Dynamic earth pressures against a retaining wall caused by Rayleigh waves

An approximate procedure for studying harmonic soil-structure interaction problems is presented. The presence of Rayleigh waves is considered and the resulting governing equations of the dynamic soil-structure system are solved in the time domain. With this method the transient and steady states of a vibratory motion and also the nonlinear behaviour of the soil can be studied. As an example, the dynamic earth pressure against a rigid retaining wall is investigated. The loads are assumed to be harmonic Rayleigh waves with both static and dynamic surface surcharges. The dependence of the results on the excitation frequency is shown.

Sub-wavelength resonators as seismic Rayleigh waves shield

We explore the thesis that tall structures can be protected by means of seismic metamaterials. Seismic metamaterials can be built as some elements are created over soil layer with different shapes, dimensions, patterns and from different materials. Resonances in these elements are acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. Analytically we proved that if we put infinite chain of SDOF resonator over the soil layer as an elastic, homogeneous and isotropic material, vertical component of Rayleigh wave, longitudinal resonance of oscillators will couple with each other, they would create a Rayleigh bandgap frequency, and wave will experience attenuation before it reaches the structure. As it is impossible to use infinite chain of resonators over soil layer, we considered finite number of resonators throughout our simulations. Analytical work is interpreted using finite element simulations that demonstrates the observed attenuation is due to bandgaps when oscillators are arranged at sub-wavelength scale with respect to the incident Rayleigh wave. For wavelength less than 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when impedance of oscillators matches impedance of soil. Since longitudinal resonance of SDOF resonator are proportional to its length inversely, a formed array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground. Optimum number of vertical pillars and their interval spacing called effective area of resonators are investigated. For 10 pillars with effective area of 1 meter and resonance frequency of 4.9 Hz, bandgap frequency causes attenuation and a sinusoidal impulsive force illustrate wave steering down phenomena. Simulation results proved analytical findings of this work.

Resonant metamaterials for the control of Rayleigh waves

Since their emergence, locally resonant metamaterials have found several applications for the control of surface waves, from micrometer-sized electronic devices to meter-sized seismic barriers. The interaction between Rayleigh-type surface waves and resonant metamaterials has been investigated through the realization of locally resonant metasurfaces, thin elastic interfaces constituted by a cluster of resonant inclusions or oscillators embedded near the surface of an elastic waveguide. When such resonant metasurfaces are embedded in an elastic homogeneous half-space, they can filter out the propagation of Rayleigh waves, creating low-frequency bandgaps at selected frequencies. In the civil engineering context, heavy resonating masses are needed to extend the bandgap frequency width of locally resonant devices, a requirement that limits their practical implementations. In this dissertation, the wave attenuation capabilities of locally resonant metasurfaces have been enriched by proposing (i) tunable metasurfaces to open large frequency bandgaps with small effective inertia, and by developing (ii) an analytical framework aimed at studying the propagation of Rayleigh waves propagation in deep resonant waveguides. In more detail, inertial amplified resonators are exploited to design advanced metasurfaces with a prescribed static and a tunable dynamic response. The modular design of the tunable metasurfaces allows to shift and enlarge low-frequency spectral bandgaps without modifying the total inertia of the metasurface. Besides, an original dispersion law is derived to study the dispersive properties of Rayleigh waves propagating in thick resonant layers made of sub-wavelength resonators. Accordingly, a deep resonant wave barrier of mechanical resonators embedded inside the soil is designed to impede the propagation of seismic surface waves. Numerical models are developed to confirm the analytical dispersion predictions of the tunable metasurface and resonant layer. Finally, a medium-size scale resonant wave barrier is designed according to the soil stratigraphy of a real geophysical scenario to attenuate ground-borne vibration.

