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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
41

Investigação experimental da fadiga ao cisalhamento em lajes de pontes com pré-lajes. / Fatigue experimental research to shear in brigges slabs with pré-slabs.

Paulo de Sá Pereira Cavalcanti 14 December 2010 (has links)
Um número significativo de pontes têm sido construídas na forma de grelhas de vigas pré-moldadas, sobre as quais apoiam-se pré-lajes com posterior concretagem de capa, finalizando a execução das lajes das mesmas. Esse processo construtivo tem sido largamente utilizado tendo em vista a racionalização da construção dispensando o uso de cimbramentos, abreviando consideravelmente os prazos de construção e consequentemente reduzindo os custos. Todavia no desenvolvimento do projeto, sabe-se que essas lajes são elementos altamente suscetíveis à fadiga e, tendo-se em vista a existência de concretagem em duas etapas (pré-laje e capa final) e concretos de idades diferentes, geram-se dúvidas obre o comportamento desta interface com relação às cargas dinâmicas atuantes no decorrer da vida útil da obra. A escassez de estudos ou pesquisas relacionadas a essa questão, levaram à realização do presente trabalho, de cunho experimental, e com o objetivo de se estudar o comportamento desses elementos submetidos às cargas de fadiga e as suas resistências finais no que se refere às cargas de ruptura antes e depois de fatigadas. Foram ensaiadas 9 lajes de concreto sendo 6 lajes com rugosidade normal (saliência dos agregados brita 1) e 3 com baixa rugosidade (alisamento com espátula de madeira). Não foram identificadas rupturas por fadiga e a resistência das lajes fatigadas se mantiveram, quando levadas a ruptura no final dos ensaios, no mesmo nível daquelas não fatigadas. / A significant number of bridges have been built in the form of grids of pre-cast beams on which pre-slab are supported, with posterior concreting of concrete cover, completing the execution of the slabs. This construction process has been widely used in order to rationalize the construction without shoring, shortening considerably the time of construction and thereby reducing costs. However in developing the project, it is known that these slabs are elements highly susceptible to fatigue and, keeping in mind the existence of concrete in two stages (pre-slab and final cover) and different ages, doubts about the behavior of this interface with respect to dynamic loads acting over the lifetime are generated. The scarcity of studies and researches related to this issue led to the realization of this experimental work, in order to study the behavior of these elements subjected to fatigue loading and their final resistance in relation to the failure load before and after fatigue loading. Tests were made in 9 concrete slabs, 6 with usual surface roughness (salience of crushed aggregates 1) and 3 with low roughness (smoothing with wooden spatula). It was verified that no rupture due to fatigue loading were identified and the resistance of the slabs submitted to fatigue loading remained on the same level of those not fatigued, when carried to cracking at the end of the tests.
42

Análise de provas de carga dinâmica em tubulões a céu aberto no campo experimental de fundações da EESC/USP / Analysis of dynamic loading test in large diameter bored piles, in the experimental field of EESC

Fábio Lopes Soares 13 March 2003 (has links)
Apresenta-se o conceito de elemento isolado de fundação em tubulão, e analisa-se 10 provas de carga dinâmica de energia crescente, nos tubulões, considerando as provas de carga estática realizadas anteriormente nos mesmos. Os ensaios são realizados em tubulões a céu aberto, situados em maciço de solo da formação Rio Claro e Itaqueri, no campo experimental de fundações da USP/EESC. As análises baseiam-se em curvas de resistência x deslocamento e gráficos que mostram a evolução da resistência mobilizada com o aumento da energia aplicada, resultantes dos impactos do ensaio dinâmico de energia crescente (metodologia PDA e análises CAPWAP). Analisam-se também a influência da pré-inundação e da variação da sucção do maciço de solos nos ensaios dinâmicos, o efeito do reensaio e a variabilidade nos resultados de ensaios de investigação geotécnica (SPT e CPT), realizados no campo experimental. Os resultados das provas de carga dinâmica de energia crescente mostram que a resposta do sistema isolado de fundação em tubulão é diferente a cada nível de energia aplicada e que a história de carregamento do elemento isolado de fundação é de extrema importância para análise dos ensaios nele realizado. / The concept of an isolated foundation element in large diameter bored pile is presented and 10 dynamic loading tests with increased energy are analysed. The interpretation of the dynamic loading tests has been proceeded with due consideration of the results of static loading tests performed previously. The loading tests have been carried out in large diameter bored piles founded in Rio Claro and Itaqueri soil formation, situated in the experimental foundation field of USP/EESC. The analyses are based on resistance x displacement curves and selected graphics illustrating the development of mobilized resistance with increasing applied energy during a dynamic loading test (PDA methodology and CAPWAP type analysis). The influence of previous inundation in soil mass and suction variation are also analysed, as well as the effect of test repetition and variability in SPT and CPT results. The results obtained with the dynamic loading tests with increasing energy revealed a distinct behaviour of the isolated foundation system for each level of applied energy, showing that the loading history is an aspect of extreme relevance to an adequate analysis of the dynamic tests perfomed.
43

