Analysis and visualization of seismic data using mutual information

Seismic data is difficult to analyze and classical mathematical tools reveal strong limitations in exposing hidden relationships between earthquakes. In this paper, we study earthquake phenomena in the perspective of complex systems. Global seismic data, covering the period from 1962 up to 2011 is analyzed. The events, characterized by their magnitude, geographic location and time of occurrence, are divided into groups, either according to the Flinn-Engdahl (F-E) seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Two methods of analysis are considered and compared in this study. In a first method, the distributions of magnitudes are approximated by Gutenberg-Richter (G-R) distributions and the parameters used to reveal the relationships among regions. In the second method, the mutual information is calculated and adopted as a measure of similarity between regions. In both cases, using clustering analysis, visualization maps are generated, providing an intuitive and useful representation of the complex relationships that are present among seismic data. Such relationships might not be perceived on classical geographic maps. Therefore, the generated charts are a valid alternative to other visualization tools, for understanding the global behavior of earthquakes.

Analysis of the Out-Of-Plane Seismic Behavior of Unreinforced Masonry: A Literature Review

Although the issue of the out-of-plane response of unreinforced masonry structures under earthquake excitation is well known with consensus among the research community, this issue is simultaneously one of the more complex and most neglected areas on the seismic assessment of existing buildings. Nonetheless, its characterization should be found on the solid knowledge of the phenomenon and on the complete understanding of methodologies currently used to describe it. Based on this assumption, this article presents a general framework on the issue of the out-of-plane performance of unreinforced masonry structures, beginning with a brief introduction to the topic, followed by a compact state of art in which the principal methodologies proposed to assess the out-of-plane behavior of unreinforced masonry structures are presented. Different analytical approaches are presented, namely force and displacement-based, complemented with the presentation of existing numerical tools for the purpose presented above. Moreover, the most relevant experimental campaigns carried out in order to reproduce the phenomenon are reviewed and briefly discussed.

Nova metodologia de execução do ensaio SCPTu com avaliação da influência da fonte sísmica quanto à sua dimensão e afastamento

O objectivo deste trabalho consiste na determinação das Ondas de Corte, onda S, através de uma nova metodologia de ensaio do piezocone sísmico, SCPTu. A nova metodologia adoptada de aquisição de dados, consiste na aquisição da onde de corte no movimento ascendente de remoção de varas, após execução do já conhecido ensaio CPTu, ao invés da tradicional aquisição, no movimento descendente, previamente ao acréscimo de nova vara. Além da introdução de uma nova metodologia de aquisição sísmica, tentou-se avaliar a influência da dimensão da fonte geradora da onda de corte e a influência do afastamento das mesmas ao ponto de cravação, do ensaio de penetração estática mencionado. Na avaliação das influências foram usadas três fontes de madeira de secção rectangular, com uma chapa de ferro a topo e diferenciadas entre si pelas dimensões de 1m, 2m e 3m e afastamentos até 4m.

Edifícios altos – problemas associados e análise estrutural de um caso prático

Com a presente dissertação pretende-se analisar alguns dos problemas associados aos edifícios altos, na fase de projeto, bem como compilar um conjunto de informações e conhecimentos científicos sobre a área abordada. São descritas algumas soluções de sistemas estruturais possíveis de idealizar para edifícios altos. Posteriormente, tendo por base um projeto de estruturas de um edifício com 25 pisos localizado em Luanda, capital de Angola, o objetivo consistiu em analisar estática e dinamicamente o seu comportamento quando solicitado fundamentalmente pelas ações do vento e dos sismos. A análise estrutural foi realizada com recurso a dois softwares de cálculo automático, nomeadamente, o Cypecad e o Robot Structural Analysis Professional e pelos métodos preconizados no Regulamento de Segurança e Ações para estruturas de edifícios e pontes e o Eurocódigo 8 – “Projeto de estruturas para resistência aos sismos”. Aborda-se a temática do faseamento construtivo, assunto que revela algumas limitações dos programas de cálculo utilizados, sendo descrito um método simplificado para prever os seus efeitos em termos de dimensionamento final. Os resultados obtidos permitiram avaliar o bom comportamento da estrutura no que respeita ao cumprimento dos estados limites últimos e de serviço. Conclui-se que o sistema estrutural adotado no modelo em estudo se encontra bem dimensionado relativamente ao colapso e à limitação de danos.

