Publicações

Traditional stone masonry walls are structural elements in most historic build-ings. To preserve them and improve their ability to withstand extreme events, such asearthquakes, it is necessary to implement effective reinforcement solutions. This paperpresents the modeling of traditional Portuguese rubble stone masonry walls, reinforcedwith external steel mesh, sprayed micro-concrete layers and transverse confinement bysteel connectors, which were developed and tested experimentally in uniaxial compression.The modeling is carried out using micro-modeling through a 2D particle model (PM).The process of calibrating the properties of both micro-concrete and concrete is presented,the methodology for generating the numerical models is described and the numericalresponse is compared with the experimental results. The numerical results show thatthe PM can adequately reproduce the experimentally observed behavior of this type ofreinforcement solution.

This study presents a robust contact constitutive model in the distinct element method (DEM) framework for simulating the mechanical behavior of masonry structures. The model is developed within the block-based modeling strategy, where the masonry unit is modeled as deformable blocks with potential crack surfaces in the middle of the bricks, while the mortar joints are defined as zero-thickness interfaces. The modeling strategy implements multi-surface plasticity with damage mechanics, including a tension cut-off, Coulomb failure criterion, and an elliptical compressive cap for the damage in tension, shear, and compression, respectively. Two new features are introduced in this contact model: a piecewise linear softening function for strength degradation in tension and shear and a hardening/softening function to phenomenologically define the compressive damage of masonry composite into the unit-mortar interface. The constitutive model is implemented in commercial DEM software using the small displacement configuration and validated against material and experimental tests on masonry walls subjected to constant pre-compression and monotonically increasing in-plane load. The experimental and numerical results regarding the force-displacement relationship and damage pattern produced by the proposed constitutive model are compared and critically discussed, demonstrating the capability of DEM coupled with the suitable constitutive law in simulating the behavior of masonry structures.

o obtain predictions closer to concrete behaviour, it is necessary to employ a particle model(PM) that considers contact softening. A bilinear softening contact model (BL) has been adoptedin PM studies. Several limitations in PM predictions have been identified that may be due to BLassumptions. For this reason, this paper compares BL predictions with those obtained with morecomplex models to assess if PM predictions can be improved. As shown, it is possible to calibrateeach contact model to reproduce the complex behaviour observed in concrete in uniaxial and biaxialloading. The predicted responses are similar, and the known PM limitations still occur independentlyof the adopted model. Under biaxial loading, it is shown that a response closer to that observed inconcrete can be obtained (higher normal-to-stiffness ratio of

Among the various important monuments impacted by the April 25, 2015 Mw7.8 Nepal earthquake, the Dharahara Tower located in Kathmandu suffered complete collapse. The collapse of the tower, a slender 60-meter-high old brick masonry structure with an almost cylindrical hollow shape, was captured by a low-quality video camera, which nonetheless helped to identify the critical moments. Initially, the tower descended more than 10 meters vertically after a rupture at the base. After a few seconds, it overturned, disintegrating upon impact on the ground. At a distance of 1.3 km, an accelerometric station recorded the strong motion which was used as input of a discrete element model of the structure. Mechanical properties were taken from lab tests made on similar building materials. The Dharahara Tower had previously been analysed by other researchers using various methods. However, since they were apparently not aware of the mechanism observed in the video footage, their collapse models do not agree with this new evidence. For the initial phase of the collapse the present model explains with great accuracy the observations of the video footage, but the final phase is dependent on various details, and modelling is not so robust.

Discrete element block models provide a suitable tool for the numerical analysis of masonry structures, particularly apt to represent the nonlinear response governed by shearing and separation along the structure

