Publications

The uplift pressures change the stress state of the rock mass foundation in a coupled hydromechanical process and may compromise the dam stability. Consequently, dam safety regulations specify the maximum values of the hydraulic conductivity and uplift pressures that can usually only be fulfilled after the execution of seepage and uplift control measures. The design of waterproofing and drainage systems is still based on an equivalent continuum approach, even though rock mass foundations are discontinuous media. The analysis of the piezometric monitoring data of several Portuguese large concrete dam foundations reveals that uplift pressures are site-specific and may even vary considerably across a given site, which can be critical for the safety assessment. From the data gathered in several dams, a probabilistic model that can be seen as an a priori prediction model for uplift pressures is proposed. Considering the difficulty in classifying the geologic foundation conditions beneath each piezometer in existing dams, it is assumed that the data come from a mixture of two beta distributions, representing foundations with regular and unfavorable geologic conditions. This model is a significant improvement over available approaches and will be instrumental for the assessment of existing dams and the design of new dams.

The characterization of the dynamic behavior of an arch dam, and its evolutionthroughout the structure's lifetime, provides important data for the safetycontrol process. Forced vibration tests remain a reliable technique for this purpose.The Baixo Sabor dam is a 123 m high arch dam recently built in Portugal.Forced vibration tests were performed before and after the reservoir filling.Two techniques for forced vibration test are compared, discrete frequencyscanning, the standard methodology, and continuous frequency scanning (sinesweep), a new proposed methodology, which allowed faster results withoutloss of precision. For the interpretation of test results two numerical models ofthe dam-reservoir-foundation system were built, and calibrated with the experimentaldata. A good match of numerical and experimental results wasobtained for the six lowest frequencies and corresponding mode shapes.

This study proposes an alternative approach to modeling the failure mechanisms of brickwork assemblages under combined shear

The Western Anatolia Region of Turkey is an important region of high seismic activity.The active dynamics of the region are shaped by a compression and expansion mechanism. This activemechanism is still ongoing and causes strong seismic activity in the region. The Frontinus Gate is amonument in the Roman city of Hierapolis of Phrygia located in southwestern Anatolia. The aim ofthis study is to investigate the seismic behavior of this stone masonry structure using discrete elementmodeling. For this purpose, nonlinear dynamic analyses were performed to simulate the structuralresponse of the gate under seismic excitation. Deformation, damage, and failure patterns induced inthe masonry gate for di erent levels of seismic action are evaluated and discussed. An earthquakewith a return period of 475 years is expected to cause some damage, but no collapse, while for areturn period of 2475 years, the models indicate collapse of the monument.

In this paper three historical masonry minarets in Istanbul, Turkey, are assessed for thedependency between the input harmonic motion and structural response parameters. Theirheights are 40, 73 and 74 m, while the slenderness is 12, 6 and 12, respectively. The discreteelement method is used in dynamic nonlinear analyses. Models were calibrated withmeasured natural frequencies. A series of sine-wave excitations is created for different frequency-amplitude pairs varying between 0.4 and 10 Hz, and between 0.1 and 1 m/s. Fromthe results of dynamic simulations, a general trend was observed for masonry minarets.Especially, slenderness and wall thickness play an important role on their dynamic responseand damage pattern. Dynamic behavior of these minarets cannot reliably be estimated bystatic non-linear analysis. Two engineering demand parameters (EDPs) are defined to characterizethe displacement of the minaret top and the inter-ring shear displacements alongthe minaret body. Damage performance criteria for minarets are proposed based on fourdamage states and tentative limit values are given. We were able to identify the occurrenceof those limit states as a function of frequency and amplitude of sinusoidal input motion.