Fractional dynamics and MDS visualization of earthquake phenomena

This paper analyses earthquake data in the perspective of dynamical systems and fractional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a powerful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects that are perceived to be similar in some sense are placed on the MDS maps forming clusters. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analysed. The events are characterized by their magnitude and spatiotemporal distributions and are divided into fifty groups, according to the Flinn–Engdahl (F–E) seismic regions of Earth. Several correlation indices are proposed to quantify the similarities among regions. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools for understanding the global behaviour of earthquakes.

Dynamic analysis of earthquake phenomena by means of pseudo phase plane

This paper analyses earthquake data in the perspective of dynamical systems and its Pseudo Phase Plane representation. The seismic data is collected from the Bulletin of the International Seismological Centre. The geological events are characterised by their magnitude and geographical location and described by means of time series of sequences of Dirac impulses. Fifty groups of data series are considered, according to the Flinn-Engdahl seismic regions of Earth. For each region, Pearson’s correlation coefficient is used to find the optimal time delay for reconstructing the Pseudo Phase Plane. The Pseudo Phase Plane plots are then analysed and characterised.

Film thickness in a ball-on-disc contact lubricated with greases, bleed oils and base oils

Three different lubricating greases and their bleed and base oils were compared in terms of film thickness in a ball-on-disc test rig through optical interferometry. The theoretical values calculated according to Hamrock's equation are in close agreement with the base oil film thickness measurements, which validates the selected experimental methodology. The grease and bleed oil film thickness under fully flooded lubrication conditions presented quite similar behaviour and levels. Therefore, the grease film thickness under full film conditions might be predicted using their bleed oil properties, namely the viscosity and pressure-viscosity coefficient. The base and bleed oil lubricant parameter LP are proportional to the measured film thickness. A relationship between grease and the corresponding bleed oil film thickness was evidenced.

Estudo de atirantamentos ancorados no plano perpendicular às fachadas de Alvenaria. Análise de proposta de dimensionamento

O conceito de atirantamento surgiu no contexto de promover a interação global dos edifícios, nomeadamente, estabelecer as referidas ligações, de modo a prevenir o derrubamento para o exterior das paredes de fachada, perante a ocorrência de ação sísmica ou assentamento das fundações. Neste sentido, o presente trabalho tem como objetivo, estudar o comportamento dos atirantamentos ancorados no plano perpendicular das fachadas, quando solicitados à tração. No entanto, como as alvenarias são elementos heterogéneos, houve necessidade de desarticular os atirantamentos e estudar cada uma das partes que o compõe: tirantes injetados em alvenarias e sistemas de ancoragem. Em primeiro lugar, foi elaborado um estudo preliminar sobre tirantes injetados em alvenarias, o qual incidiu no seu dimensionamento, na análise de sensibilidade, apresentação de um caso de estudo e comparação de resultados. Numa segunda fase fez-se uma revisão bibliográfica dos tipos de Sistemas de Ancoragens mais comuns, onde foram mencionados alguns aspetos, nomeadamente a importância, o objetivo e condições da sua aplicação. Por último, associaram-se as duas componentes e foram estudados os Atirantamentos. Fezse um estudo da sua utilização e do seu interesse de aplicação. Foi também analisada uma forma de metodologia de dimensionamento, quando inseridos em alvenarias de tijolo e pedra. Finalizado este estudo foram traçadas as conclusões e sugeridas perspetivas futuras.