The unreinforced masonry (URM) walls are the common load-bearing structural elements in most existing buildings, consisting of masonry units (bricks) and mortar joints. They indicate a highly nonlinear and complex behaviour when subjected to combined compression-shear load-ing influenced by different factors, such as pre-compression load and boundary conditions, among many others, which makes predicting their structural response challenging. To this end, the present study offers a discontinuum-based modelling strategy based on the discrete element method (DEM) to investigate the in-plane cyclic response of URM panels under different vertical pressures with and without a damp-proof course (DPC) membrane. The adopted modelling strategy represents URM walls as a group of discrete rigid block systems interacting along their boundaries through the contact points. A novel contact constitutive model addressing the elasto-softening stress-displacement behaviour of unit-mortar interfaces and the associated stiffness degradation in tension-compression regimes is adopted within the implemented discontinuum-based modelling framework. The proposed modelling strategy is validated by comparing a re-cent experimental campaign where the essential data regarding geometrical features, material properties and loading histories are obtained. The results show that while the proposed compu-tational modelling strategy can accurately capture the hysteric response of URM walls without the DPC membrane, it may underestimate the load-carrying capacity for URM walls with the DPC membrane.

This paper presents the development of a novel crack-based damage quantification method to assess the damage accumulation in masonry arch bridges subjected to externally applied loading. Initially, a damage index was proposed, considering the initiation and extension of tensile and sliding cracks. Then, the proposed damage indexing was adopted into a two-dimensional discrete element code of analysis to evaluate single and multi-ring masonry arch bridges. The numerical model was validated by comparing the computational outputs against the experimental results obtained from the literature. Following the validation, masonry arch bridge models were developed, featuring the four most representative bond configurations in arch barrels. Also, different bond properties were assigned to investigate their impact on the global failure characteristics of single- and multi-ring masonry arch bridges. From the analyses of results of the multi-ring masonry arch bridges investigated in this study, it was shown that the rapid growth of tensile cracks in radial joints and the occurrence of shear slippage in circumferential joints between adjacent rings were observed to be early signs for multi-ring bridges before the ultimate load reached. By analysing the correlation between the normalised damage index with the normalised load, damage accumulation in different masonry arch bridges were identified. This study offers a novel perspective on quantitively evaluating the damage accumulation and failure mechanism of masonry arch bridges and the findings may provide valuable insights into the assessment and management of existing masonry arch bridges.

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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

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.

A brief description of the phenomena and problems associated with underground structures in hydraulic projects is presented, namely in what concerns the powerhouses, surge chambers and pressure tunnels and shafts. An analysis of the calculation methodologies followed in the structural design of this works is presented, as well as of the numerical models usually adopted, namely finite and boundary element models. Finally, some applications of computational mechanics are presented. First, a parameter study for underground powerhouses, with special emphasis in the definition of shapes, existence of several caverns,and in the tridimensional equilibria is described. Afterwards, examples of application to some hydraulic projects are illustrated: a large underground powerhouse in Mozambique, the Alto Lindoso hydroelectric power scheme in construction in the north of Portugal, and the Castelo do Bode tunnel, in operation, integrated in the water supply system to Lisbon.

O presente trabalho aborda a origem do estado de tensão interna dos maciços rochosos e apresenta os factores que o influenciam. Apresentam-se as técnicas e a aparelhagem correntemente utiiizada na determinação do estado de tensão, bem como a interpretação dos ensaios mais comuns, dando-se maior relevo aos ensaios com macacos planos pequenos (S F J) e com o extensómetro tridimensional (S T T),efectuados correntemente pelo LNEC.

Descreve-se sucintamente uma técnica para amostragem linear de descontinuidades em faces expostas de maciços rochosos e referem-se métodos para tratamento dos dados de campo com vista à definição defamílias de descontinuidades e caracterização de uma forma estatística da sua orientação, espaçamento e extensão. Apresentam-se os resultados obtidos para o caso de uma galeria subterrânea no aproveitamentohidroeléctrico do Alto Lindoso. Para as famílias de descontinuidade identificadas apresenta-se um estudo dos blocos tetraédricos que se poderão formar nas diferentes faces de rocha e analisam-se as suas condições de estabilidade.

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Apresentam-se, neste relatório, modelos numéricos baseados no método dos elementos da fronteira, desenvolvidos no LNEC para análise de estruturas subterrâneas. Tecem-se algumas considerações sobre o método dos elementos de fronteira, descrevem-se os modelos desenvolvidos para equilíbrios planos e tridimensionais e apresentam-se alguns exemplos de aplicação.

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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.