This study presents a numerical investigation on the fracture mechanism of tension stiffening phenomenon in reinforced concrete members. A novel approach using the discrete element method (DEM) is proposed, where three-dimensional randomly generated distinct polyhedral blocks are used, representing concrete and one-dimensional truss elements are utilized, representing steel reinforcements. Thus, an explicit representation of reinforced concrete members is achieved, and the mechanical behavior of the system is solved by integrating the equations of motion for each block using the central difference algorithm. The inter-block interactions are taken into consideration at each contact point with springs and cohesive frictionalelements. Once the applied modeling strategy is validated, based on previously published experimental findings, a sensitivity analysis is performed for bond stiffness, cohesion strength, and the number of truss elements. Hence, valuable inferences are made regarding discontinuum analysis of reinforced concrete members, including concrete

Nowadays, the management and safety control of large dams is generally based on automatic monitoring, including the socalledseismic and structural health monitoring systems (SSHM), using the latest technology for automatic data measurement,acquisition and transmission. These systems should include software for automatic management and analysis of continuousmonitoring data and software for numerical simulation of the dam dynamic behavior using 3D finite element models. Thissoftware should be designed to provide useful and reliable information to meet the needs and expectations of stakeholders,and to support the studies of researchers and engineers responsible for structural health monitoring. This paper is focusedon the experience gathered from the SSHM system of Cabril dam, a 132 m high-arch dam, in Portugal, that has been undercontinuous dynamic monitoring since 2008. The importance of the software specifically developed for automatic modalidentification, automatic detection of seismic vibrations (distinct from vibrations due to the operation of discharge gates andpower groups), and automatic comparison between experimental data and computed results from a reference finite elementmodel of the dam-reservoir-foundation system, is highlighted. This software includes: (1) the generation of graphics withthe evolution of the identified natural frequencies over time and the comparison with calculated frequencies using differenthypothesis for concrete damage evolution; and (2) a service to automatically send emails summarizing key dynamic monitoringresults to stakeholders to provide the necessary support for informed management and engineering decision making.The main results from SSHM of Cabril dam are presented, namely regarding the evolution of modal parameter over time,considering the influence of water level variations, and the measured response during an earthquake event.

In this study, a novel computational modeling strategy is proposed to estimate the lateral load capacity andbehavior of unreinforced masonry (URM) structures. All commonly noted failure mechanisms are captured viathe proposed modeling strategy using the discrete element method (DEM) in three-dimensions (3D). Masonrywalls are represented as a system of elastic discrete blocks, where the nodal velocities are evaluated by integrating the equations of motion using the central difference method. Then, the mechanical interactions among adjacent blocks are examined utilizing the relative contact displacements and employed in the contact stress calculation. Through this research, a new stress-displacement contact constitutive model is considered and implemented in the commercial software 3DEC, which includes softening stress-displacement behavior for tension, shear, and compression along with the fracture energy concept. The results of the discontinuum models are validated on small- and large-scale experimental studies available in the literature with good agreement. Furthermore, important inferences are made regarding the effect of block size, the number of contact points, and contact stiffness values for robust and accurate simulations of masonry walls.

De acordo com a legislação portuguesa e tendo em consideração o risco sísmico da zona de construção das barragens é obrigatório a implementação de um Sistema de Observação Sísmica (SOS), incorporando instrumentação para caracterizar a ação sísmica induzida nas obras e a respetiva resposta estrutural. Em complemento, têm sido instalados Sistema de Monitoramento Dinâmico Contínuo (SMDC). O SOS permite não apenas a caracterização da ação sísmica, mas também a sua propagação ao longo do maciço rochoso, bem como a resposta estrutural da barragem. O SMDC visa identificar as características dinâmicas da barragem e sua evolução ao longo do tempo, considerando a variação das condições ambientais e operacionais, bem como a possível evolução das propriedades mecânicas dos materiais. Os processamentos são efetuados automaticamente incluindo a caracterização do nível de aceleração e a identificação dos parâmetros modais da barragem. Os valores obtidos pelo processamento automático são armazenados em base de dados, sendo enviados alertas quando são atingidos os patamares de alarme previamente definidos.Os resultados provenientes destes sistemas são comparados com os resultados de modelos numéricos sofisticados, calibrados com o recurso a ensaios experimentais de caraterização dinâmica realizados na obra durante a fase de primeiro enchimento.A combinação da monitorização dinâmica com os modelos numéricos é uma ferramenta fundamental no controlo de segurança estrutural e gestão de risco das barragens.