Inversão de dados de ondas de superfície Rayleigh

Neste trabalho compilamos informações sobre um grande número de medidas de velocidade de grupo para ondas Rayleigh do modo fundamental, com período até 100 segundos. Tais dados consistiram de informações retiradas da literatura geofísica e cobriram toda a Terra. Parte dos dados foi organizada em trabalhos anteriores e uma segunda parte foi apresentada aqui de forma inédita. Para a América do Sul, selecionamos os principais conjuntos de dados de tais ondas e elaboramos diversos perfis onde a distribuição de velocidade de ondas cisalhantes foi obtida a partir da inversão das curvas de dispersão de velocidade de grupo. Tais perfis serviram para termos uma ideia inicial da estrutura interna da Terra em nosso continente. Com o conjunto global de dados de velocidade de grupo foi possível obtermos os mapas de distribuição lateral de valores de velocidade para cada período referencial entre 20 e 100 segundos. Tais mapas foram produzidos da mesma forma que os mapas de velocidade de fase de ROSA (1986), onde a amostragem for para realizada para blocas medindo 10x10 graus, englobando toda a Terra, em projeção mercator. O valor de velocidade de grupo em cada bloco, para cada período, foi obtido a partir da inversão estocástica dos dados de anomalia de velocidade em relação aos modelos regionalizados de JORDAN (1981) com os valores de velocidade de grupo de ROSA et al. (1992). Os mapas de velocidade de grupo obtidos aqui foram então empregados, na América do Sul, com os valores de velocidade de fase dos mapas obtidos por ROSA (1986). Assim, foi possível determinarmos, em profundidade, os mapas de variação de velocidade de onda cisalhante e os mapas de distribuição de valores de densidade. Com isto, pudemos construir o primeiro mapa de profundidade do Moho (todo do Manto Superior) da América do Sul.

The Rayleigh disk as a wave direction indicator.

Mode of access: Internet.

Mechanische Charakterisierung von Konstruktionskeramik im oberflächennahen Bereich

Engineering ceramics, indentation methods, crack-resistance, Rayleigh waves, acoustic microscopy, machining parameters, green ceramic bodies, ultrasonic contact impedance, acoustic impedance, residual stress

Estudo do Ruído Sísmico no Arquipélago de Cabo Verde

Traditionally the study of Earth's internal structure has been based on analysis of seismic waves recorded during the occurrence of earthquakes. Recently, some researchers have shown to be possible to use ambient seismic noise (generally generated by ocean storms) to obtain dispersion curves with satisfactory results. Moreover, the use of ambient seismic noise measurement has advantages because they are independent of the earthquake-station geometry. This study aims to determine the dispersion curves of Rayleigh waves from the analysis of ambient seismic noise records, obtained in Cape Verde archipelago, whose origin and structure has attracted interest from several researchers. Analyzing the data collected between November 2007 and September 2008, Green's functions were determined. The analysis of these functions allowed to construct energy diagrams and to measure dispersion curves of group velocities between pairs of stations.

Representações espectrais de sistemas complexos: aplicações à síntese de superfícies brownianas fracionárias anisotrópicas, filtragem de sinais e identificação de correlações

In this thesis, we study the application of spectral representations to the solution of problems in seismic exploration, the synthesis of fractal surfaces and the identification of correlations between one-dimensional signals. We apply a new approach, called Wavelet Coherency, to the study of stratigraphic correlation in well log signals, as an attempt to identify layers from the same geological formation, showing that the representation in wavelet space, with introduction of scale domain, can facilitate the process of comparing patterns in geophysical signals. We have introduced a new model for the generation of anisotropic fractional brownian surfaces based on curvelet transform, a new multiscale tool which can be seen as a generalization of the wavelet transform to include the direction component in multidimensional spaces. We have tested our model with a modified version of the Directional Average Method (DAM) to evaluate the anisotropy of fractional brownian surfaces. We also used the directional behavior of the curvelets to attack an important problem in seismic exploration: the atenuation of the ground roll, present in seismograms as a result of surface Rayleigh waves. The techniques employed are effective, leading to sparse representation of the signals, and, consequently, to good resolutions

Dynamic structure-soil-structure interaction between nearby piled buildings under seismic excitation by BEM-FEM model

[EN]The dynamic throug-soil interaction between nearby pile supported structures in a viscoelastic half-space, under incident S and Rayleigh waves, is numerically studied. To this end, a three-dimensional viscoelastic BEM-FEM formulation for the dynamic analysis of piles and pile groups in the frequency domain is used, where soil is modelled by BEM and piles are simulated by one-dimensional finite elements as Bernouilli beams.

Application of the dynamic models to the detection of imperfections in plate Structures

This paper is part of a set of publications related with the development of mathematical models aimed to simulate the dynamic input and output of experimental nondestructive tests in order to detect structural imperfections. The structures to be considered are composed by steel plates of thin thickness. The imperfections in these cases are cracks and they can penetrate either a significant part of the plate thickness or be micro cracks or superficial imperfections. The first class of cracks is related with structural safety and the second one is more connected to the structural protection to the environment, particularly if protective paintings can be deteriorated. Two mathematical groups of models have been developed. The first group tries to locate the position and extension of the imperfection of the first class of imperfections, i.e. cracks and it is the object of the present paper. Bending Kirchoff thin plate models belong to this first group and they are used to this respect. The another group of models is dealt with membrane structures under the superficial Rayleigh waves excitation. With this group of models the micro cracks detection is intended. In the application of the first group of models to the detection of cracks, it has been observed that the differences between the natural frequencies of the non cracked and the cracked structures are very small. However, geometry and crack position can be identified quite accurately if this comparison is carried out between first derivatives (mode rotations) of the natural modes are used instead. Finally, in relation with the analysis of the superficial crack existence the use of Rayleigh waves is very promising. The geometry and the penetration of the micro crack can be detected very accurately. The mathematical and numerical treatment of the generation of these Rayleigh waves present and a numerical application has been shown.

