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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

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

The out-of-plane flexural bending capacity of masonry is a fundamental property for understanding the behavior of masonry structures. This study investigates the behavior of unreinforced masonry wallettes subjected to combined compression-flexural loading using the discrete element method (DEM), and provides a novel framework to estimate the masonry strength. A simplified micro-modeling strategy is utilized to analyze a masonry wallette, including the variation of the mechanical properties in masonry units and joints. Stochastic DEM analyses are performed to simulate brickwork assemblages, assuming a strong unit-weak joint material model typical of most masonry buildings, including historical ones. Once the proposed computational approach is validated against the experimental findings, the effect of spatial and non-spatial variation of mechanical properties is explored. Two failure types are identified: joint failure and brick failure. For each failure mechanism, the variability of the response and the effects of the modeling parameters on the load-carrying capacity is quantified. Afterward, Lasso regression is employed to determine predictive equations in terms of the material properties and vertical pressure on the wallette. The results show that the most important parameters changing the response are the joint tensile strength and the amount of vertical stress for joint failure, whereas the unit tensile strength dominates the response for brick failure. Overall, this research proposes a novel framework adopting validated advanced computational models that feed on simple test results to generate data that is further utilized for training response prediction models for complex structures.

Discrete element models are being increasingly applied to model rock failure processes.Bonded-particle models, based on circular or spherical particle systems, have been successfully usedfor two decades. More recently, bonded-block models, using polygonal or polyhedral elements, have proven to be a powerful alternative. This paper describes the basis of the application of these models in the numerical simulation of failure in rock materials. The critical governing parameters are identified, and their influence is discussed. The model calibration procedure based on the analysis of laboratory tests is discussed. An application example of an underground excavation problem is presented using a simple bonded-block model employing rigid blocks and a bilinear softening contact model. The results show the capability of this approach to reproduce observed failure modes involving block fractures.

Masonry arches are a fundamental component of historical structures. The assessment of the vulnerability ofthese heritage constructions to seismic loading requires reliable and efficient numerical models. Discrete element models are an alternative to finite element models, being particularly effective in modelling collapse mechanisms created by shearing and separation of the units along the joints. Discrete element codes typically rely on explicit methods of integration of the equations of motion for dynamic analysis, which may require large run times when the recommended stiffness-proportional component of Rayleigh damping is applied. A novel approach is proposed using an alternative damping model, Maxwell damping, which involves placing multiple spring-dashpot elements in the joints, in parallel with the standard stiffness springs. This damping model is tested in the dynamic analysis of masonry arches, under pulse and earthquake loading. The results obtained in this early investigation show a good performance in the simulation of collapse under dynamic loads, in general agreement with the analyses conducted with classical stiffness-proportional damping, but reducing significantly the computational effort.

Rigid particle models based on the discrete element method (DEM) have been adopted to model creep, fracture, and the viscoelastic behaviour of asphalt mixtures considering an irregular micro-structure and particle contacts. Within a DEM framework, the Burgers contact model, which is known to have a narrow frequency and temperature range, is usually adopted to model viscoelastic properties. In this study, a new explicit three-dimensional generalised Kelvin (GK) contact model formulation for the DEM model is proposed for asphalt materials. The model is implemented following two different methodologies (GK and GK). The models are validated in uniaxial tension-compression sinusoidal tests for predicting the dynamic modulus () and phase angle (

Encapsulated rejuvenators embedded in asphalt mixtures are a promising technology toextend the service life of asphalt pavements. However, their effects on the asphalt mixture

The structural rehabilitation of historic/traditional rubble masonry wall constructionsrequires consolidation and retrofitting solutions to be employed in order to withstand dynamic loads,high vertical loads, and differential settlements. One of these strengthening techniques is basedon the use of steel bar connectors perpendicular to the wall, considered individually or integratedinto more complex strengthening techniques. The aim of this study is to evaluate numerically thestrengthening effect of transverse steel connectors on rubble masonry walls. With this purpose, a 2Dparticle-reinforced model (2D-PMR) was devised and applied to model uniaxial compression tests.The results presented show that predictions calculated using the proposed 2D-PMR model are veryclose to known experimental results, particularly in the corresponding failure modes, the increase ofthe maximum uniaxial compression value, and ductility. Parametric studies are also conducted byvarying the diameter of the steel bars and the level of strengthening to assess the influence of thebar-bond effect and lateral plates. The presented parametric numerical studies show that (i) a two-level strengthening solution guarantees a similar response to the three-level strengthening solutionadopted in the experiments; (ii) it is not relevant to apply a grout injection during the applicationprocess of the steel connectors if lateral plates are adopted; and (iii) the 2D-PMR model can be usedin the definition of the steel bar diameter and properties; as shown, a smaller (8 mm) bar diameterpredicts a similar strengthening effect to the (12 mm) bar size adopted in the experiments. Given theperformance of the proposed 2D-PMR model, further work is underway that will allow the 2D-PMRmodel to numerically assess other reinforcement techniques, namely, reinforced micro-concrete layersand textile reinforced mortar.