Multidimensional scaling visualization of earthquake phenomena

Earthquakes are associated with negative events, such as large number of casualties, destruction of buildings and infrastructures, or emergence of tsunamis. In this paper, we apply the Multidimensional Scaling (MDS) analysis to earthquake data. MDS is a set of techniques that produce spatial or geometric representations of complex objects, such that, objects perceived to be similar/distinct in some sense are placed nearby/distant on the MDS maps. The interpretation of the charts is based on the resulting clusters since MDS produces a different locus for each similarity measure. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analyzed. The events, characterized by their magnitude and spatiotemporal distributions, are divided into groups, either according to the Flinn–Engdahl seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Space-time and Space-frequency correlation indices are proposed to quantify the similarities among events. MDS has the advantage of avoiding sensitivity to the non-uniform spatial distribution of seismic data, resulting from poorly instrumented areas, and is well suited for accessing dynamics of complex systems. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools, for understanding the global behavior of earthquakes.

Análise comparativa de métodos de prospeção direta e indireta na determinação do topo rochoso para fundações

Com o decorrer dos tempos e com a evolução da indústria, acresce a necessidade de aparecimento de novas construções e consequentemente de novos desafios geotécnicos. Para responder a estes novos reptos que a construção nos lança é necessário aprofundar o conhecimento acerca dos materiais que constituem o subsolo e estudar o seu comportamento quando sujeito a novas solicitações, como por exemplo sobrecargas, pois parte do cálculo de dimensionamento de fundações das novas construções dependerá destas características. Existem duas possíveis formas de identificar os materiais existentes no subsolo e caracterizá‐los: através de ensaios de laboratório e de ensaios in situ, sendo nestes últimos que nos iremos focar. Os ensaios in situ, para além de outros dados, permitem‐nos estimar com algum grau de incerteza a profundidade a que se encontra o horizonte com capacidade de suporte pretendida, quer se trate ou não do bedrock, e identificar o processo mais indicado para a retirada do material: através de um meio mecânico de escavação ou por recurso a explosivos. Com a realização de ensaios de sísmica de refração e igualmente recorrendo a ensaios executados com o penetrómetro dinâmico médio (DPM), tentamos dar resposta a estas incógnitas através do cruzamento dos dados obtidos. No entanto, este cruzamento de dados pode não ser completamente esclarecedor, levando ao aparecimento de novas incógnitas às quais não seja possível dar resposta recorrendo‐se unicamente à informação recolhida por meio destes dois métodos, pois poderão revelar‐se insuficientes. Contudo, existem muitos outros ensaios in situ que podem ser realizados e capazes de nos ajudar a complementar os dados inicialmente obtidos no sentido de diminuir ou até mesmo eliminar as incógnitas existentes, e desta forma poder identificar e caraterizar o material existente com o maior grau de segurança possível.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

Using neural networks and support vector regression to relate marchetti dilatometer test parameters and maximum shear modulus

In the last two decades, small strain shear modulus became one of the most important geotechnical parameters to characterize soil stiffness. Finite element analysis have shown that in-situ stiffness of soils and rocks is much higher than what was previously thought and that stress-strain behaviour of these materials is non-linear in most cases with small strain levels, especially in the ground around retaining walls, foundations and tunnels, typically in the order of 10−2 to 10−4 of strain. Although the best approach to estimate shear modulus seems to be based in measuring seismic wave velocities, deriving the parameter through correlations with in-situ tests is usually considered very useful for design practice.The use of Neural Networks for modeling systems has been widespread, in particular within areas where the great amount of available data and the complexity of the systems keeps the problem very unfriendly to treat following traditional data analysis methodologies. In this work, the use of Neural Networks and Support Vector Regression is proposed to estimate small strain shear modulus for sedimentary soils from the basic or intermediate parameters derived from Marchetti Dilatometer Test. The results are discussed and compared with some of the most common available methodologies for this evaluation.

