Publications

Traditional stone masonry walls are structural elements in most historic build-ings. To preserve them and improve their ability to withstand extreme events, such asearthquakes, it is necessary to implement effective reinforcement solutions. This paperpresents the modeling of traditional Portuguese rubble stone masonry walls, reinforcedwith external steel mesh, sprayed micro-concrete layers and transverse confinement bysteel connectors, which were developed and tested experimentally in uniaxial compression.The modeling is carried out using micro-modeling through a 2D particle model (PM).The process of calibrating the properties of both micro-concrete and concrete is presented,the methodology for generating the numerical models is described and the numericalresponse is compared with the experimental results. The numerical results show thatthe PM can adequately reproduce the experimentally observed behavior of this type ofreinforcement solution.

This study presents a robust contact constitutive model in the distinct element method (DEM) framework for simulating the mechanical behavior of masonry structures. The model is developed within the block-based modeling strategy, where the masonry unit is modeled as deformable blocks with potential crack surfaces in the middle of the bricks, while the mortar joints are defined as zero-thickness interfaces. The modeling strategy implements multi-surface plasticity with damage mechanics, including a tension cut-off, Coulomb failure criterion, and an elliptical compressive cap for the damage in tension, shear, and compression, respectively. Two new features are introduced in this contact model: a piecewise linear softening function for strength degradation in tension and shear and a hardening/softening function to phenomenologically define the compressive damage of masonry composite into the unit-mortar interface. The constitutive model is implemented in commercial DEM software using the small displacement configuration and validated against material and experimental tests on masonry walls subjected to constant pre-compression and monotonically increasing in-plane load. The experimental and numerical results regarding the force-displacement relationship and damage pattern produced by the proposed constitutive model are compared and critically discussed, demonstrating the capability of DEM coupled with the suitable constitutive law in simulating the behavior of masonry structures.

o obtain predictions closer to concrete behaviour, it is necessary to employ a particle model(PM) that considers contact softening. A bilinear softening contact model (BL) has been adoptedin PM studies. Several limitations in PM predictions have been identified that may be due to BLassumptions. For this reason, this paper compares BL predictions with those obtained with morecomplex models to assess if PM predictions can be improved. As shown, it is possible to calibrateeach contact model to reproduce the complex behaviour observed in concrete in uniaxial and biaxialloading. The predicted responses are similar, and the known PM limitations still occur independentlyof the adopted model. Under biaxial loading, it is shown that a response closer to that observed inconcrete can be obtained (higher normal-to-stiffness ratio of

Among the various important monuments impacted by the April 25, 2015 Mw7.8 Nepal earthquake, the Dharahara Tower located in Kathmandu suffered complete collapse. The collapse of the tower, a slender 60-meter-high old brick masonry structure with an almost cylindrical hollow shape, was captured by a low-quality video camera, which nonetheless helped to identify the critical moments. Initially, the tower descended more than 10 meters vertically after a rupture at the base. After a few seconds, it overturned, disintegrating upon impact on the ground. At a distance of 1.3 km, an accelerometric station recorded the strong motion which was used as input of a discrete element model of the structure. Mechanical properties were taken from lab tests made on similar building materials. The Dharahara Tower had previously been analysed by other researchers using various methods. However, since they were apparently not aware of the mechanism observed in the video footage, their collapse models do not agree with this new evidence. For the initial phase of the collapse the present model explains with great accuracy the observations of the video footage, but the final phase is dependent on various details, and modelling is not so robust.

