Publications

The Baixo Sabor hydroelectric power plant, located in the northeast of Portugal, includes a reservoir with a storage capacity of 630 million m3 of water created by a concrete double-curvature arch dam, 100 m high, which was equipped with a 20-channel vibration based structural health monitoring system.This paper, apart from describing the dam, presents the main characteristics of the monitoring system and the results obtained during the first 6 months of operation and the first filling of the reservoir. These results include in particular the characterization of the accelerations amplitude and the evolution of the dam modal parameters (natural frequencies, modal damping ratios and mode shapes). It is particular interesting to observe the influence of the water level on the modal parameters and the development of statistical models to mitigate this effect.

Earthquakes cause severe damage to masonry structures due to inertial forces acting in the normaldirection to the plane of the walls. The out-of-plane behavior of masonry walls is complex anddepends on several parameters, such as material and geometric properties of walls, connectionsbetween structural elements, the characteristics of the input motions, among others. Differentanalytical methods and advanced numerical modeling are usually used for evaluating the out-ofplanebehavior of masonry structures. Furthermore, different types of structural analysis can beadopted for this complex behavior, such as limit analysis, pushover, or nonlinear dynamic analysis.Aiming to evaluate the capabilities of different approaches to similar problems, blind predictionswere made using different approaches. For this purpose, two idealized structures were tested on ashaking table and several experts on masonry structures were invited to present blind predictions on theresponse of the structures, aiming at evaluating the available tools for the out-of-plane assessment ofmasonry structures. This article presents the results of the blind test predictions and the comparisonwith the experimental results, namely in terms of formed collapsed mechanisms and control outputs(PGA or maximum displacements), taking into account the selected tools to perform the analysis.

The analysis of the shaking table test of a 3-wall stone masonry structure performed with a discreteelement model is presented. The numerical model, created with the code 3DEC, employed a rigidblock representation and a Mohr-Coulomb joint model. Joint stiffness calibration to match theexperimental natural frequencies is discussed, as well as the boundary conditions to simulate theshake table. Comparisons are made with themeasured displacements at key locations, and themodesof deformation and fracture of the walls. The DEM model was able to reproduce important features ofthe shaking table tests. The experimental deformation and near collapse patterns were clearlyidentifiable in the numerical simulations, which produced displacements within the observed ordersof magnitude, for the various levels of excitation.

This paper 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

The 1:10 scale model of the 15th century Mustafa Pasha Mosque in Skopje, that underwent a comprehensiveshake table program, is modeled by the discrete elements approach. A rigid block model withnonlinear behavior concentrated at the joints was developed and calibrated by comparison with theobserved response. Time domain analyses of the discrete model were performed under the various levelsof dynamic excitation used in the shake table test. Under the lower levels of input, the time and frequencydomain characteristics of the shake table experimental response were fairly well simulated by thenumerical model. This model also predicted well the zones and the level of damages. For the higher inputlevels, the comparison was less satisfactory. Overall, the discrete element approach showed the capabilityto handle the dynamic nonlinear modeling of relatively complex masonry structures.

This work investigates tensile crack propagation in concrete gravity dams by using some recently developed numerical techniques (crack-path field and strain injection techniques). The work carefully addresses aspects related to mesh independence, robustness and computational cost, which are the main issues in fracture modeling. The novel technique consists of a procedure to insert, in the selected domain areas, specific strain fields for enhancing the performance of the underlying finite elements in modeling fracture. Representative numerical simulations of concrete dams show the accuracy and robustness of the methodology.

Block models have been shown to provide a realistic representation of the behavior of many types of masonry structures under static and dynamic loads. When the strength of the units is such that movements along the joints govern the behavior, it is acceptable to make the simplifying assumption that blocks act as rigid bodies. This assumption is particularly useful when dealing with seismic problems, for which the computational times for time domain analysis may be substantial. In this paper, the application of discrete element models for dynamic analysis of masonry structures is addressed. The emphasis is on the seismic behavior of block stone masonry, but the treatment is general to cover other types of masonry. First, the assumptions involved in the choice of a block representation are discussed, stressing in particular the case of rigid block models. Numerical issues are examined, including contact models, calculation of natural frequencies, time stepping algorithms, damping and boundary conditions. A review is presented of modeling examples published in the literature for various types of masonry structures. The choice of numerical representation and its main features are discussed for each case.