Using neural networks and support vector regression to relate marchetti dilatometer test parameters and maximum shear modulus

In the last two decades, small strain shear modulus became one of the most important geotechnical parameters to characterize soil stiffness. Finite element analysis have shown that in-situ stiffness of soils and rocks is much higher than what was previously thought and that stress-strain behaviour of these materials is non-linear in most cases with small strain levels, especially in the ground around retaining walls, foundations and tunnels, typically in the order of 10−2 to 10−4 of strain. Although the best approach to estimate shear modulus seems to be based in measuring seismic wave velocities, deriving the parameter through correlations with in-situ tests is usually considered very useful for design practice.The use of Neural Networks for modeling systems has been widespread, in particular within areas where the great amount of available data and the complexity of the systems keeps the problem very unfriendly to treat following traditional data analysis methodologies. In this work, the use of Neural Networks and Support Vector Regression is proposed to estimate small strain shear modulus for sedimentary soils from the basic or intermediate parameters derived from Marchetti Dilatometer Test. The results are discussed and compared with some of the most common available methodologies for this evaluation.

Projeto de estruturas do edifício administrativo de um polo logístico em Viana-Angola

O objetivo deste trabalho consiste em efetuar o dimensionamento estrutural de um edifício em betão armado, contemplando as diferentes fases, desde a conceção inicial, com a definição do modelo estrutural e escolha criteriosa dos elementos e soluções constituintes, até à fase final de dimensionamento, considerando para além das cargas gravíticas, a ação do vento e a ação sísmica. No âmbito deste trabalho considerou-se o dimensionamento de elementos estruturais nomeadamente, sapatas, paredes, pilares, vigas e lajes, com a verificação de segurança à flexão simples, flexão composta, esforço transverso e punçoamento, consoante a necessidade de cada elemento. Para tal, foi desenvolvido uma folha de cálculo automático (Macro) que permite a verificação da capacidade resistente de secções, à flexão simples e ao esforço transverso, quer em elementos com ou sem armadura de esforço transverso. Os esforços atuantes que estiveram na origem das verificações estruturais foram calculados com base na aplicação de um programa tridimensional de elementos finitos, nomeadamente o programa de cálculo ROBOT STRUCTURAL ANALYSIS. Os Critérios Gerais de Dimensionamento considerados, com base na regulamentação em vigor em Portugal – RSA, REBAP e Eurocódigos, bem como as Hipóteses de Cálculo consideradas na verificação aos estados limites últimos dos elementos estruturais são detalhadamente enunciados ao longo do trabalho. Os desenhos de elementos estruturais dimensionados, bem como os desenhos de dimensionamento do edifício encontram-se em Anexo.

A simplified four-branch model for the analytical study of the out-of-plane performance of regular stone URM walls

During the last years, several studies have been made aiming to assess the out-of-plane seismic response of unreinforced stone masonry structures. This fact led to the development of a wide variety of models and approaches, ranging from simple kinematic based analytical models up to complex numerical simulations. Nevertheless, for the sake of simplicity, the out-of-plane seismic response of a masonry wall pier may be obtained by means of a simple single-degree-of-freedom system while still providing good results. In fact, despite the assumptions associated with such a simple formulation, it is also true that the epistemic uncertainty inherent with the selection of appropriate input parameters in more complex models may render them truly ineffective. In this framework, this paper focuses on the study of the out-of-plane bending of unreinforced stone masonry walls (cantilevers) by proposing a simplified analytical approach based on the construction of a linearized four-branch model, which is used to characterize the linear and nonlinear response of such structural elements through an overturning moment-rotation relationship. The formulation of the four-branch model is presented and described in detail and the meaningful parameters used for its construction are obtained from a set of experimental laboratory tests performed on six full-scale unreinforced regular sacco stone masonry specimens. Moreover, a parametric analysis aiming to evaluate the effect of these parameters’ variation on the final configuration of the model is presented and critically discussed. Finally, the results obtained from the application of the developed four-branch model on real unreinforced regular sacco stone masonry walls are thoroughly analysed and the main conclusions obtained from its application are summarized.