Publicações

Concrete gravity dams are mass concrete structures, often built on rock mass foundations, conceived to rely upon their weight for stability. To prevent sliding, these structures are usually keyed/embedded into the foundation, a good construction practice particularly relevant in medium to high intensity seismic zones. In stability analysis, the extra strength obtained by keying the dam into the foundation is usually either neglected or taken as a passive resistance, which, such as explored in this paper, do not reflect the real structural response in pre-collapse situations. Limit state philosophy requires the ultimate equilibrium conditions to be expressed as accurately as possible. In this paper, the rigid-body equilibrium of a wedgy model representing the dam and a downstream rock wedge is analyzed according to the large displacement regime. Failure mechanisms were identified, analytically described and numerically validated. Application to two Portuguese large concrete gravity dams led to safety factors considerably larger than those computed assuming the usual practice. The proposed approach is intended to support probabilistic and/or semi-probabilistic methodologies for safety assessment of concrete gravity dams, in the design and feasibility phases, in which the limit state approach is inherently followed.

A detailed modelling approach to represent masonry at the meso-scale is proposed, basedon the discrete element method, considering the nonlinear behavior of the joints and the units. Thefracture of units is represented by the bonded-block concept, in which a random network of potentialcracks is created, allowing the progressive development of failure mechanisms. For simplicity, onlythe 2D case is presented, but the extension to 3D is straightforward. A key component of the proposedmodel is a framework for a joint or interface constitutive model, including the post-peak softeningrange, taking into account the experimental fracture energies. In this model, the softening curves intension or shear are defined by piecewise linear segments, calibrated to reproduce the most commonmasonry constitutive models. The essential issues involved in the application of bonded-blockmodels to masonry are examined, namely the block shape, either Voronoi polygons or triangles; size;deformability; and the influence of the main constitutive parameters. Uniaxial compression tests areanalyzed in detail. The simulation of a well-known experiment of a brick panel under shear showsthe good performance of the proposed approach. The investigation results demonstrate the model

To predict the structural behaviour of ancient stone masonry walls is still a challenging task due to their strong heterogeneity. A rubble-stone masonry modeling methodology using a 2D particle model (2D-PM), based on the discrete element method is proposed given its ability to predict crack propagation by taking directly into account the material structure at the grain scale. Rubble-stone (ancient) masonry walls tested experimentally under uniaxial compression loading conditions are numerically evaluated. The stone masonry numerical models are generated from a close mapping process of the stone units and of the mortar surfaces. A calibration procedure for the stone-stone and mortar-mortar contacts based on experimental data is presented. The numerical studies show that the 2D-PM wall models can predict the formation and propagation of cracks, the initial stiffness and the maximum load obtained experimentally in traditional stone masonry walls. To reduce the simulation times, it is shown that the wall lateral numerical model adopting a coarser mortar discretization is a viable option for these walls. The mortar behaviour under compression with lateral confinement is identified as an important micro-parameter, that influences the peak strength and the ductility of rubble-masonry walls under uniaxial loading.

This paper is focused on the study of the dynamic behaviour of two large arch dams, and it presents some innovations for the improvement of Seismic and Structural Health Monitoring (SSHM) systems for dams. The work describes a methodology based on the integrated use of software for automatic monitoring data analysis and of computational 3D finite element (3DFE) models for dam dynamic behaviour simulation. The monitoring data analysis software was developed for automatic modal identification, in order to obtain natural frequencies and mode shapes, for automatic detection of vibrations induced by seismic events, to be distinguished from those caused by other operational sources, and for comparison between results retrieved from measured vibrations and numerical results from 3DFE modelling. The numerical simulations are carried out using a 3DFE program developed for dynamic analysis of dam-reservoir-foundation systems, based on a solid–fluid coupled formulation and considering the dam-water dynamic interaction, including calculation modules for complex modal analysis and for linear and non-linear seismic analysis. The case studies are two large arch dams that have been under continuous dynamic monitoring over the last ten years: Cabril dam (132 m high), the highest dam in Portugal, and Cahora Bassa dam (170 m high), in Mozambique, one of the highest dams in Africa. The SSHM systems installed in both dams have similar schemes and were designed to continuously record accelerations in several locations at the upper part of the dam body and near the dam-foundation interface, using uniaxial and triaxial accelerometers. The most significant experimental results from continuous dynamic monitoring are presented and compared with numerical results for both dams, with emphasis on the evolution of natural frequencies over time, including the vibration mode shapes for various water levels, and on the measured accelerations during low-intensity seismic events. Furthermore, the main results of non-linear seismic response simulations are provided, considering the effects due to joint movements and tensile and compressive concrete damage, aiming to assess the seismic performance of both dams based on the Endurance Time Analysis method.