Today, there are several computational models to predict the mechanical behaviour of masonry structures subjected to external loading. Such models require the input of material parameters to describe the mechanical behaviour and strength of masonry constructions. Although such masonry materialparameters are characterised by stochastic

The numerical analysis of concrete dam failure scenarios requires computational tools that candeal with the formation, propagation and localization of cracks and their effects on the overall dambehaviour. It is well known that assemblies of discrete part icles connected through simpleinteraction laws can capture the global behaviour of quasi-brittle macro-material, like concrete.In this work a particle model based on the discrete element method is used. Due to computationalrestrictions some simplifications are adopted: i) a finite element model is adopted in thefoundation and in the dam zone where an elastic behaviour is expected; ii) the adopted particlesize is higher than the maximum aggregate size of dam concrete. In order to further reducecomputational times a hybrid discrete/finite model is proposed that replaces the stiffness of thefinite elements where nonlinear behaviour is expected by a discrete particle assembly in itsinterior.The hybrid discrete/finite model is validated for several case studies. The results are comparedwith those obtained with a finite element based two scalar damage model. The results show theapplicability of particle models to the study of failure scenarios of concrete dams, including itsinitial elastic response, even when the adopted aggregate structure is much larger in size than theadopted concrete aggregate.

This paper presents the relevant results of the monitoring data analysis of the Chicamba dam(Mozambique), which confirmed the existence of an ongoing concrete swelling process in the dam

This paper presents a study on the seismic response of the 132 m high Cabril arch dam, for an earthquake measured in-situ with the installed Seismic and Structural Health Monitoring system (in operation since 2008). The measured acceleration time histories are compared with results from finite element analysis in various positions in the dam body, using the seismic accelerations recorded at the dam-rock interface as inputs. The numerical simulations are conducted using two programs: i) DamDySSA4.0, a 3D finite element program develop in LNEC for dynamic analysis of arch dams

In the last decade Portugal made a significant set of investments in new hydroelectric projects under the National Dams Program with High Hydroelectric Potential. EDP Produção SA, a company of EDP - Energias de Portugal Group, played a fundamental role in the construction of these projects, in which new dams and reservoirs of significant dimensions are integrated.According to Portuguese legislation, with relevance to the RSB-Dam Safety Regulation (Decree-Law no. 21/2018 of 28 March), the DTA-Technical Documents to Support the RSB and taking into account the seismic risk associated with the region where the dams were built, it was recommending the implementation of a set of Seismic Monitoring Systems (SMS) to characterize the seismic actions and the respective structural response, as well as the assessment of the reservoirs induced seismicity.For that, it was necessary, in the design phases, to carry out several studies to define the type of dynamic monitoring systems, especially those related to the seismic monitoring systems (SMS). In their most extensive configuration, these systems, based on triaxial accelerometers sensors, may incorporate remote stations installed along the reservoirs for studying the propagation of seismic actions. For the higher dams, and to ensure a good characterization of the dynamic behaviour, continuous dynamic monitoring system (CDMS) was also installed.This paper presents the main aspects of the legislation, refers the main studies and methodologies that were used, and the general aspects of the regional geological and tectonic framework. Also, is presented several seismic monitoring systems that were implemented by EDP, namely those related to the hydroelectric projects of Baixo Sabor, Foz Tua, Ribeiradio and Alto Ceira II dams.

This paper focuses on the experience gathered from the continuous dynamic monitoring of Cahora Bassa dam, a 170 m high arch dam in Mozambique, over the past decade. The installed Seismic and Structural Health Monitoring system was designed to continuously record acceleration time series in several locations in the dam body (crest gallery) and near the dam-rock interface, under ambient/operational vibrations and during seismic events, using uniaxial and triaxial accelerometers. The system was complemented with the development of software for automatic modal identification and automatic detection of seismic vibrations. The numerical simulations are carried out using a 3D finite element program, based on a solid-fluid coupled formulation to simulate the dam-reservoir-foundation system, considering dam-water dynamic interaction and propagation of pressure waves throughout the reservoir. The main experimental outputs are presented and compared with results from 3D finite element analysis, including the evolution of identified natural frequencies over time, vibration mode shapes for specific water levels, and the dynamic response in accelerations under seismic ground motion.

