Publicações

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.

N/A

N/A

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

Neste trabalho apresentam-se os primeiros resultados obtidos com um sistema de observação do comportamento dinâmico instalado na barragem do Cabril, em que se mostra a evolução no tempo das primeiras quatro frequências naturais da obra durante um período de observação de cerca de um ano. Descreve-se um conjunto de rotinas implementadas para a identificação automática das frequências naturais da estrutura; a filosofia de gestão dos dados que são adquiridos em contínuo; o controlo remoto do sistema e a transmissão de dados via internet, entre o centro de controlo do sistema instalado em obra e o centro de análise situado no Laboratório Nacional de Engenharia Civil (LNEC). Este sistema, baseado na medição de vibrações em contínuo, permite a caracterização do comportamento dinâmico desta obra ao longo do tempo, tendo em conta os diversos tipos de excitação, tais como o vento, a vibração provocada pelo funcionamento dos grupos de produção de energia e dos órgãos de descarga, micro tremores e sismos de média e elevada intensidade.

Rock blasting in urban settings is always extremely demanding in what regards the control of ground vibrations and other environmental impacts. Extensive underwater blasting was performed in the Leixões Harbour, an important harbour surrounded by a dense urban mesh. Macro-seismometers were installed in the perimeter and recorded more than one thousand blasts. After completion of the works classical curve fitting statistical analysis of peak particle velocity (PPV) as a function of charge and distance to the blast was performed. PPV spatial distributions were determined for the duration of the construction and maps of ground peak vibration velocity drawn. The results showed that the accuracy of the attenuation law is within the usual range for this kind of phenomenon. However, factors like terrain morphology or geology variations cannot easily be included in a regression law but can be treated in a simple numerical model. A dynamic finite-difference model was developed and the influence of these features was studied thus increasing the understanding of the problem and providing valuable insights into some aspects of the usually large dispersion in the PPV.

The presented work explores a combination of strain localization methods and strong discontinuity ap-proaches to remove the flaws (stress-locking and mesh bias dependence) of the classical strain localization methods, and reduce the sophistication of the strong-discontinuity based methods. The concept of strong discontinuity is initially substituted by that of weak discontinuity capturing the displacement jump through its distribution (smearing) in a finite length: the oriented with of a finite element through which the fracture passes in a rather diffuse manner. In other words, the classical strain localization concept is brought to the approach, no strong discontinuity enrichment is made and standard constitutive models are used in a classi-cal strain localization setting. The standard mesh refinement recovers the strong discontinuity concept by taking the element width to zero. However, in order to remove the spurious mesh orientation dependence, in a second stage specific localization modes are injected, via mixed finite elements formulations, to the path of elements that are going to capture the cracks. These modes, as well as their injection time, are character-ized from the information provided by the SDA. Then, the obtained approach enjoys the benefits of the strong discontinuities one, at a complexity similar to the classical, and simpler, localization methods.

A 3D spherical rigid particle discrete element formulation based on the Discrete Element Method, DEM, which has been used to model concrete, is described. The model has been shown to give a good agreement in terms of peak strength, fracture localization and crack patterns for various load conditions. An explicit formulation for the reinforcement model which allows the model to be applied to reinforced concrete is presented. The reinforced rigid particle model is validated against known shear transfer tests due to dowel action. It is shown that the model is able to predict the influence of the dowel stiffness and the localized fracture in the vicinity of the initial crack.

The paper presents the 2 main methods for the determination of the in-situ state of stress in rock masses, developed by the LNEC, and refers to a practical case in which they were used, at an underground powerhouse in northern Portugal.

Abstract. The application of discrete element models based on rigid block formulations to theanalysis of masonry walls under horizontal out-of-plane loading is discussed. The problemsraised by the representation of an irregular fabric by a simplified block pattern are addressed.A test problem provides a comparison of various regular and random block patterns, showingtheir influence on the failure loads. An example of application of a rigid block model to a wallcapacity problem is presented.

This paper presents a study, which describes the influence of the dynamic behaviour of the intake tower on the experimental results obtained from operational modal analysis of Cabril dam. A 3D finite element model, for the intake tower of Cabril dam, was developed in order to study the dynamic behaviour of this neighbour structure of the dam. The main dynamic parameters computed and evaluated experimentally for this structure are summarized and discussed, to understand how they can interfere in the modal identification of Cabril dam.

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

A libertação do estado de tensão inicial nos maciços rochosos é a principal acção a considerar em escavações subterrâneas. Como o estado de tensão é muito influenciado pela topografia e por condições geológicas particulares de cada local, a sua determinação a partir de ensaios de campo necessita de uma abordagem particular que, tendo em conta a natureza pontual dos ensaios e a sua variabilidade, permita estimar o estado de tensão global no maciço. Apresentam-se os ensaios realizados para o projecto de uma central subterrânea, com destaque para a modelação numérica que permitiu integrar os resultados dos ensaios e determinar o estado de tensão global mais provável. Os modelos usados permitiram considerar no estado de tensão inicial o efeito erosivo do rio ao escavar o vale e da abertura das galerias onde os ensaios foram executados.