Avaliações e testes dos métodos MASW e ReMi por meio do tratamento de dados empíricos e sintéticos em um programa de processamento e inversão desenvolvido em MATLAB e sua implicação em um problema geológico na Bacia de Taubaté

Os métodos de ondas superficiais com ênfase nas ondas Rayleigh foram utilizados como o núcleo desse trabalho de Doutorado. Inicialmente, as ondas Rayleigh foram modeladas permitindo o estudo de sensibilidade de suas curvas de dispersão sob diferentes configurações de parâmetros físicos representando diversos modelos de camadas, em que pôde ser observado parâmetros com maior e menor sensibilidade e também alguns efeitos provocados por baixas razões de Poisson. Além disso, na fase de inversão dos dados a modelagem das ondas Rayleigh foi utilizada para a construção da função objeto, que agregada ao método de mínimos quadrados, a partir do método de Levenberg-Marquardt, permitiu a implementação de um algoritmo de busca local responsável pela inversão de dados das ondas superficiais. Por se tratar de um procedimento de busca local, o algoritmo de inversão foi complementado por uma etapa de pré-inversão com a geração de um modelo inicial para que o procedimento de inversão fosse mais rápido e eficiente. Visando uma eficiência ainda maior do procedimento de inversão, principalmente em modelos de camadas com inversão de velocidades, foi implementado um algoritmo de pós-inversão baseado em um procedimento de tentativa e erro minimizando os valores relativos da raiz quadrada do erro quadrático médio (REQMr) da inversão dos dados. Mais de 50 modelos de camadas foram utilizados para testar a modelagem, a pré-inversão, inversão e pós-inversão dos dados permitindo o ajuste preciso de parâmetros matemáticos e físicos presentes nos diversos scripts implementados em Matlab. Antes de inverter os dados adquiridos em campo, os mesmos precisaram ser tratados na etapa de processamento de dados, cujo objetivo principal é a extração da curva de dispersão originada devido às ondas superficiais. Para isso, foram implementadas, também em Matlab, três metodologias de processamento com abordagens matemáticas distintas. Essas metodologias foram testadas e avaliadas com dados sintéticos e reais em que foi possível constatar as virtudes e deficiências de cada metodologia estudada, bem como as limitações provocadas pela discretização dos dados de campo. Por último, as etapas de processamento, pré-inversão, inversão e pós-inversão dos dados foram unificadas para formar um programa de tratamento de dados de ondas superficiais (Rayleigh). Ele foi utilizado em dados reais originados pelo estudo de um problema geológico na Bacia de Taubaté em que foi possível mapear os contatos geológicos ao longo dos pontos de aquisição sísmica e compará-los a um modelo inicial existente baseado em observações geomorfológicas da área de estudos, mapa geológico da região e informações geológicas globais e locais dos movimentos tectônicos na região. As informações geofísicas associadas às geológicas permitiram a geração de um perfil analítico da região de estudos com duas interpretações geológicas confirmando a suspeita de neotectônica na região em que os contatos geológicos entre os depósitos Terciários e Quaternários foram identificados e se encaixaram no modelo inicial de hemi-graben com mergulho para Sudeste.

Surface wave techniques for the study of engineering structures and materials

A wire drive pulse echo method of measuring the spectrum of solid bodies described. Using an 's' plane representation, a general analysis of the transient response of such solids has been carried out. This was used for the study of the stepped amplitude transient of high order modes of disks and for the case where there are two adjacent resonant frequencies. The techniques developed have been applied to the measurenent of the elasticities of refractory materials at high temperatures. In the experimental study of the high order in-plane resonances of thin disks it was found that the energy travelled at the edge of the disk and this initiated the work on one dimensional Rayleigh waves.Their properties were established for the straight edge condition by following an analysis similar to that of the two dimensional case. Experiments were then carried out on the velocity dispersion of various circuits including the disk and a hole in a large plate - the negative curvature condition.Theoretical analysis established the phase and group velocities for these cases and experimental tests on aluminium and glass gave good agreement with theory. At high frequencies all velocities approach that of the one dimensional Rayleigh waves. When applied to crack detection it was observed that a signal burst travelling round a disk showed an anomalous amplitude effect. In certain cases the signal which travelled the greater distance had the greater amplitude.An experiment was designed to investigate the phenanenon and it was established that the energy travelled in two nodes with different velocities.It was found by analysis that as well as the Rayleigh surface wave on the edge, a seoond node travelling at about the shear velocity was excited and the calculated results gave reasonable agreement with the experiments.