A monumental tetrastyle canopy (four columns topped by a hollow cap overlaying a statue), built in 1948 at the centre of Kathmandu, Nepal, has suffered full collapse during the April 25, 2015 Mw7.8 earthquake. Two video camera recordings let us recover the most important movements of the structure. At a distance of 2.9 km from the monument, an accelerometric station (KATNP) recorded the motion which we used as input of a model structure made with DEM. Geometry and dimensions of main elements were mostly obtained from satellite images. Concrete and steel in columns were considered as the common practice at that time. We performed some sensitivity analyses varying the mechanical properties due to the possibility of aging alterations in concrete and steel and to incorporate uncertainties on the geometric characteristics. Albeit the response has a significant variability, results show that it is possible to reproduce well the video images, attesting the importance of video cameras to capture the dynamic performance of structures, providing insight into their behaviour and data to support numerical investigations.

In this study, the in-plane structural behavior, capacity, and performance of dry-joint stone masonry walls (DJSMWs) and the effects of the vertical stress level on these factors are investigated via a stochastic discontinuum analysis that considers the material uncertainty. A discontinuum type of analysis is performed based on the discrete element method (DEM), where each stone masonry unit is explicitly represented in the computational model. To better simulate the cracking and shear failure modes within the stone units, a coupled fracture energybased contact constitutive model is implemented into a commercial discrete element code, 3DEC. First, the proposed modeling approach is validated by comparing to experimental findings in literature. Then, the approach is used to explore the failure mechanism and the force–displacement behavior of DJ-SMWs, considering different vertical stress levels and material properties. The results of the novel modeling strategy provide a better understanding of the progressive collapse mechanism of DJ-SMWs and the influence of the vertical stress level. Furthermore, the outcomes of this research indicate the major role of the frictional resistance at the joints in the safety and performance assessment of the dry-joint load-bearing masonry walls. Finally, important inferences are made regarding the non-spatial and spatial stochastic discontinuum analysis.

The installation of vibration-based structural health-monitoring systems relying in the study of natural frequencies to assess the condition of civil engineering structures is becoming more and more common. The extraction of these monitoring features can be achieved through automated operational modal analysis, combining output-only identification methods with cluster analyses, and comparing the identified modal properties with references, in a process known as modal tracking. However, changing environmental and operational conditions affect the dynamic behaviour of structures, disturbing the process of modal tracking, which may lead to the loss of important information and to misidentifications. In this context, this paper proposes a new methodology for modal tracking within the scope of automated operational modal analysis, especially prepared for scenarios with strong external influence on modal properties. A concrete arch dam with large variations of some natural frequencies is used as case study, and the proposed methodology is compared to a standard procedure using a quite unique monitoring data set continuously collected for 3 years.

Neste artigo apresenta-se a formulação e resultados da aplicação de dois modelos descontínuos tridimensionais que simulam a interação hidromecânica. Nestes modelos o comportamento mecânico é simulado de forma idêntica mas o comportamento hidráulico é simulado com duas abordagens diferentes. O primeiro modelo baseia-se numa formulação que admite o escoamento através de elementos planos de interface. O segundo modelo, que se propõe neste artigo, baseia-se numa discretização unidimensional, ocorrendo o escoamento através de elementos de canais. Os modelos hidromecânicos implementados no módulo computacional Parmac3D Fflow são verificados e validados através de exemplos simples, e o modelo proposto é calibrado de modo a serem obtidos, com os dois modelos, os mesmos valores de pressão e de caudal. Foi desenvolvido um modelo hidromecânico de um conjunto barragem/fundação, tendo em consideração a existência de cortina de impermeabilização e de sistema de drenagem na fundação. Salientam-se as vantagens do modelo proposto no estudo do comportamento hidromecânico de fundações de barragens.