This paper deals with issues related to the evaluation of design parameters from some types of in situ and laboratory tests performed, during the geotechnical investigations, to characterize the most relevant geotechnical properties of the rock mass and also the actions. Some considerations regarding safety evaluation and limit state design are presented. Several types of Rock Mechanics tests are introduced in some detail, and a few application examples covering different Rock Engineering projects are presented to show how test results can be analysed to determine their values to be used in the design. The following examples are shown: triaxial tests to determine the strength of the intact rock, a joint network study for a dam foundation, laboratory shear tests to assess the shear strength of rock joints, flat jack and overcoring tests to estimate the in situ state of stress for an underground cavern, and borehole dilatometer and large flat jack tests to evaluate the deformability of a concrete dam foundation.

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

N/A

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

N/A

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

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

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

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto DEMRock6m do P2I/LNEC 2013-2020. Os resultados da atividade desenvolvida são analisados e avaliados em face dos objetivos inicialmente previstos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto MEBAD do P2I/LNEC 2013-2020, no período 2016-2023. Os resultados da atividade são analisados e avaliados, em face dos objetivos previstos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto RockGeoStat do P2I/LNEC 2013-2020. Os resultados da atividade desenvolvida são analisados e avaliados em face dos objetivos inicialmente previstos.

The main goal of this report is to present DamDamage3D1.0, a 3D finite element-based program for non-linear static analysis of arch dams, developed using MATLAB. The non-linear simulations are performed using a damage law and an iterative numerical method based on the stress-transfer technique, considering the redistribution of unbalanced forces in each iteration due to material damage. The concrete

The main goal of this report is to present DamDamage3D1.0, a 3D finite element-based program for non-linear static analysis of arch dams, developed using MATLAB. The non-linear simulations are performed using a damage law and an iterative numerical method based on the stress-transfer technique, considering the redistribution of unbalanced forces in each iteration due to material damage. The concrete

In this work we present the version 1.0 of the GDams2D 1.0 program developed for 2D analysis of gravity dams using the finite element method. This initial version of the program is prepared to analyze the structural behavior of gravity dams for static loads, considering linear-elastic behavior, and using Lagrange finite elements of 4 sides, with 9 nodal points. The GDams2D 1.0 program, developed in MATLAB, includes a module for automatic generation of meshes with a great level of refinement (generated from coarse meshes of quadrilaterals, with 4 nodal points at the vertices) and is designed for easy adaptation to non-linear analyzes, using stress-transfer modules such as those recently developed for the DamSlide3D and DamDamage3D programs. After a brief reference to the fundamentals of solid mechanics and to the simplified hypotheses of plane elasticity, the Fundamentals of the Finite Element Method (FEM) are presented, referring in particular the formulation of the four-node, linear and isoparametric, finite element (FE4nos), with two translation d.o.f per node, and the quadrangular FEs of 9 nodes (FE9nos) used in GDams2D 1.0. Based on some examples of application to simple 2D structures whose response is knownanalytically, the advantages of FEs are emphasized in relation to FE4nos and the verification and operability of GDams2D 1.0 is made using various discretizations. Finally, the case of a gravity dam (25 m high) is presented. The dam

The main objective of this work is the development and presentation of a three-dimensional finite element program, DamSlide3D, to study the behavior of gravity dams for scenarios of sliding through the dam-foundation interface. The DamSlide3D, developed using MATLAB, includes cube-type finite elements with 20 nodal points ("serendipity") and finite interface elements with 16 nodal points (joint elements). Initially, we present the fundamental equations of Solid Mechanics, referring to the main simplified hypotheses considered in the computationally implemented formulation, which is presented mathematically as a problem of boundary values using a displacement formulation. For the structure body and for the foundation, the hypothesis of isotropic materials with linear elastic behavior is assumed and for the interfaces the hypothesis of non-linear behavior is considered using the Mohr- Coulomb criterion. The DamSlide3D input data is provided in an excel file and includes structure geometry data, material properties, support conditions and load parameters. As output, the program graphically displays the stress field (principal stresses) and the displacement field (deformed structure). The program was verified throughout three numerical tests with known theoretical solutions. In these tests a simple structure was used, composed by a column discretized in 3DFE. At the contact surface between the column and the base (horizontal surface) it was considered an interface discretized using joint finite elements. A plane surface that crosses the column with a given slope is also considered, discretized using the same type of joint finite elements. In the first test, the field of elastic stresses at the base, due to self-weight (SW) and hydrostatic pressure (HP), was compared with the theoretical results. In the second test the nonlinear column response was studied for different values of thefriction angle at the inclined interface (in this test the structure is only submitted to SW). In the third test, for the main SW + HP loads, the stability of the column is studied for a variation of the friction angle, and for a variation of the water level. In these three numerical tests the results were always consistent with the theoretical solutions. Finally, as an example of application, a gravity dam structural behavior was analyzed considering the non-linear behavior in the dam-foundation interface. The dam was subjected to self-weight and hydrostatic pressure. A parametric study was developed in order to study the dam stability for differentvalues of water level and friction angle.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto CoMatFail até ao final de 2017. É feita a apreciação da atividade desenvolvida, nomeadamente quanto ao grau de cumprimento do plano de trabalhos, bem como dos objetivos específicos e dos indicadores de desempenho propostos na ficha de projeto. São ainda referidas as aplicações dos resultados da investigação em trabalhos contratados ao LNEC e as candidaturas a financiamento externo desenvolvidas no âmbito do projeto. Inclui-se em anexo a ficha do projeto atualizada, que contempla a revisão do plano de trabalhos.

