravíticas entre o Sol e os planetas e entre os planetas entre si. Apenas requer como dadosiniciais uma observação anterior das órbitas em termos de posição e velocidade. A correcçãoda interacção entre planetas não é suavizada, o que se justifica pelos seus valores. A correcçãorelativista é importante.

As equações de Navier-Stokes são equações de derivadas parciais. As incógnitas nocaso de incompressibilidade consistem no campo de velocidades. As pressões numa 1ªaproximação resultam de um equilíbrio estático.A principal causa de problemas relacionados com a solução destas equações é devida àparcela das acelerações convectivas que está na origem da turbulência.Pesando estas equações e integrando duas vezes por partes obtém-se uma forma fracadestas equações.Em problemas 3D as variáveis independentes são 3 espaciais e 1 temporal. Admite-seque o campo de velocidades pode ser desenvolvido em série de distribuições de Delta deDirac espaciais e suas derivadas com coeficientes funções do tempo. Com funções deteste polinomiais obtém-se a formulação distribucional proposta das equações deNavier-Stokes.

N/A

O objectivo deste relatório é o estudo da matemática aplicada à solução de problemasfísicos de propagação de ondas esféricas com operador espacial biharmónico,consideradas quânticas.As técnicas matemáticas usadas incluem a transformada de Laplace da função de ondaf e o cálculo de sua inversa tal como sugerida por Pipes e Harvill.O método matemático usado para descrever as ondas esféricas quânticas é compequenas adaptações o método causal não-linear descrito por Croca.

N/A

N/A

N/A

A análise do comportamento de barragens de betão com base em modelos de elementos finitos tridimensionais exige a definição da discretização a adoptar para o conjunto barragem-fundação, ou barragem-fundação-albufeira. A realização desta tarefa sem o recurso a programas de geração automática é muito dispendiosa pelo que tem vindo a ser desenvolvido no NMMF um módulo computacional para geração automática de malhas de elementos finitos tridimensionais especialmente adaptado para a geração de malhas tridimensionais de barragens abóbada. Inicialmente desenvolvido em FORTRAN, o referido módulo computacional para geração de malhas de elementos finitos tridimensionais tem vindo a ser objecto de diversos melhoramentos, os mais recentes centrados ao nível da interface com o utilizador. Assim, apresenta-se neste relatório o módulo computacional

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.