Realistic assessments of liver injury risk for the entire occupant population require incorporating inter-subject variations into numerical human models. The main objective of this study was to quantify the variations in shape and material properties of the human liver. Statistical shape analysis was applied to analyze the geometrical variation using a surface set of 15 adult human livers recorded in an occupant posture. Principal component analysis was then utilized to obtain the modes of variation, the mean model, and a set of 95% statistical boundary shape models. Specimen-specific finite element (FE) models were employed to quantify material and failure properties of human liver parenchyma. The mean material model parameters were then determined, and a stochastic optimization approach was utilized to determine the standard deviations of the material model parameters. The distributions of the material parameters were used to develop probabilistic FE models of the liver implemented in THUMS human FE model to simulate oblique impact tests under three impact speeds. In addition, the influence of organ preservation on the biomechanical responses of animal livers was investigated using indentation and tensile tests. Results showed that the first five modes of the human liver shape models accounted for more than 70% of the overall anatomical variations. The Ogden material model with two parameters showed a good fit to experimental tensile data before failure. Significant changes of the biomechanical responses of liver parenchyma were found after cooling or freezing storage. The force-deflection responses of THUMS model with probabilistic liver material models were within the test corridors obtained from cadaveric tests. Significant differences were observed in the maximum and minimum principal Green-Lagrangian strain values recorded in the THUMS liver model with the default and updated average material properties. The results from this study could help in the development of more biofidelic human models, which may provide a better understanding of injury mechanisms of the liver during automobile collisions. / Ph. D.

[pt] Freqüentemente as análises de estabilidade de taludes são feitas por métodos determinísticos, nos quais é obtido um Fator de Segurança (FS). Estes métodos não quantificam as incertezas existentes nas variáveis de entrada (parâmetros de resistência) na análise. Tampouco mostram detalhes sobre qual variável afeta mais o resultado. Os métodos probabilísticos permitem superar estes problemas. A presente pesquisa tem como objetivo comparar dois métodos probabilísticos geralmente utilizados (Estimativas Pontuais e Segundo Momento). Três projetos utilizados comumente na geotecnia são analisados: barragem de rejeitos, talude de solo e aterro sobre argila mole.Um aspecto importante na análise probabilística é a quantificação adequada do desvio padrão. É sabido que as propriedades dos solos mostram uma correlação no espaço, pelo que o desvio padrão calculado por métodos clássicos da estatística é superestimado em comparação ao valor real no campo. El-Ramly (2001) desenvolveu uma metodologia para o cálculo da probabilidade de ruptura considerando a correlação espacial das propriedades do solo. Esta metodologia é de difícil aplicação prática. Serão, portanto, avaliadas na presente pesquisa as técnicas geralmente usadas de probabilidade e estabilidade de taludes, juntamente com um fator de correção proposto por Vanmarcke (1977a). Estas técnicas de probabilidade de estabilidade de taludes são factíveis de serem utilizadas junto com este fator de correção. Verificou-se que o Método de Segundo Momento é de mais fácil utilização, e portanto adequado para emprego em projetos geotécnicos. / [en] The analysis of slope stability is often determined by deterministic methods, in which a Factor of Security (FS) is obtained. These methods do not quantify the uncertainty in the input variables (strength parameters). Neither these methods show details which variable affects mostly the outcome results. The probabilistic methods allow overcoming these restrictions. This study aims at comparing two probabilistic methods of general use (Point Estimates and First Order Second Moment). Three projects commonly used in geotechnical engineering are analyzed: tailings dam, slope soil and embankment on soft clay. An important aspect of the probabilistic analysis is the proper quantification of the standard deviation. It is known that the soil properties show a correlation in space, so the standard deviation, calculated by traditional methods of statistics, is overestimated when compared to the real field value. El-Ramly (2001) developed a methodology for calculating the probability of failure considering the spatial correlation of the soil properties. This methodology is difficult to apply in practice. The present study will therefore evaluate the techniques generally used in probability of failure of slopes. These probability techniques applied to slope stability can be used together with a correction factor proposed by Vanmarcke (1977b). The Second Moment Method was found to be easier to use, and therefore more suitable for geotechnical projects.