Load-carrying and energy-dissipation capacities of ultra-high-performance concrete under dynamic loading

Buck, Jonathan J. 06 April 2012 (has links)
The load-carrying and energy-dissipation capacities of ultra-high-performance concrete (UHPC) under dynamic loading are evaluated in relation to microstructure composition at strain rates on the order of 10⁵ s⁻¹ and pressures of up to 10 GPa. Analysis focuses on deformation and failure mechanisms at the mesostructural level. A cohesive finite element framework that allows explicit account of constituent phases, interfaces, and fracture is used. The model resolves essential deformation and failure mechanisms in addition to providing a phenomenological account of the effects of the phase transformation. Four modes of energy dissipation are tracked, including pressure-sensitive inelastic deformation, damage through the development of distributed cracks, interfacial friction, and energy released through phase transformation of the quartz silica constituent. Simulations are carried out over a range of volume fractions of constituent phases to quantify trends that can be used to design materials for more damage-resistant structures. Calculations show that the volume fractions of the constituents have more influence on the energy-dissipation capacity than on the load-carrying capacity, that inelastic deformation is the source of over 70% of the energy dissipation, and that the presence of porosity changes the role of fibers in the dissipation process. The results also show that the phase transformation has a significant effect on the load-carrying and energy-dissipation capacities of UHPC for the conditions studied. Although transformation accounts for less than 2% of the total energy dissipation, the phase transformation leads to a twofold increase in the crack density and yields nearly an 18% increase to the overall energy dissipation. Microstructure-behavior relations are established to facilitate materials design and tailoring for target-specific applications.
44

The application of signal processing and artificial intelligence techniques in the condition monitoring of rotating machinery / Nicolaas Theodor van der Merwe

Van der Merwe, Nicolaas Theodor January 2003 (has links)
Condition monitoring of critical machinery has many economic benefits. The primary objective is to detect faults, for example on rolling element bearings, at an early stage to take corrective action prior to the catastrophic failure of a component. In this context, it is important to be able to discriminate between stable and deteriorating fault conditions. A number of conventional vibration analysis techniques exist by which certain faults in rotating machinery may be identified. However, under circumstances involving multiple fault conditions conventional condition monitoring techniques may fail, e.g. by indicating deteriorating fault conditions for stable fault situations or vice versa. Condition monitoring of rotating machinery that may have multiple, possibly simultaneous, fault conditions is investigated in this thesis. Different combinations of interacting fault conditions are studied both through experimental methods and simulated models. Novel signal processing techniques (such as cepstral analysis and equidistant Fourier transforms) and pattern recognition techniques (based on the nearest neighbour algorithm) are applied to vibration problems of this nature. A set of signal processing and pattern recognition techniques is developed for the detection of small incipient mechanical faults in the presence of noise and dynamic load (imbalance). In the case investigated the dynamic loading consisted of varying degrees of imbalance. It is demonstrated that the proposed techniques may be applied successfully to the detection of multiple fault conditions. / Thesis (Ph.D. (Electronical Engineering))--North-West University, Potchefstroom Campus, 2004.
45

The application of signal processing and artificial intelligence techniques in the condition monitoring of rotating machinery / Nicolaas Theodor van der Merwe