Neste relatório apresenta-se de forma sucinta a descrição da atividade de investigação realizada no âmbito do projeto DEMRock6m no período 2016-2017. Os resultados da atividade são analisados e avaliados em face dos objetivos inicialmente previstos, sendo proposta uma revisão do plano de atividades para os próximos três anos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto RockGeoStat no período 2016-2017. Os resultados da atividade são analisados e avaliados em face dos objetivos inicialmente previstos, sendo proposto um prolongamento do projeto até ao final de 2018.

This document presents a back analysis procedure for identification of the elastic parameters of transversely isotropic rock cores, containing an overcoring triaxial strain probe, from the strains measured during a biaxial test. A three-dimensional finite element model was developed to simulate the biaxial test on the overcored rock specimen and to compute the strains at the location of the strain gauges. Different optimisation algorithms were tested and the most suitable one was selected. The back analysis procedure was tested for identification of the five elastic parameters and the two orientation angles that characterise a transversely isotropic rock core. In spite that, with the developed methodology, convergence was reached and all those parameters could be identified, sensitivity analyses demonstrated that the results obtained were not stable and therefore they were not reliable. By introducing constrains based on common practice and previous experience, a stable and robust methodology was achieved: the three elastic parameters, E1, E2 and ?2, are reliably identified using the value of G2 calculated with Saint-Venant’s expression and a fixed value of ?1, while the orientation parameters are obtained from observation of overcored rock. Analysis of the results shows that application of this methodology represents an enormous step forward when compared with the traditional use of isotropy. Besides, the methodology is general and can also be used with other types of overcoring equipment. The five elastic parameters and the two orientation angles obtained can then be used, together with the overcoring strains, to compute the complete in situ state of stress.

This document presents the work developed by the PhD student Margarida Espada in the scope of the course unit Risk Analysis in Geotechnical Works of the Doctoral Program in Civil Engineering of the Faculty of Engineering of the University of Porto (FEUP). This work presents a reliability analysis, using the response surface method (RSM), for the case study of the left bank excavation slopes of the Baihetan arch dam foundation, which is one of the case studies of Margarida Espada's PhD thesis. The aim was to approximate an implicit limit state function by computing safety factors, using a discrete element model of the Baihetan left bank developed in 3DEC software, where the shear strength parameters of two important rock discontinuities were considered as random variables. The probability of failure was then obtained through an iterative process, using approximation methods. This work presents the 3DEC model developed to analyse the stability conditions in the Baihetan left bank and the results of the reliability analysis.

O problema da solução das equações de Navier Stokes é abordado neste trabalhopropondo-se uma técnica de representação das incógnitas deslocamentos e pressõesvariáveis no espaço e no tempo em série de Delta de Dirac e suas derivadas no tempocujos coeficientes se determinam com base na solução de sistemas de equaçõesdiferenciais definidos no espaço (problema com três variáveis espaciais independentesque pode ser estudado pelo método de Monge).

Neste relatório apresentam-se as equações básicas da elastodinâmica linear, as soluçõesfundamentais e o teorema da representação no domínio de tempo e de frequência.Para movimentos finitos de casca formula-se o teorema dos trabalhos virtuais e a suaimplementação pelo método dos elementos finitos.

Neste relatório apresentam-se os principais aspectos da modelação sísmica de barragensabóbada. Assim propõe-se: modelos numéricos de geração de sismos por uma falha; aforma como o sismo actua na barragem; modelos para estudar a influência da albufeirana vibração do conjunto; métodos para solução das equações do movimento; e novasformulações de elementos finitos para o problema estrutural.

In pressure tunnels and shafts, in addition to the mechanical effect that excavation has on the rock mass and the disturbance that it introduces in the water flow, also the contained water can interact from the mechanical and hydraulic points of view with the rock mass. Seepage in fractured rock masses is dominated by the flow that takes place through the joints, and this is highly d(;pendent on their properties, namely aperture and roughness. Joint aperture, in tum, i::; very sensitive to stress changes. Special attention must therefore be paid to the joints in hydromechanical analyses. In this report are presented some studies that were carried out for the hydromechanical characterization of joints of the Alto Lindoso rock mass and numerical simulations of the hydromechanical behaviour of two selected sections of the high pressure circuit.