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A series of very shallowearthquakes occurred in the late afternoon ofMay 11, 2011 near the city ofLorca and 55 kmfromMurcia in Spain. The main shock (Mw5.2) occurred at 17:47 (UTC), causing9 deaths and over 250 injured with widespread damage and panic.The strong motion generated by the event was recorded in the town of Lorca near the epicenter.It was a short duration record with peak ground acceleration higher than 0.37 g. In the vicinity ofthe recorded motion (360 m), there is an obelisk composed of 11 frustums resting on a 1-m-highfoundation with a total height of 5.71 m. The general motion observed after the event was of theorder of 1 cm (translation) for most interfaces, while at the upper two, the motionwas of rotationof 2° to 4° in the counterclockwise direction seen from above.In order to understand the behavior of such a structure, numerical simulations of the obeliskwereperformed with the discrete element code 3DEC, employing a rigid block model. The deformationis assumed to be concentrated at the joints between the blocks, governed in the linear range by thejoint stiffness parameters, in the normal and shear directions. In the nonlinear range, a purelyfrictional behavior is adopted, without tensile strength. An elastic joint was introduced at thebase of the model, simulating the deformability of the foundation. The global model deformabilitywas calibrated by means of in situ dynamic characterization.Dynamic analyses were performed, taking into account the large displacement effects that governthe block rocking motion, applying the recorded seismic motion in the 3 directions. Parametricstudies were undertaken to assess the influence of the various input parameters. The modelresults are compared with the observed permanent displacements of the structure.

It is known that rigid circular particle models proposed in the literature do not properly reproduce therock friction angle and the rock tensile strength to compressive strength ratio. A 2D rigid particle model is herepresented which tries to overcome these issues while keeping the simplicity and the reduced computational costs characteristic of circular particle models. A particle generation algorithm is adopted which generates polygonal shape particles based on the Laguerre

The hydrodynamic interaction between a solid (dam and foundation) and a fluid(reservoir) should be considered whenever the reservoir is present. A fluid displacement-basedformulation is presented, and two fluid elements are proposed: an 8-node fluid cubic elementsub-integrated (F8N-1GP), and an 8-node mixed discretization cubic element formed by twoindependent 5 tetrahedra overlay (F8N-MDE). A forced vibration analysis, and a maximumdesign earthquake equivalent loading, are carried out in two different dams. The performanceof the proposed fluid displacement-based finite elements is compared with the performanceobtained with the degenerated solid (DS) concept, and with the simplified Westergaard addedmass approach. It is shown that the SD approach can lead to erroneous pressure values at thefluid domain, and that the penalty term which prevents circulation modes needs to be consideredwhen less regular meshes are adopted in the fluid discretization.

Apresenta-se a formulação explícita de um modelo hidromecânico em pequenos deslocamentos, baseado numa tecnologia de elementos finitos de junta. O modelo hidromecânico proposto requer um esquema de pré-processamento robusto, de modo a garantir que os contactos entre os diversos blocos que representam o maciço rochoso de fundação e a barragem são somente aresta/aresta. A parte mecânica do modelo, apesar de limitada a pequenos deslocamentos, tem a vantagem de permitir uma representação rigorosa da distribuição de tensões ao longo das juntas. A parte hidráulica do modelo é perfeitamente compatível com a parte mecânica. O modelo hidromecânico é validado recorrendo a uma situação hipotética de uma barragem gravidade fundada num maciço com fraturação regular e a uma situação real de uma barragem em serviço, comparando os resultados com os obtidos com um modelo discreto em grandes deslocamentos. São também comparados os resultados de análises de estabilidade, concluindo-se que é possível avaliar a segurança ao deslizamento de barragens gravidade em betão recorrendo a modelos de interação em pequenos deslocamentos.

A numerical model for analysis of masonry gravity dams based on the Discrete Element Method is presented.The dam and the rock foundation are represented as block assemblies, using elementary 3- and 4-node blocks. Complex block shapes are obtained by assembling the elementary blocks into macroblocks,allowing the model to be applied in various situations ranging from equivalent continuum to fully discontinuumanalysis. A contact formulation was developed, which represents the interaction between macroblocksin terms of contacts established between elementary blocks, based on an accurate edge

The work presents two new numerical techniques devised for modeling propagating material failure, i.e. cracks in fracture mechanics or slip-lines in soil mechanics. The first one is termed crack-path-field technique and is conceived for the identification of the path of those cracks, or slip-lines, represented by strain-localization based solutions of the material failure problem. The second one is termed strain-injection, and consists of a procedure to insert, during specific stages of the simulation and in selected areas of the domain of analysis, goal oriented specific strain fields via mixed finite element formulations. In the approach, a first injection, of elemental constant strain modes (CSM) in quadrilaterals, is used, in combination of the crack-path-field technique, for obtaining reliable information that anticipates the position of the crack-path. Based on this information, in a subsequent stage, a discontinuous displacement mode (DDM) is efficiently injected, ensuring the required continuity of the crack-path across sides of contiguous elements. Combination of both techniques results in an efficient and robust procedure based on the staggered resolution of the crack-path-field and the mechanical failure problems. It provides the classical advantages of the