This study highlights the continued need for numerical simulation methods to predict the earthquakeresponse and damage of masonry mosques, despite recent advances in research. TheKamanl

Circular/spherical rigid particle models that were initially applied to rock fracture studieswere not able to match the ratio of the compressive strength to tensile strength that occurs in rock.In addition, the predicted macroscopic friction angle was much lower than the known hard rockexperimental values. Several enhancements have been proposed to address these issues, namelythe use of a clumped particle logic or the adoption of polygonal/polyhedral grain structures, eitherrigid or flexible. In this work, a flexible 2D DEM based particle model (PM) that allows deformableparticles to interact in a simplified way is presented. The proposed flexible PM model keeps thecontact interaction simplicity and the reduced computational costs characteristic of circular rigidparticle models. The PM model is tested using biaxial tests and Brazilian tests. A discussion re-garding the influence of the grain deformability on the macroscopic elastic and strength response ispresented. It is shown that, when compared with a rigid model, the proposed flexible PM modelpredicts more reasonable indirect tensile strength to direct tensile strength ratio and requires asmaller value of contact fracture energy to give a good agreement with known experimental data.It is also shown that the proposed flexible PM model can predict a behaviour similar to that ob-tained using a flexible PM model through inner particle discretization that is more computationallydemanding.

O comportamento resultante da micro-fendilhação generalizada e/ou da presença de macro-fendas é dificilmente caracterizado a partir de uma formulação contínua. Por este motivo, na modelação da fractura em geo-materiais têm sido propostos modelos detalhados de partículas, inicialmente desenvolvidos para estudo do comportamento micro-mecânico de meios granulares, que têm em consideração a interacção física entre as partículas e a influência da estrutura granular do material. Neste trabalho, é apresentado um modelo de partículas rígidas esféricas que tem sido desenvolvido tendo em vista o estudo da fractura no betão e em rocha. O modelo é validado em ensaios triaxiais, e em ensaios de compressão diametral, em rocha, sendo estudada a influência do modelo constitutivo do contacto.

The safety control of large dams under static and dynamic loads, involving observation data and numerical modeling, is now one of the challenges of structural engineering. The complexity of the dam-reservoir-foundation geometry, the presence of different types of discontinuities, the water-structure interaction, the influence of thermal and water level variations, the development of deterioration processes over time and the occurrence of exceptional events such as major floods or earthquakes, makes the structural safety control of large dams an activity that requires a continuous updating, both in terms of the equipment for measuring, transmission, and storage of the observation data, and in terms of computer applications to support the automation process of collecting, processing, analysis and management of all information required to the safety control. The recent LNEC and EDP experience on the revision of the monitoring system of Cabril dam, the highest portuguese arch dam, is presented as a case study in this paper. After a brief presentation of the main dam characteristics

Esta comunicação descreve um trabalho de monitorização e estudo da geração e propagação das vibrações produzidas por uma operação subaquática de desmonte de rocha que teve lugar no Porto de Leixões em 2006. Terminada a monitorização, que exigiu um acompanhamento cuidado dos impactos dos rebentamentos na malha urbana circundante, definiram-se leis empíricas de atenuação e um modelo de inteligência artificial (redes neuronais perceptrão multicamada) que forneceram estimativas da velocidade máxima de vibração em função da carga e da distância. Estes métodos tornaram possível a definição de distribuições espaciais de vibração para todo o desenrolar da obra. Finalmente, desenvolveu-se um modelo dinâmico de diferenças-finitas tridimensional de parte da obra, no qual foram estudados diversos cenários de geração e propagação. Este modelo permitiu, por uma lado extrair conclusões qualitativas interessantes sobre a propagação da vibração deste caso, e por outro comprovar a aplicabilidade da modelação numérica nesta classe de problemas, tanto em obras superficiais como em obras subterrâneas, tais como a escavação de túneis e cavernas em rocha.

A aplicação de modelos de identificação modal na análise de resultados de ensaios de vibração ambiental efectuados na barragem do Cabril (a maior barragem portuguesa - abóbada simples com 132 m de altura) mostrou a ocorrência de picos espectrais importantes, cuja frequência não correspondia às conhecidas frequências naturais da obra, tendo-se colocado a hipótese desses picos estarem relacionados com o comportamento dinâmico da torre das tomadas de água

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.

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 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.