Van der Merwe, Nicolaas Theodor January 2003 (has links)
Condition monitoring of critical machinery has many economic benefits. The primary objective is to detect faults, for example on rolling element bearings, at an early stage to take corrective action prior to the catastrophic failure of a component. In this context, it is important to be able to discriminate between stable and deteriorating fault conditions. A number of conventional vibration analysis techniques exist by which certain faults in rotating machinery may be identified. However, under circumstances involving multiple fault conditions conventional condition monitoring techniques may fail, e.g. by indicating deteriorating fault conditions for stable fault situations or vice versa. Condition monitoring of rotating machinery that may have multiple, possibly simultaneous, fault conditions is investigated in this thesis. Different combinations of interacting fault conditions are studied both through experimental methods and simulated models. Novel signal processing techniques (such as cepstral analysis and equidistant Fourier transforms) and pattern recognition techniques (based on the nearest neighbour algorithm) are applied to vibration problems of this nature. A set of signal processing and pattern recognition techniques is developed for the detection of small incipient mechanical faults in the presence of noise and dynamic load (imbalance). In the case investigated the dynamic loading consisted of varying degrees of imbalance. It is demonstrated that the proposed techniques may be applied successfully to the detection of multiple fault conditions. / Thesis (Ph.D. (Electronical Engineering))--North-West University, Potchefstroom Campus, 2004.
46

The behaviour of rollover protective structures subjected to static and dynamic loading conditions

Clark, Brian January 2005 (has links)
The Rollover of heavy vehicles operating in the construction, mining and agricultural sectors is a common occurrence that may result in death or severe injury for the vehicle occupants. Safety frames called ROPS (Rollover Protective Structures) that enclose the vehicle cabin, have been used by heavy vehicle manufacturers to provide protection to vehicle occupants during rollover accidents. The design of a ROPS requires that a dual criteria be fulfilled that ensures that the ROPS has sufficient stiffness to offer protection, whilst possessing an appropriate level of flexibility to absorb some or most of the impact energy during a roll. Over the last four decades significant research has been performed on these types of safety devices which has resulted in the generation of performance standards that may be used to assess the adequacy of a ROPS design for a particular vehicle type. At present these performance standards require that destructive full scale testing methods be used to assess the adequacy of a ROPS. This method of ROPS certification can be extremely expensive given the size and weight of many vehicles that operate in these sectors. The use of analytical methods to assess the performance of a ROPS is currently prohibited by these standards. Reasons for this are attributed to a lack of available fundamental research information on the nonlinear inelastic response of safety frame structures such as this. The main aim of this project was to therefore generate fundamental research information on the nonlinear response behaviour of ROPS subjected to both static and dynamic loading conditions that could be used to contribute towards the development of an efficient analytical design procedure that may lessen the need for destructive full scale testing. In addition to this, the project also aspired to develop methods for promoting increased levels of operator safety during vehicle rollover through enhancing the level of energy absorbed by the ROPS. The methods used to fulfil these aims involved the implementation of an extensive analytical modelling program using Finite Element Analysis (FEA) in association with a detailed experimental testing program. From these studies comprehensive research information was developed on both the dynamic impact response and energy absorption capabilities of these types of structures. The established finite element models were then used to extend the investigation further and to carry out parametric studies. Important parameters such as ROPS post stiffness, rollslope inclination and impact duration were identified and their effects quantified. The final stage of the project examined the enhancement of the energy absorption capabilities of a ROPS through the incorporation of a supplementary energy absorbing device within the frame work of the ROPS. The device that was chosen for numerical evaluation was a thin walled tapered tube known as frusta that was designed to crush under a sidewards rollover and hence lessen the energy absorption demand placed upon the ROPS. The inclusion of this device was found to be beneficial in absorbing energy and enhancing the level of safety afforded to the vehicle occupants.
47

Incertezas de modelo na análise de torres metálicas treliçadas de linhas de transmissão / Model uncertainties in the transmission lines latticed steel towers analysis