The underground structures of the Venda NovaII reversible hydroelectric power scheme present features that make it an interesting case study. Worthy of mention are the inclination and length of the unlined pressure tunnel, the high water head and the great depth of the powerhouse cavern. In projects of this type, the main effect ofthe internal water pressure in the pressure tunnel is the establishment of seepage from the tunnel into the rock mass, which can reach the adits and the powerhouse cavern.This seepage is influenced by several factors, such as the geometry of the underground openings, the rock massproperties

Ground vibration is the most important environmental effect of blasting, and tools for its understanding and control are a prime necessity for the excavation of tunnels and caverns in hard ground. This paper contributes to an improved understanding of the way waves travel in the ground, particularly when there are excavations in the path of propagation, while also enhancing existing numerical models to better simulate that behaviour and thus provide better means to address underground vibration impacts. To this purpose, twenty low intensity blast between neighbour tunnels of an underground complex were performed, followed by a numerical study of the test. The test and simulation showed that, contrary to what is implied in semi-empirical attenuation laws, factors like the propagation path or local amplification can be more important than instant explosive weight and distance to blast.

tThis paper presents the development of a three dimensional computational model, based on the DiscreteElement Method (DEM), which was used to investigate the effect of the angle of skew on the load carryingcapacity of twenty-eight different in geometry single span stone masonry arches. Each stone of the archwas represented as a distinct block. Mortar joints were modelled as zero thickness interfaces which canopen and close depending on the magnitude and direction of the stresses applied to them. The variablesinvestigated were the arch span, the span: rise ratio and the skew angle. At each arch, a full width verticalline load was applied incrementally to the extrados at quarter span until collapse. At each load increment,the crack development and vertical deflection profile was recorded. The results compared with similar

Purpose - The rigid spherical particle models proposed in the literature for modeling fracture in rock have some difficulties in reproducing both the observed macroscopic hard rock triaxial failure enveloped and compressive to tensile strength ratio. With the purpose of obtaining a better agreement with the experimental behaviour, a 3D generalized rigid particle contact model based on a multiple contact point formulation is presented which allows moment transmission and includes in a straightforward manner the effect of friction at the contact level.Design/methodology/approach

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

Modelos de análise com base em formulações de elementos discretos ou de elementos finitos com juntastêm sido propostos para a análise de estabilidade de barragens de betão para cenários que envolvem a rotura da fundação. Nesta comunicação é proposto um algoritmo de interação entre blocos deformáveis do tipo partícula esférica /superfície triangular. Para tal, o domínio interior de cada bloco é discretizado com partículas esféricas que interagem com as superfícies triangulares adotadas na discretização dos blocos vizinhos. A presentam-se várias análises de estabilidade/equilíbrio limite efetuadas com o modelo proposto,incluindo o exemplo da fundação de uma barragem abóbada. Verifica-se que os resultados obtidos, de interação partícula esférica/superfície triangular, são próximos dos obtidos com modelos que utilizam elementos discretos do tipo poliédrico, baseados em modelos de interação mais complexos.

Um modelo numérico para a análise de estruturas de betão armado deve incorporar ferramentas capazes de representar a formação e propagação de fendas, o efeito destas no comportamento global da estrutura, e a interação entre as armaduras e o betão. Para a modelação da fratura em materiais quase-frágeis têm sido utilizados modelos detalhados de partículas, inicialmente desenvolvidos para estudo do comportamento micro-mecânico de meios granulares, que têm em consideração a interação física entre as partículas e a influência da meso-estrutura do betão. Os modelos de partículas em 3D apresentam boa correlação com resultados experimentais de provetes de betões, nomeadamente em termos de resposta elástica, valores de pico, processo de fratura e localização da fratura.Nesta comunicação é apresentada a formulação explícita da modelação dos varões de aço em 3D através de elementos discretos com geometria cilíndrica. A incorporação de elementos de aço permite a aplicação do modelo de partículas à análise da fratura em estruturas de betão armado. Os elementos rígidos de geometria cilíndrica interagem com o betão, modelado por partículas esféricas, através de uma interface de contacto. O modelo é validado em ensaios de flexão em viga a três pontos, sem armaduras de esforço transverso. Os resultados numéricos obtidos no ensaio de flexão permitem verificar que o modelo proposto simula de forma correta o comportamento real, representando o processo de evolução da fratura e a relação carga-deslocamento.