Earthquake damage in historic masonry buildings is generally caused by the collapse of individual portions that become detached form the structure and fail by overturning. These mechanisms are mainly governed by the discrete nature and geometry of the block units. Analyses based on explicit micro-modelling in which each block is considered separately are therefore of increasing importance. This paper offers a robust tool for the seismic assessment of masonry structures under either, quasi-static or dynamic loading. Algorithms for performing dynamic pulses and pushover analyses through the Discrete Element Method are developed and described, taking into account the actual discrete nature and geometry of masonry. A numerical procedure is proposed that automatically detects the collapse mode and follows the evolution of the analysis until collapse. The implemented method is able to give a reliable estimate of the expected failure mechanism, providing the seismic acceleration required to trigger the motion and the ultimate displacement beyond which the collapse occurs. Finally, the implemented algorithms are applied to two case studies and the results are compared with the traditional analysis based on rigid-block kinematics to outline the features and potentialities of the proposed approach.

Conservation of the European-built heritage is nowadays closely related to interventions in masonry construction. Since a significant part of these structures are located in earthquake prone zones, designing protective measures that ensure their preservation requires the assessment of the associated seismic vulnerability and the understanding of their degradation mechanisms. However, due to the presence of discontinuities between its constituent elements, the numerical simulation of the non-linear response of masonry structures subjected to strong earthquakes is a cumbersome task, especially when performed using the traditional finite element method. As an alternative, the discrete element method is particularly suitable for the numerical analysis of such structures under large, damaging loads. By allowing discrete displacements/rotations of individual bodies, and by automatically recognising new contacts between bodies, while eliminating obsolete ones, this numerical approach can simulate the complete detachment of discrete bodies initially in contact.The present paper illustrates the use of the discrete element method to assess the seismic vulnerability of stone arches. A probabilistic approach allows to consider the variability of theseismic action and the uncertainties in the definition of the material properties. First, an unreinforced masonry arch is considered. Based on non-linear multi-directional incremental dynamic analyses, five damage states are proposed and the respective fragility curves are elaborated. Toimprove the arch’s seismic performance, two reinforcing solutions using steel elements are considered and analysed comparatively.

In this work three constitutive contact models that include softening are adopted for particle model fracture studies in both rock and concrete. For a single local contact, the constitutive contact model performance is initially compared in tensile, pure shear and shear tests under constant axial. Additionally, compression, direct tensile, and confined triaxial tests of quasi-britlle material discretized with spherical particles are presented and the predicted macroscopic response is compared. For a single local contact, the three contact models predict a similar behaviour. As shown, it is possible to calibrate each contact model to reproduce complex macroscopic behaviour observed in rock and concrete, but each contact model requires different contact properties or particle generation procedures.