Neste trabalho efetuam-se estudos de simulação numérica da resposta sísmica de uma grande barragem abóbada, considerando uma dada lei de amortecimento de Rayleigh com vista a analisar a influência da cota da albufeira. A modelação do sistema barragem-fundação-albufeira é efetuada com um modelo coupled, baseado numa formulação em deslocamentos e pressões, que permite simular a interação dinâmica barragem-albufeira considerando a propagação de ondas de pressão na albufeira. A discretização do sistema coupled é efetuada utilizando elementos finitos 3D com 20 nós. A resposta sísmica é calculada por meio de integração direta no domínio do tempo com base no método de Newmark. São apresentados os resultados da análise sísmica de uma barragem com 290 m de altura, utilizando acelerogramas sísmicos em três direções, com aceleração de pico máxima de 0.3g na direção montante-jusante. Nomeadamente, analisam-se os campos de deslocamentos e de tensões no corpo da obra para diferentes cotas de água na albufeira.

A determinação da resposta dinâmica das obras e o acompanhamento da evolução do seu comportamento durante as várias fases da vida é muito importante, estando inserido nas atividades do controle de segurança estrutural. A realização de ensaios de vibração forçada em barragens de betão para a determinação do comportamento dinâmico continua a ser uma das técnicas mais fiáveis nesta área. Nesta comunicação descreve-se a metodologia de ensaio, e apresentam-se os resultados relativos a um caso de estudo, referente à caraterização do comportamento dinâmico da barragem do Baixo Sabor. Foi desenvolvido um modelo numérico, com representação do sistema barragem-albufeira-fundação, para apoio na preparação do ensaio e interpretação dos resultados experimentais.

Os trabalhos de escavação para a implantação de grandes obras, (barragens, centrais subterrâneas, tuneis, etc.) utilizam frequentemente metodologias de desmonte da rocha com recurso a explosivos. Esta técnica sendo rápida e eficientemente produtiva, obriga ao controle da propagação de vibrações no meio circundante com ênfase ao parque edificado e respetivas infraestruturas.Recentemente foram efetuadas obras de aumento da capacidade de descarga de uma barragem de betão, nas quais, foi necessário efetuar desmonte de rocha com o recurso a explosivos nas imediações da barragem existente.Estes pressupostos impulsionaram ao desenvolvido de um modelo numérico híbrido descontínuo de elementos discretos e elementos finitos recorrendo ao 3DEC, representando os blocos da abóbada, as juntas de contração e o maciço de fundação. O objetivo deste modelo é estudar o efeito das vibrações provocadas pelas explosões no comportamento da barragem de betão e respetiva fundação, avaliando a sua segurança estrutural. A correta modelação do comportamento da fundação é fundamental para uma avaliação estrutural adequada.No presente trabalho apresentam-se os resultados do modelo numérico comparando com as medições de velocidades efetuadas em vários pontos da fundação e da estrutura no decorrer das obras, sendo posteriormente analisado os efeitos na barragem. O presente trabalho, deu início ao desenvolvimento de um modelo numérico capaz de representar a resposta da estrutura às vibrações, minimizando a subjetividade da classificação do seu grau de resistência.A elaboração deste modelo numérico permitiu desenvolver novas abordagens para a simulação das explosões, da propagação ao longo do maciço e respetivos efeitos na estrutura. Estas abordagens, devidamente adaptadas, são passiveis de serem implementadas em estudos futuros.

. The nowadays-available dynamic monitoring equipment integrating very sensitive low noise sensors creates an opportunity to implement continuously operating dynamic monitoring systems in dams and validate the suitability of these systems to monitor such massive structures with the goal of detecting damage. The detection of abnormal structural behaviour, that may indicate the occurrence of damage, can be based on control charts and is associated with shifts in the modal parameters values that are not explained by other physical phenomena but a change in the structure

In this paper the seismic response of a large arch dam (290 m high), located in a high seismicity region, is analysed. The goal is to study the influence of the reservoir water level in the dam

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.