Cracks propagating deep inside gravity dams can seriously affect theirstructural safety. Due to the potential catastrophic scenarios associated to the collapseof large concrete dams, it is a fundamental issue to realistically predict the eventualcrack profiles and the ultimate structural resistance associated to the failuremechanisms.This work investigates tensile crack propagation in concrete gravity dams by usingsome new recently developed numerical techniques (crack-path field and strain injectiontechniques) [1-3] associated to a Rankine-type plasticity model. The work carefullyaddresses aspects related to mesh independence (mesh bias and stress locking),robustness, and computational cost, which are the main issues in material failuremodeling. The numerical simulations presented in the paper show the advantages of thepresented approach.

Aborda-se a aplicação de modelos de elementos discretos a pontes de alvenaria, no quadro dos métodos disponíveis para a análise destas estruturas por modelos de meio descontínuo. Discutem-se as principais opções para a representação numérica, e as suas implicações práticas, tendo em vista principalmente estudos de avaliação da segurança.

En este trabajo se presenta un estudio del ensayo "Trapdoor" mediantemodelización numérica, empleando para ello dos modelos, uno continuo, construido conel código FLAC, y otro discreto, construido con el código PFC2D. Se incide en lasdiferencias de ambas metodologías a la hora de analizar un problema de rotura activa enel que la pérdida de material tiene un efecto significativo, como es el caso del ensayo"Trapdoor". Por un lado, el modelo continuo no representa fielmente la realidad delfenómeno, puesto que no considera la pérdida de material. Esto es especialmenteimportante en el caso de materiales con ángulos de dilatancia bajos en los que se produceuna evolución de la rotura a partir de un primer arco estable. Sin embargo, el modelodiscreto presenta importantes dificultades para asignar las propiedades macromecánicasdel material, lo cual limita notablemente la posibilidad de realizar estudios paramétricossobre las variables que caracterizan el material.

The objective of this work is to reconstruct and analyze the seismic response of a pre Doric temple from the Panhellenic sanctuary at Nemea, Greece. Archaeological and historical evidence suggests that this temple, previously posited to have been damaged or destroyed in a battle, may have been damaged by an earthquake. Using Itasca

Given the results of triaxial tests, regressions are commonly used to evaluate the parameters of failure criteria that model intact rock strength, and to perform statistical inferences used to evaluate characteristic values defined in EC7. These inferences are only possible if the basic hypothesis underlying regression are followed, namely homoscedasticity (constant variance of the errors). This paper presents analyses of 23 sets of triaxial tests, starting by the evaluation of the regression parameters of the Mohr-Coulomb linear criterion and of the Hoek-Brown non-linear criterion, followed by carrying several statistical tests to check the homoscedasticity null hypothesis of independence between the variance of intact rock strength and the confining stress.

Rigid particle models taking directly into consideration the physical mechanisms and the influence of the material grain structure have been developed for fracture studies of quasi-brittle material such as rock. A 2D rigid particle generalized contact model (VGCM2D) has been recently proposed which properly reproduces the rock friction angle and the rock tensile strength to compressive strength ratio, while keeping the simplicity and the reduced computational costs characteristic of circular particle models. In this work the VGCM2D contact model is extended in order to include the particle deformability by considering in each particle an inner finite element mesh triangular discretization. The VGCM2D flexible contact model is tested against known experimental data on a granite rock, namely uniaxial and biaxial tests and Brazilian tests. The study carried out shows the importance of considering the particle deformability in order to obtain results closer to the experimental data.

Minarets are important elements of mosques that constitute the essence of Islamic art. They aretall and slender structures. Old ones are mostly made of cut-stone-block masonry andoccasionally of brick masonry, while the new ones are generally of reinforced concrete. Theyhave suffered significant damage during past earthquakes, the most recent event being the 23October 2011 Van, Turkey earthquake, underlining the need for their maintenance, preservationand protection. Istanbul, the largest city of Turkey, is home to many historical and modernminarets. Assessment of their dynamic behavior is significant due to the expectation of a largeevent in the near future. This study shows the results of the dynamic nonlinear analysis of twomasonry minarets of different heights to better understand their structural behavior under seismicconditions. The numerical models are created using 3DEC by discrete element method. Thenumerical analyses are performed using a series of sine-wave excitations by gradually changingthe frequency and amplitude of input velocity. Displacement magnitudes, maximum shear andnormal stresses, maximum shear and normal displacements, relative displacements and residualdisplacements are recorded. The results are evaluated and compared with those previouslyobtained from the analyses carried out under real and synthetic earthquake inputs.

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.