Discrete element block models provide a suitable tool for the numerical analysis of masonry structures, particularly apt to represent the nonlinear response governed by shearing and separation along the structure

The unreinforced masonry (URM) walls are the common load-bearing structural elements in most existing buildings, consisting of masonry units (bricks) and mortar joints. They indicate a highly nonlinear and complex behaviour when subjected to combined compression-shear load-ing influenced by different factors, such as pre-compression load and boundary conditions, among many others, which makes predicting their structural response challenging. To this end, the present study offers a discontinuum-based modelling strategy based on the discrete element method (DEM) to investigate the in-plane cyclic response of URM panels under different vertical pressures with and without a damp-proof course (DPC) membrane. The adopted modelling strategy represents URM walls as a group of discrete rigid block systems interacting along their boundaries through the contact points. A novel contact constitutive model addressing the elasto-softening stress-displacement behaviour of unit-mortar interfaces and the associated stiffness degradation in tension-compression regimes is adopted within the implemented discontinuum-based modelling framework. The proposed modelling strategy is validated by comparing a re-cent experimental campaign where the essential data regarding geometrical features, material properties and loading histories are obtained. The results show that while the proposed compu-tational modelling strategy can accurately capture the hysteric response of URM walls without the DPC membrane, it may underestimate the load-carrying capacity for URM walls with the DPC membrane.

This paper presents the development of a novel crack-based damage quantification method to assess the damage accumulation in masonry arch bridges subjected to externally applied loading. Initially, a damage index was proposed, considering the initiation and extension of tensile and sliding cracks. Then, the proposed damage indexing was adopted into a two-dimensional discrete element code of analysis to evaluate single and multi-ring masonry arch bridges. The numerical model was validated by comparing the computational outputs against the experimental results obtained from the literature. Following the validation, masonry arch bridge models were developed, featuring the four most representative bond configurations in arch barrels. Also, different bond properties were assigned to investigate their impact on the global failure characteristics of single- and multi-ring masonry arch bridges. From the analyses of results of the multi-ring masonry arch bridges investigated in this study, it was shown that the rapid growth of tensile cracks in radial joints and the occurrence of shear slippage in circumferential joints between adjacent rings were observed to be early signs for multi-ring bridges before the ultimate load reached. By analysing the correlation between the normalised damage index with the normalised load, damage accumulation in different masonry arch bridges were identified. This study offers a novel perspective on quantitively evaluating the damage accumulation and failure mechanism of masonry arch bridges and the findings may provide valuable insights into the assessment and management of existing masonry arch bridges.

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A three-dimensional particle model, based on the asphalt mastic micro-structure representation following a discrete element model framework, was developed to investigate the influence of sunflower oil (rejuvenator) on the rheological properties of asphalt mastic. Dynamic shear rheometer tests in laboratory, for a frequency range of 0.1

The integration of healing capsules into asphalt mixtures has demonstrated promising advancements in their intrinsic self-healing properties. However, the efficacy of this technology still requires further investigation. Rigid particle models, utilizing the discrete element method (DEM), have been adopted to simulate the creep, fracture, and viscoelastic behavior of asphalt mixtures, accounting for their irregular microstructure and particle contacts. This study utilizes the previously developed VirtualPM3DLab, a three-dimensional DEM framework, to numerically assess the impact of rejuvenator-modified mastic particles on the stiffness properties of post-healed asphalt mixtures where the asphalt mixture has undergone healing. Simulations consider different capsule proportions (0.30, 0.75, and 1.20 wt%) incorporated in the specimens. Numerical results reveal that the encapsulated rejuvenator reduces the stiffness modulus of asphalt mixtures, with this impact becoming more pronounced as the capsule amount increases due to the additional rejuvenator representation in the specimen. In addition, the phase angle remains unaffected across all numerical scenarios, suggesting that the viscoelastic behavior of asphalt mixtures is not significantly impacted and indicating the suitability of capsules for pavement applications. The findings also suggest that the percentage of these healing elements can slightly surpass the traditional amounts commonly used in laboratory settings.