Asphalt mixture faces damage due to vehicle speed, repeated loads, and ultravioletradiation over time, regardless of being a self-healing material. Induced healing mechanismsare necessary to promote autonomous pavement recovery due to adverse in-service conditions,and the capsule-asphalt mixture system incorporating low-viscosity oils (rejuvenators) hasshown to be a possible solution in laboratory tests. This study aims to numerically investigatethe effect of rejuvenator-modified mastic (activated capsules) on the stiffness properties ofasphalt mixtures within the discrete element method. A three-dimensional model previouslyvalidated for rejuvenator-modified mastics with different rejuvenator-to-bitumen ratios (0, 2.5,and 10 wt%) is adopted. A generalised Kelvin contact model represents the time-dependentcontacts, and its contact parameters define the rejuvenator amount in the mastic phase. Theanalysis assesses the impact of the modified mastic amount and the rejuvenator-to-bitumenratio. Results show that the increasing modified mastic content progressively reduces themixture dynamic modulus. When the total mastic phase has rejuvenator-modified properties,the mixture stiffness modulus significantly reduces, and the phase angle performs differentlyfrom the expected (decrease with frequency) at a 10% rejuvenator-to-bitumen ratio due to theexcessively softened state, possibly compromising the pavement mechanical performance. Fora 0.30 wt% modified mastic ratio case adopting a local effect, the embedded elements do notsignificantly influence the mixture rheological properties, especially the stiffness modulus,which may be insufficient for self-healing purposes. Nevertheless, the negligible impact on thephase angle highlights the potential of the rejuvenator-modified asphalt mixture across differenttraffic and temperature conditions.

Micromechanical modelling based on the Discrete Element Method (DEM) has been widely used to investigate asphalt behaviour due to its ability to represent an irregular microstructure with variable-sized aggregates, bitumen and voids. The 3D rigid particle models with randomly distributed spherical particles and adopting elastic and/or simple viscoelastic models at the contacts are the standard approach, however, in recent years, a significant research effort is noted to incorporate real particle morphologies in the numerical models.In this study, a previously developed 3D DEM model of asphalt employing a generalised Kelvin contact model formulation for the viscoelastic contacts is further improved with realistic particle shapes representing the coarse aggregates. A digital library of aggregate shapes was created from the X-ray computed tomography (CT) scan of an asphalt specimen, using an adaptive image-processing method to separate the aggregates in the CT images and the Delaunay triangulation method to define the aggregate 3D surface model. Several virtual aggregates with different sizes were selected from the library to represent the coarse aggregate gradation of the modelled 3D DEM asphalt specimen. Each virtual aggregate is discretized with smaller spherical particles and its deformability is taken into account through the inner particle contacts. The numerical asphalt specimens with realistic particle shapes were submitted to uniaxial tension-compression cyclic tests to determine the stiffness properties, and the results were compared with those of the numerical specimens with all constituents represented by single spherical rigid particles. As shown, the proposed methodology greatly enhances the 3D DEM model's ability to simulate the asphalt behaviour.

O artigo considera um caso de estudo intencionalmente simples

This paper presents the development of a three-dimensional micromechanical model based on the Laguerre-Voronoi diagrams of the grain structure to study the viscoelastic behaviour of asphalt mastic with the use of the discrete element method (DEM). Usually, the DEM models of asphalt mastics adopt a Burger's contact model to reproduce the known viscoelastic behaviour. A generalized Kelvin chain model (GK) was developed within a particle model (PM) framework in order to obtain a better agreement in the determination of dynamic properties of mastics. Numerical cyclic tests under a frequency range varying from 10 to 0.10 Hz were implemented to analyse the dynamic response. The parameters of the DEM model are determined from macroscale material properties, which are obtained by fitting lab-based dynamic modulus and phase angle results. The influence of the parameters defining the contact models on the dynamic response was investigated. An iterative procedure was derived to convert the macroscale properties into calibrated contact parameters of the proposed model. Simulation tests show a good correlation between the numerical results obtained with the GK contact model and the experimental data when compared with the agreement obtained with the Burger's model.

N/A

N/A

The safety of concrete arch dams depends to a large extent on the soundness of the foundation rock mass. The large arch dams presently under design and construction apply very significant loads to their abutments and foundations. The assessment of the foundation stability requires the analysis of the potential failure mechanisms defined by the major rock mass discontinuities and joint sets. For dams located in areas of intense seismic activity, the analysis needs to take into account the potential effects of earthquakes, not only on the concrete arch, but also in the nearby rock discontinuities. The discrete element method is a major numerical tools for discontinuum modelling, allowing the analysis of block systems defined by multiple joint planes. In the paper, the key issues involved in its application to arch dam foundations are reviewed. In particular, the representation of the discontinuities in models intended for failure analysis is discussed. The evaluation of safety factors under static loading is addressed. The framework for seismic analysis of arch dams is also examined, namely the dynamic boundary conditions. Options to analyse the dynamic dam-water interaction and model calibration issues are discussed, based on practical examples.