Kaminski Junior, Joao January 2007 (has links)
Incertezas de modelo invadem todos os estágios de uma análise de confiabilidade estrutural, desde a determinação das ações e do próprio sistema estrutural, até o processo pelo qual o efeito destas ações é avaliado. Neste trabalho, o enfoque é dado nesse último tópico, mais especificamente na avaliação das incertezas de modelo mecânico em torres metálicas treliçadas de linhas de transmissão (LT), o qual tem permanecido ignorado nas estimativas de confiabilidade até então, em parte devido a sua natureza elusiva. Logo, o problema consiste em avaliar as incertezas na predição da resposta estrutural, uma vez que todos os parâmetros que definem as ações externas e o próprio sistema são claramente definidos. A principal motivação deste trabalho partiu de um estudo conduzido pela CIGRÉ sobre torres metálicas treliçadas de LT submetidas a cargas estáticas, o qual sugere que as incertezas de modelo neste tipo de estrutura são relevantes e não podem ser desprezadas, podendo influenciar significativamente na estimativa da confiabilidade. Neste trabalho, são avaliados diferentes modelos mecânicos de torres de LT sujeitos a ações estáticas, além de modelos de torres e trechos de LT submetidos à ação dinâmica de ruptura de cabo, adotada por ser um carregamento dinâmico “bem definido”. Na análise estática, são estudados desde modelos simplificados de torres autoportantes, adotados na prática usual de projeto, até modelos mais aprimorados. A dispersão nos resultados numéricos entre os modelos é usada para quantificar as incertezas relacionadas ao modelo mecânico, e os resultados disponíveis de ensaios estáticos em protótipos são utilizados para encontrar os modelos cuja resposta mais se aproxima dos valores experimentais. A resposta dinâmica de torres metálicas treliçadas de LT submetidas à ruptura de cabo, é comparada entre vários modelos, com diferentes graus de sofisticação e detalhe. São estudados desde o modelo usual de análise e projeto de torres para este tipo de carregamento, passando por modelos relativamente simples, com uma única torre sujeita a uma carga variável no tempo, simulando o efeito da ruptura de um cabo, até modelos mais complexos de trechos de LT, os quais incluem várias torres, cabos e cadeias de isoladores. Diversas fontes de incerteza são avaliadas, considerando a influência de fatores relevantes tais como: a discretização dos elementos de cabo, as condições de contorno dos elementos de cabo das extremidades, as leis constitutivas dos elementos de barra e de cabo e o amortecimento estrutural. Por fim, são discutidas e apresentadas possíveis maneiras de considerar explicitamente a incerteza de modelo na estimativa da confiabilidade e em códigos de projeto de estruturas de linhas de transmissão. / Model uncertainties pervade all stages of a structural reliability analysis, from the description of loads and the system itself, to the process by which the effect of loads on the system is evaluated. In this study, attention is focused on the last issue, specifically in the evaluation of model uncertainties on transmission lines (TL) latticed steel towers, which has remained largely ignored in previous developments of structural reliability, in part due to its elusive nature. In essence, the problem consists of evaluating the uncertainty in response predictions, once all parameters that define the external actions and the system itself have been unequivocally prescribed. The main motivation of this thesis was a study conducted by CIGRÉ on TL latticed steel towers subjected to static loads, among other exploratory assessments, which suggests that model uncertainty is a relevant factor and cannot be disregarded, could significantly influence the outcome of reliability assessments. Herein, different mechanical models of TL self-supporting towers subjected to static loads are evaluated, besides the models of towers and TL segments submitted to dynamic load due to cable rupture, adopted by being a “well defined” loading. In the static analysis, from simplified models of self-supporting towers, like adopted in usual practice of project, to more refined models are studied. The dispersion in the numeric results among the models, together with the data of static prototype tests, are used to quantify model uncertainties. The dynamic response of latticed TL steel towers subjected to cable rupture is predicted by use of various models with different degrees of sophistication or detailing. The predictions of the various models are compared with the aim of quantifying model uncertainty. Several uncertainty sources are evaluated, considering the influence of relevant factors such as: the discretization of the cable elements, the boundary conditions of the end cable elements, the constitutive laws of cables and tower members and the structural damping. Finally, possible ways to explicitly consider model uncertainty in reliability assessments and in code formulations are discussed.
48

Estudo paramétrico para um muro de gravidade submetido a carregamentos sísmicos. / Parametric Study for a gravity wall subjected to seismic loads.