Much research in recent years has focused on the seismic analysis of concrete and earthfill dams,and few works have addressed the case of masonry dams. The structural behavior of masonrydams is controlled essentially by its discontinuous nature, which may induce significant nonlinearresponse during an intense earthquake. In this article, a numerical tool based on the Discrete ElementMethod is presented, aimed at the static, dynamic, and hydromechanical analysis of masonry gravitydams. The use of discontinuous models is mandatory for the study of failure mechanisms involvingthe masonry discontinuities, the dam-rock interface or the rock mass joints. The Discrete ElementMethod is able to assemble continuous and discontinuous meshes simultaneously in the same model,providing a versatile tool to consider various assumptions and levels of analysis, ranging from simplifiedto detailed structural representations. A comprehensive study of the seismic behavior of LagoaComprida Dam, located in Portugal, is presented. Both continuous and discontinuous models weredeveloped to assess the main failure mechanisms, including overstress, partial and global sliding,and overturning.

The analysis of the shaking table test of a 3-wall stone masonry structure performed with a discreteelement model is presented. The numerical model, created with the code 3DEC, employed a rigidblock representation and a Mohr-Coulomb joint model. Joint stiffness calibration to match theexperimental natural frequencies is discussed, as well as the boundary conditions to simulate theshake table. Comparisons are made with themeasured displacements at key locations, and themodesof deformation and fracture of the walls. The DEM model was able to reproduce important features ofthe shaking table tests. The experimental deformation and near collapse patterns were clearlyidentifiable in the numerical simulations, which produced displacements within the observed ordersof magnitude, for the various levels of excitation.

A computationally affordable modeling of dynamic fracture phenomena is performed in this study by using strain injectiontechniques and Finite Elements with Embedded strong discontinuities (E-FEM). In the present research, classical strain localizationand strong discontinuity approaches are considered by injecting discontinuous strain and displacement modes in the finite elementformulation without an increase of the total number of degrees of freedom. Following the Continuum Strong DiscontinuityApproach (CSDA), stress

The Baixo Sabor hydroelectric power plant, located in the northeast of Portugal, includes a reservoir with a storage capacity of 630 million m3 of water created by a concrete double-curvature arch dam, 100 m high, which was equipped with a 20-channel vibration based structural health monitoring system.This paper, apart from describing the dam, presents the main characteristics of the monitoring system and the results obtained during the first 6 months of operation and the first filling of the reservoir. These results include in particular the characterization of the accelerations amplitude and the evolution of the dam modal parameters (natural frequencies, modal damping ratios and mode shapes). It is particular interesting to observe the influence of the water level on the modal parameters and the development of statistical models to mitigate this effect.

Minarets are important elements of mosques. These slender structures have suffered notable damage as a result of past earthquakes. In this paper three historical masonry minarets located in Istanbul, Turkey are studied in the inelastic range using the Discrete Element Method. They are the minarets of the Hagia Sophia Museum, Süleymaniye Mosque and Mihrimah Sultan Mosque. The selected minarets are 16th century structures having different heights and body diameters. Dynamic behavior is simulated by means of ten different loading configurations as real and simulated earthquake time histories. Nonlinear dynamic response is characterized by the relative horizontal and normal dislocations of adjacent drums along the minaret body, as well as by its top displacement, all normalized by the body diameter. Damage patterns and collapse mechanisms are studied.

Minarets are important elements of mosques. These slender structures have suffered notable damage as a result of past earthquakes. In this paper three historical masonry minarets located in Istanbul, Turkey are studied in the inelastic range using the Discrete Element Method. They are the minarets of the Hagia Sophia Museum, Süleymaniye Mosque and Mihrimah Sultan Mosque. The selected minarets are 16th century structures having different heights and body diameters. Dynamic behavior is simulated by means of ten different loading configurations as real and simulated earthquake time histories. Nonlinear dynamic response is characterized by the relative horizontal and normal dislocations of adjacent drums along the minaret body, as well as by its top displacement, all normalized by the body diameter. Damage patterns and collapse mechanisms are studied.