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

N/A

Masonry is a combination of units such as stones, bricks or blocks usually laid in a cementitious or lime mortar. It is probably the oldest material used in construction and has proven to be both simple to build and 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 for that. Careful and periodic assessment of such structures is necessary in order to evaluate their structural capacity and safety levels. However, performing the structural analysis of masonry construction is not an 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 11 countries (Canada, France, Greece, Hungary, Iran,Italy, Mexico, Norway, Portugal, UK, USA), which were 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.

This chapter is focused on the Portuguese experience on the development and exploration of systems for continuously monitoring dam vibrations, using accelerometers. The pioneer system for seismic and structural health monitoring (SSHM) installed in Cabril dam (the highest Portuguese arch dam: 132 m high) is described in detail. The design of this system was the result of a long-term LNEC research program, still ongoing. These monitoring systems should include software developed to automatically perform the analysis of collected data, including the automatic comparison with numerical results from 3DFE models. In view of the good results obtained with the system in operation in Cabril dam since 2008, similar systems have been installed in other large dams in Portugal, particularly in recently built dams. Finally, Baixo Sabor dam is presented as an example of a new Portuguese dam with a complete SSHM system, in operation since 2015. Themain experimental results obtained for both dams are shown, namely the evolution of natural frequencies over 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 à segurança ao colapso (cenários de rotura), é essencial utilizar modelos de simulação ou de interpretação (no caso de obras existentes) do seu comportamento. Estes modelos são 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, quantifica parâmetros da resposta das estruturas que permitem avaliar a sua segurança, utilizando critérios 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 de barragens. No caso de cenários de rotura, não existe muita experiência de comparação destes 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 métodos experimentais, para o estudo de cenários de rotura, tem uma importância acrescida. Assim o principal objectivo deste trabalho é contribuir para melhorar a capacidade de avaliação da segurança de barragens de betão envolvendo cenários de rotura pela fundação. Neste trabalho desenvolveram-se dois ensaios experimentais em modelos físicos: um primeiro envolvendo uma barragem abóbada, para o estudo de cenários de rotura da fundação para acções estáticas; e um segundo de uma barragem gravidade ensaiado em mesa sísmica, com vista a estudar a rotura pela fundação para acções dinâmicas. A previsão e interpretação dos ensaios foram efectuadas com modelos matemáticos adequados, que permitiram a sua validação e posterior utilização no estudo de outros cenários.

As estruturas de membrana são caracterizadas por terem secções transversais muito pequenas (espessura no caso da membranas). Desta forma verifica-se que este tipo de estruturas não tem capacidade para desenvolver esforços de flexão e portanto, a única maneira de equilibrar as acções transversais é adaptando a sua forma ao carregamento. Contrariamente ao tradicional método dos elementos finitos (FEM), o método de Galerkin livre de elementos desenvolvido por Belytschko [1] não necessita de elementos na aproximação do campo de variáveis. No EFGM, os elementos são substituídos por um conjunto de nós em que cada um possui um determinado domínio de influência. Assim, a função de aproximação é construída em cada ponto com base nos nós incluídos no seu domínio de influência. As funções de aproximação são obtidas utilizando o método dos mínimos quadrados móveis (MLS) que não é mais do que um método de mínimos quadrados que se move consoante o domínio de influência do nó em questão. Neste trabalho é apresentado a implementação de um método sem malha, o método livre de elementos de Galerkin para a análise de estruturas de membrana com comportamento ortotrópico. Para a utilização deste método na análise de estruturas de membrana utilizou-se uma técnica de mapeamento da geometria tridimensional para um espaço bidimensional, sendo que as bases deste sistema são utilizadas na expressão das componentes de deformação e tensão na equação do princípio dos trabalhos virtuais. Com base nesta técnica, os nós da malha são gerados no espaço bidimensional e as suas coordenadas são utilizadas no método dos mínimos quadrados móveis para a aproximação do campo de deslocamentos. Para uma estrutura de membrana, a rigidez geométrica da estrutura de suporte não pode ser desprezada sendo que a análise geometricamente não linear é essencial na formulação do problema. Para tal, com base numa formulação Lagrangeana total desenvolveu-se uma formulação de análise geometricamente não linear considerando o método livre de elementos de Galerkin. Neste trabalho foram analisados alguns exemplos de estruturas de membrana com comportamento isotrópico e ortotrópico para validar o método proposto sendo que os respectivos resultados foram comparados directamente com os resultados obtidos com o programa generalista de elementos finitos ADINA .