Tatiana Galvão Kurz 18 November 2014 (has links)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A presente dissertação apresenta um estudo do comportamento de um muro de gravidade flexível submetido a carregamentos sísmicos. A influência do carregamento sísmico, e mais precisamente da variação da aceleração horizontal de pico é avaliada num estudo paramétrico, através da análise dos resultados obtidos para os deslocamentos e acelerações horizontais que ocorreram no paramento do muro de gravidade. Optou-se pela análise ao longo do tempo, introduzindo o carregamento sísmico ao modelo numérico do qual fazia parte o muro de gravidade através de 5 históricos temporais de acelerogramas horizontais normalizados em 0,05g, 0,10g, 0,15g, 0,20g e 0,25g. O evento sísmico de origem dos acelerogramas normalizados foi o terremoto ocorrido no Chile em 27 de fevereiro de 2010 e medido na estação em San Jose de Maipo, a 332,7km do epicentro do terremoto. Utiliza-se um software computacional aplicado à Geotecnia, o Plaxis, para a calibração de um modelo numérico em situação estática e posterior desenvolvimento das análises paramétricas em condições sísmicas. As análises realizadas para avaliação do comportamento do muro de gravidade em condição sísmica foram a verificação da influência da variação do acelerograma horizontal normalizada introduzido na base do modelo nos valores das acelerações e deslocamentos horizontais atuantes no muro e a verificação da influência do carregamento sísmico em comparação com a situação estática, comparando-se os valores dos deslocamentos horizontais obtidos na análise estática e nas análises dinâmicas. Os fatores que influenciam potencialmente nos resultados numéricos em condições sísmicas foram apresentados, destacando-se os aspectos relacionados à modelagem numérica em condição de sismo. Os modelos constitutivos oferecidos, a possibilidade de incorporação do carregamento sísmico na base do modelo e a possibilidade de consideração do amortecimento visco-elástico de Rayleigh nos materiais são as principais qualidades do Plaxis, utilizado na modelagem numérica. Avaliou-se positivamente a potencialidade do Plaxis, visto que o programa mostrou-se uma ferramenta capaz de simular o comportamento de muros de gravidade sujeitos a carregamentos sísmicos.
49

Incertezas de modelo na análise de torres metálicas treliçadas de linhas de transmissão / Model uncertainties in the transmission lines latticed steel towers analysis

Kaminski Junior, Joao January 2007 (has links)
Incertezas de modelo invadem todos os estágios de uma análise de confiabilidade estrutural, desde a determinação das ações e do próprio sistema estrutural, até o processo pelo qual o efeito destas ações é avaliado. Neste trabalho, o enfoque é dado nesse último tópico, mais especificamente na avaliação das incertezas de modelo mecânico em torres metálicas treliçadas de linhas de transmissão (LT), o qual tem permanecido ignorado nas estimativas de confiabilidade até então, em parte devido a sua natureza elusiva. Logo, o problema consiste em avaliar as incertezas na predição da resposta estrutural, uma vez que todos os parâmetros que definem as ações externas e o próprio sistema são claramente definidos. A principal motivação deste trabalho partiu de um estudo conduzido pela CIGRÉ sobre torres metálicas treliçadas de LT submetidas a cargas estáticas, o qual sugere que as incertezas de modelo neste tipo de estrutura são relevantes e não podem ser desprezadas, podendo influenciar significativamente na estimativa da confiabilidade. Neste trabalho, são avaliados diferentes modelos mecânicos de torres de LT sujeitos a ações estáticas, além de modelos de torres e trechos de LT submetidos à ação dinâmica de ruptura de cabo, adotada por ser um carregamento dinâmico “bem definido”. Na análise estática, são estudados desde modelos simplificados de torres autoportantes, adotados na prática usual de projeto, até modelos mais aprimorados. A dispersão nos resultados numéricos entre os modelos é usada para quantificar as incertezas relacionadas ao modelo mecânico, e os resultados disponíveis de ensaios estáticos em protótipos são utilizados para encontrar os modelos cuja resposta mais se aproxima dos valores experimentais. A resposta dinâmica de torres metálicas treliçadas de LT submetidas à ruptura de cabo, é comparada entre vários modelos, com diferentes graus de sofisticação e detalhe. São estudados desde o modelo usual de análise e projeto de torres para este tipo de carregamento, passando por modelos relativamente simples, com uma única torre sujeita a uma carga variável no tempo, simulando o efeito da ruptura de um cabo, até modelos mais complexos de trechos de LT, os quais incluem várias torres, cabos e cadeias de isoladores. Diversas fontes de incerteza são avaliadas, considerando a influência de fatores relevantes tais como: a discretização dos elementos de cabo, as condições de contorno dos elementos de cabo das extremidades, as leis constitutivas dos elementos de barra e de cabo e o amortecimento estrutural. Por fim, são discutidas e apresentadas possíveis maneiras de considerar explicitamente a incerteza de modelo na estimativa da confiabilidade e em códigos de projeto de estruturas de linhas de transmissão. / Model uncertainties pervade all stages of a structural reliability analysis, from the description of loads and the system itself, to the process by which the effect of loads on the system is evaluated. In this study, attention is focused on the last issue, specifically in the evaluation of model uncertainties on transmission lines (TL) latticed steel towers, which has remained largely ignored in previous developments of structural reliability, in part due to its elusive nature. In essence, the problem consists of evaluating the uncertainty in response predictions, once all parameters that define the external actions and the system itself have been unequivocally prescribed. The main motivation of this thesis was a study conducted by CIGRÉ on TL latticed steel towers subjected to static loads, among other exploratory assessments, which suggests that model uncertainty is a relevant factor and cannot be disregarded, could significantly influence the outcome of reliability assessments. Herein, different mechanical models of TL self-supporting towers subjected to static loads are evaluated, besides the models of towers and TL segments submitted to dynamic load due to cable rupture, adopted by being a “well defined” loading. In the static analysis, from simplified models of self-supporting towers, like adopted in usual practice of project, to more refined models are studied. The dispersion in the numeric results among the models, together with the data of static prototype tests, are used to quantify model uncertainties. The dynamic response of latticed TL steel towers subjected to cable rupture is predicted by use of various models with different degrees of sophistication or detailing. The predictions of the various models are compared with the aim of quantifying model uncertainty. Several uncertainty sources are evaluated, considering the influence of relevant factors such as: the discretization of the cable elements, the boundary conditions of the end cable elements, the constitutive laws of cables and tower members and the structural damping. Finally, possible ways to explicitly consider model uncertainty in reliability assessments and in code formulations are discussed.
50