Análise dos microssismos registrados no arquipélago de São Pedro e São Paulo (ASPSP) e suas relações com variáveis oceanográficas

Microseisms are continuous vibrations pervasively recorded in the mili Hertz to 1 Hz frequency range. These vibrations are mostly composed of Rayleigh waves and are strongest in the 0.04 to 1 Hz frequency band. Their precise source mechanisms are still a matter of debate but it is agreed that they are related to atmospheric perturbations and ocean gravity waves. The Saint Peter Saint Paul Archipelago (SPSPA) is located in the equatorial region of the Atlantic Ocean about 1,100 km distant from the Brazilian northeastern coast. The SPSPA is composed by a set of several small rocky formations with a total area of approximately 17,000 m². Due to its remote distance from the continent and the lack of cultural noise, this location is a unique location for measuring microseismic noise and to investigate its relation with some climate and oceanographic variables. In the SPSPA we have recorded both primary microseisms (PM) at 0.04 – 0.12 Hz and the secondary microseisms (SM) at 0.12 – 0.4 Hz during 10 months in 2012 and 2013. Our analysis indicates a good correlation between the microseismic noise in the region and a seasonal dependency. In particular, the winter in the northern hemisphere. We have also shown that most of the PM is generated in the SPSPA itself. The SM source location depends with the seasonal climatic and oceanographic variables in the northern hemisphere

Estudo da estrutura subsuperficial da província Borborema com correlação de ruído sísmico

Ambient seismic noise has traditionally been considered as an unwanted perturbation in seismic data acquisition that "contaminates" the clean recording of earthquakes. Over the last decade, however, it has been demonstrated that consistent information about the subsurface structure can be extracted from cross-correlation of ambient seismic noise. In this context, the rules are reversed: the ambient seismic noise becomes the desired seismic signal, while earthquakes become the unwanted perturbation that needs to be removed. At periods lower than 30 s, the spectrum of ambient seismic noise is dominated by microseism, which originates from distant atmospheric perturbations over the oceans. The microsseism is the most continuous seismic signal and can be classified as primary – when observed in the range 10-20 s – and secondary – when observed in the range 5-10 s. The Green‘s function of the propagating medium between two receivers (seismic stations) can be reconstructed by cross-correlating seismic noise simultaneously recorded at the receivers. The reconstruction of the Green‘s function is generally proportional to the surface-wave portion of the seismic wavefield, as microsseismic energy travels mostly as surface-waves. In this work, 194 Green‘s functions obtained from stacking of one month of daily cross-correlations of ambient seismic noise recorded in the vertical component of several pairs of broadband seismic stations in Northeast Brazil are presented. The daily cross-correlations were stacked using a timefrequency, phase-weighted scheme that enhances weak coherent signals by reducing incoherent noise. The cross-correlations show that, as expected, the emerged signal is dominated by Rayleigh waves, with dispersion velocities being reliably measured for periods ranging between 5 and 20 s. Both permanent stations from a monitoring seismic network and temporary stations from past passive experiments in the region are considered, resulting in a combined network of 33 stations separated by distances between 60 and 1311 km, approximately. The Rayleigh-wave, dispersion velocity measurements are then used to develop tomographic images of group velocity variation for the Borborema Province of Northeast Brazil. The tomographic maps allow to satisfactorily map buried structural features in the region. At short periods (~5 s) the images reflect shallow crustal structure, clearly delineating intra-continental and marginal sedimentary basins, as well as portions of important shear zones traversing the Borborema Province. At longer periods (10 – 20 s) the images are sensitive to deeper structure in the upper crust, and most of the shallower anomalies fade away. Interestingly, some of them do persist. The deep anomalies do not correlate with either the location of Cenozoic volcanism and uplift - which marked the evolution of the Borborema Province in the Cenozoic - or available maps of surface heat-flow, and the origin of the deep anomalies remains enigmatic.