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’s non-linear behaviour up to failure is simulated using an isotropic damage model with softening, considering two independent scalar damage variables: d+ for tension damage and d- for compression damage. The implemented code was verified and optimized for a simple test structure, more specifically a concrete frame structure with three columns. According to the defined material properties for the structural elements, the concrete failure is expected to occur only at the central column without causing the collapse of the structure, which remains in equilibrium. DamDamage3D1.0 is used to evaluate the structural safety of Cabril arch dam (132 m high) for the concrete strength decrease scenario, considering the material deterioration under tension and compression. This failure scenario is usually considered in the scope of the safety control of dams, and the main goal is to obtain a global safety factor ?s that indicates how many times the material’s resistance can be reduced without causing the dam’s structural collapse. This way ?s is the maximum admissible multiplying factor of the applied loads. The non-linear behaviour of the dam is analysed for the load combination with the self-weight (SW) and the hydrostatic pressure (HP) at the upstream face (full reservoir), using a 3D finite element mesh with three elements in thickness. The numerical simulations are performed using two different constitutive damage laws to evaluate the influence of the compression softening phenomenon in the global resistant capacity of the dam. The main results include displacements and stress fields and the distributions of tension and compression damage in the dam body.

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’s non-linear behaviour up to failure is simulated using an isotropic damage model with softening, considering two independent scalar damage variables: d+ for tension damage and d- for compression damage. The implemented code was verified and optimized for a simple test structure, more specifically a concrete frame structure with three columns. According to the defined material properties for the structural elements, the concrete failure is expected to occur only at the central column without causing the collapse of the structure, which remains in equilibrium. DamDamage3D1.0 is used to evaluate the structural safety of Cabril arch dam (132 m high) for the concrete strength decrease scenario, considering the material deterioration under tension and compression. This failure scenario is usually considered in the scope of the safety control of dams, and the main goal is to obtain a global safety factor ?s that indicates how many times the material’s resistance can be reduced without causing the dam’s structural collapse. This way ?s is the maximum admissible multiplying factor of the applied loads. The non-linear behaviour of the dam is analysed for the load combination with the self-weight (SW) and the hydrostatic pressure (HP) at the upstream face (full reservoir), using a 3D finite element mesh with three elements in thickness. The numerical simulations are performed using two different constitutive damage laws to evaluate the influence of the compression softening phenomenon in the global resistant capacity of the dam. The main results include displacements and stress fields and the distributions of tension and compression damage in the dam body.

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 known analytically, 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’s structural behavior for the main loads, self-weight and hydrostatic pressure, is simulated with GDams2D 1.0. The results obtained are analyzed based on the post-processing module of GDams2D 1.0, also developed in MATLAB in the scope of the present work. This module allows several types of representation of the displacement field and stress field.

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 the friction 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 different values 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 trabalho propondo-se uma técnica de representação das incógnitas deslocamentos e pressões variáveis no espaço e no tempo em série de Delta de Dirac e suas derivadas no tempo cujos coeficientes se determinam com base na solução de sistemas de equações diferenciais definidos no espaço (problema com três variáveis espaciais independentes que pode ser estudado pelo método de Monge).

Neste relatório apresentam-se as equações básicas da elastodinâmica linear, as soluções fundamentais 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 sua implementação pelo método dos elementos finitos.

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