Release of the in situ state of stress is often the most relevant action during the excavation of underground structures in rock masses, such as powerhouse caverns for hydroelectric schemes, which are often excavated at great depth and have large dimensions. Design of the supports, namely using numerical models, requires an estimate of the magnitude and direction of the principal stresses. However, a large number of factors influence the in situ stress field and its characterisation is a difficult task. Besides, the number of tests carried out for determination of the in situ stresses in rock masses is usually small, due to cost and time constraints, and all the testing methods have limitations inherent to their nature.The paper presents methodologies for analysis of the stress field obtained from the results of in situ stress measurements using three methods: overcoring, hydraulic fracturing and flat jacks. These methodologies integrate all stress measurements and use numerical models of the rock mass that represent the ground topography, the lithology and the underground openings geometry, so that the most likely stress field in the zone of interest for the design of the underground openings is obtained. Instances of application to three underground powerhouses are presented.

Detailed particle models by taking into account the material grain structureexplicitly consider the material randomness, including a size limiter for damage localization.A VGMC3D contact model is presented that considers the polyhedral particle shape in anapproximate way. The VGCM3D flexible contact model is validated against knownexperimental data on a granite rock, namely triaxial tests and Brazilian tests.

Esta comunicação apresenta um estudo sobre a vulnerabilidade sísmica da igreja deKuño Tambo (Peru) com recurso ao Método dos Elementos Discretos. A avaliação docomportamento sísmico da igreja foi efetuada através de dois modelos numéricos,nomeadamente: (a) Modelo da secção transversal da parede da nave considerando amorfologia do aparelho da alvenaria, tendo por objetivo avaliar o seu comportamentopara fora do plano; (b) Modelo 3D da fachada com parte das paredes ortogonais danave, tendo por objetivo avaliar a sua resposta para fora do plano. Os resultados daanálise permitiram concluir que a ligação entre paredes ortogonais têm influênciasignificativa no comportamento da fachada.

Na presente comunicação é apresentado o estudo de caracterização dinâmica da barragem do Alto Ceira II recorrendo a métodos experimentais e numéricos. Foi efetuada a caraterização deste comportamento para as situações de albufeira vazia e cheia através da realização de ensaios de vibração forçada e da medição de ruído ambiente. A interpretação dos resultados das campanhas de ensaio e a estimação das características mecânicas médias do betão da barragem foi efetuada com o recurso a um modelo numérico calibrado com os resultados experimentais.

A determinação da resposta dinâmica das obras e o acompanhamento da evolução doseu comportamento durante as várias fases da vida é muito importante, estandoinserido nas atividades do controle de segurança estrutural. A realização de ensaiosde vibração forçada em barragens de betão para a determinação do comportamentodinâmico continua a ser uma das técnicas mais fiáveis nesta área. Nesta comunicaçãodescreve-se a metodologia de ensaio, incluindo os desenvolvimentos recentementeefetuados, e apresentam-se os resultados relativos a um caso de estudo, referente àcaraterização do comportamento dinâmico da barragem do Baixo Sabor. Foi desenvolvidoum modelo numérico para apoio na preparação do ensaio e interpretação dosresultados experimentais.

The characterization of the dynamic behavior of an arch dam, and its evolution throughout the structure

Dynamic fracture phenomena are studied employing low cost computational toolsbased on Finite Elements with Embedded strong discontinuities (E-FEM). Fracture nucleationand propagation are accounted for through the injection of discontinuous strain and displace-ment modes inside the finite elements. The Crack Path Field technique is employed to computethe trace of the strong discontinuity during fracture propagation.Unstable crack propagation and crack branching are observed upon increasing loadingrates. The variation in terms of crack pattern and energy dissipation is studied and a good cor-relation is found between the maximum experimental crack speed and maximum dissipation atthe onset of branching. Comparable results are obtained against simulations employing supra-elemental techniques, such as phase-field and gradient damage models, considering coarserdiscretizations which can differ by two orders of magnitude.

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.