Determinação da capacidade de carga última de estaca cravada em ensaio de carregamento dinâmico de energia crescente / The evaluation of the ultimate bearing capacity of driven piles by using increasing energy dynamic load tests

Nelson Aoki 07 November 1997 (has links)
Esta tese aplica o conceito de energia complementar para a determinação da capacidade de carga última de estaca cravada no ensaio de carregamento dinâmico de energia crescente. O ensaio de carregamento dinâmico com impactos de energia constante só permite obter a resistência estática mobilizada do modelo de CASE ou de SMITH com base na teoria da equação da onda e no Pile Driving Analyzer. A aplicação de impactos de energia crescente mostra que a curva de resistência estática - deslocamento dinâmico apresenta: a) trecho linear crescente seguido de trecho que se curva até que a tangente se torna vertical ou b) trecho crescente quase linear até um pico de resistência, seguido de uma curva de descarga até um determinado valor que corresponde à tangente vertical ou, c) trecho linear crescente seguido de trecho curvo cuja tangente não se verticaliza e onde a resistência volta a crescer. A ruptura do sistema estaca - maciço de solos é caracterizada pela energia complementar que passa em um máximo sempre que a resistência mobilizada atinge um pico. No pós-ruptura o excesso de energia aplicada e o excesso de trabalho das forças de amortecimento do impacto, em relação ao pico máximo, crescem linearmente com o nível de energia cinética aplicada. / This thesis suggests how to evaluate the ultimate bearing capacity of driven piles by using dynamic load tests with increasing energy. The dynamic load test with constant energy blows only allows the determination of the mobilized static resistance (CASE and SMITH\'s model), by using the wave equation theory and the Pile Driving Analyzer. The application of increasing energy blows shows that this static resistance: a) increases with increasing energy and then becomes constant or; b) increases with increasing energy up to a peak resistance and thereafter first decreases and then becomes constant or, c) starts to increase with increasing energy, then remains constant and after some blows starts to increase again. lt is shown that the rupture of the pile-soil system is characterized by the kinetic complementary energy reaching an upper limit when the impact mobilizes the maximum static pile capacity. All the energy or work done by damping forces, in excess of this maximum or peak situation, increases linearly with increasing energy.

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