This paper presents an updating of the analysis and interpretation ofthe structural behavior of Covão do Meio dam (in Portugal) which concrete isaffected by an ongoing swelling process.The simulation of dam

Micromechanical modelling through the Discrete Element Method (DEM) is adopted for the study of bituminous materials given its capability to replicate complex microstructures behaviour. Typically, DEM models of bituminous materials consist of an assembly of randomly distributed spherical rigid particles which interact using elastic and/or simple viscoelastic contact models, and individual aggregates are represented by single particles. However, recent years have witnessed a notable surge in research efforts aimed at incorporating true particle morphologies into numerical models.In the context of this research, an existing 3D DEM model for bituminous materials has been refined with the representation of mineral aggregates with realistic particle shapes. To achieve this, a digital library of aggregate shapes was constructed from X-ray computed tomography (CT) scans. An adaptive image-processing technique was employed to isolate the aggregates in the CT images, and the Delaunay method was used to create a 3D surface model of the aggregates. Several virtual aggregates with varying sizes were selected from this library to mirror the gradation of coarse aggregates in the 3D DEM asphalt model. Each virtual aggregate was discretized using smaller spherical particles, with its deformability given by its inner particle contacts.To evaluate the effectiveness of this enhanced approach, numerical assemblies featuring realistic particle shapes were subjected to a cyclic loading protocol. Overall, realistic particles shapes increased the stiffness modulus and decreased the phase angle of numerical specimens, and the effect was greater with a finer discretization of aggregates. The outcomes clearly demonstrate the importance of this numerical improvement to accurately simulate the bituminous mixture behaviour.

A avaliação estrutural das paredes de alvenaria de pedra tradicional é uma tarefa complexa devido à heterogeneidade e incerteza nas propriedades dos materiais constituintes, argamassa e pedra, e à variabilidade do posicionamento e geometria destes elementos na alvenaria. Nesta comunicação, modelos experimentais de alvenaria de pedra (muretes), construídos de acordo com técnicas tradicionais portuguesas, ensaiados experimentalmente sob condições de carregamento em compressão-corte, são avaliados numericamente, adotando uma abordagem de micro-modelação através de um modelo de partículas 2D (2D-MP). Estudos anteriores demonstram que os modelos 2D-MP conseguem prever o comportamento de estruturas de alvenaria antiga, nomeadamente a propagação de fendas, os modos de rotura final, a resistência máxima ao corte e a ductilidade da parede observados experimentalmente em compressão uniaxial e compressão-corte. Neste trabalho apresentam-se os estudos numéricos desenvolvidos que permitem avaliar a influência do nível de pré-compressão na resposta monotónica em compressão-corte e o desempenho do modelo 2D-MP na reprodução de ensaios cíclicos.

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Stone masonry walls are the main structural elements of many historic buildings. Their restoration and preservation are a major concern given the increasing interest in the rehabilitation of built historical heritage and the implementation of preventive measures to mitigate seismic risk. The accurate structural assessment of the existing rubble stone masonry is a very complex and difficult task, due its composite and complex nature. The heterogeneity and uncertainty in material properties of its constituents, mortar and stone, the variability of the stone units positioning and geometry, among others, make its experimental characterization and accurate numerical modeling still nowadays a challenging task. In this context, the research presented aims to contribute to a better understanding of the in-plane shear behaviour of unreinforced two leaf rubble stone masonry walls, typical stone masonry of ancient buildings that are representative in Portugal.Rubble stone masonry specimens, built with traditional Portuguese construction techniques, tested experimentally under monotonic compression-shear loading conditions are here numerically evaluated, adopting a micro-modelling approach using a 2D particle model (2D-PM). In the 2D-PM model the stone and mortar elements are represented as particle assemblies that interact with each other, thus capable of representing their inherent physical and material heterogeneity. The numerical model is generated through a mapping process of the stone units and mortar joints. The experimental campaign conducted on rubble stone masonry wall specimens allowed to collect the data necessary for the calibration of the PM model parameters, namely the stone-stone and mortar-mortar elastic and strength contact properties. The validation of the 2D-PM models of the rubble stone masonry specimens under compression and combined compression-shear loading conditions is performed using the Parmac2D software. The presented results show that 2D-PM models can predict the crack propagation, the final failure modes, the maximum shear strength, and the wall ductility observed experimentally. Parametric studies are also presented that allow a better agreement between the numerical predictions and the experimental response showing the relevance of the stone-mortar interface strength properties in the overall macroscopic behaviour.

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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.

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 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.

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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.

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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.