[pt] Nos últimos 45 anos foram publicados muitos artigos referentes à previsão da pressão de poros em folhelhos, como resultado da necessidade de otimizar o processo construtivo de poços de petróleo. Neste trabalho se apresenta um panorama dos métodos de previsão de pressão de poros existentes, com suas vantagens e desvantagens, com seus pontos fortes e suas críticas, com seus acertos e não acertos; procurando explicar os motivos das diferenças entre o previsto e o real. Em geral são descritos 12 métodos de previsão de pressão de poros, além do conceito do Centróide, 3 técnicas para detectar descarga de tensões efetivas numa formação rochosa, e uma descrição do uso da sísmica na previsão da pressão de poros. Foram aplicados os métodos de Eaton (1975) e Bowers (1995) com o objetivo de fazer uma discussão sobre as incertezas presentes nos parâmetros de cada modelo, complementado o estudo com uma análise de sensibilidade. Como resultado das incertezas existentes se aplicou uma análise probabilística baseada na simulação de Monte Carlo e usando o método de Eaton, com o objetivo de apresentar resultados dentro de intervalos de confiança e permitir planos de contingência durante o projeto de construção do poço. Finalmente são avaliados os resultados de uma análise 3D de previsão de pressão de poros utilizando o modelo de Eaton e o Trend de Bowers. Os cubos de dados foram obtidos por interpolação espacial ponderada partindo de registros de poços. Os resultados mostram que este tipo de análise pode ser usado com fins qualitativos, obtendo cubos de gradientes de pressão de poros aonde se observam as zonas de maior e menor risco. / [en] In the last 45 years were published many articles referring to shale pore pressure prediction, due to the necessity of optimizing the constructive process of petroleum wells. In this work shows up a view of the pore pressure prediction methods with its advantages and disadvantages, with its strong points and its critics, with its hits and failures, trying to explain the causes of the differences between the predicted values and the real ones. As result of the bibliographical revision, we obtained a historical of the pore pressure prediction, furthermore gathering the principal mechanisms of generation of pore pressures and mechanisms of lateral variation of the same. Also, were described 12 methods of pore pressure prediction, the Centroid concept, 3 techniques to detect unloading of effective tensions in a rock formation, and a description of the use of the seismic in the pore pressure prediction. The Eaton (1975) and the Bowers (1995) methods were applied with the objective to discuss the uncertainties in the parameters of each model, this was complemented with sensibility analysis. As result of the existent uncertainties, we applied a probabilistic analyze, based on the Monte Carlo simulation and using the Eaton´s method, with the aim to present results within confidence intervals and to allow contingency plans during the well construction project. Finally, the results of a 3D pore pressure prediction using the Eaton model and the Bowers Trend, were assessed. The data cubes were obtained by weighted space interpolation using well logs at the same basin. We concluded that the results from this type of analysis can be used such as qualitative purposes, obtaining pore pressure gradients cubes, where can be observed bigger and lesser risk zones.

O objetivo principal deste trabalho é apresentar um modelo de análise probabilística do comportamento ao longo do tempo de estruturas de concreto. Para isso, é realizada a análise probabilística em conjunto com análise numérica. A análise numérica é realizada através de um programa computacional, baseado no método dos elementos finitos, que considera o comportamento não-linear e dependente do tempo dos materiais, assim como o processo evolutivo da construção. Para determinar o efeito das incertezas dos parâmetros é realizada uma análise probabilística, utilizando o método de amostragem por hipercubo latino. O modelo apresentado pode ser aplicado para a análise probabilística do comportamento ao longo do tempo das estruturas de concreto em geral. No entanto, foi aplicado na análise das flechas diferidas de lajes pré-moldadas formadas por vigotas com armação treliçada. Com esta análise, pôde-se propor um coeficiente multiplicador das flechas imediatas para a avaliação das flechas diferidas no tempo. O coeficiente multiplicador obtido para as lajes pré-moldadas formadas por vigotas com armação treliçada pode alcançar valores muito superiores ao fator 'alfa'f recomendado pela NBR 6118 (2003) para o caso de vigas de concreto armado. / The goal of this research is to present a probabilistic analysis model of the long-term behavior of concrete structures. For that, the probabilistic analysis is carried out together with numerical analysis. The numerical analysis is carried out using a software based on the finite element method that takes into account the nonlinear and time dependent behavior of the materials, as well as the evolutionary construction process. A probabilistic analysis is carried out in order to determine the effects of the uncertainties of the parameters, using latin hypercube sampling method. The presented model can be applied in the probabilistic analysis of the long-term behavior of concrete structures in general. However, it was applied in the analysis of the long-term deflections of precast slabs made by joist with lattice reinforcement. By this analysis, a multiplier coefficient of immediate deflections to evaluate long-term deflections could be proposed. The multiplier coefficient obtained for precast slabs made by joist with lattice reinforcement can reach values much higher than the factor 'alfa'f recommended by NBR 6118 (2003) for the case of reinforced concrete beams.

Binary Decision Diagrams (BDDs) sind eine Datenstruktur für Boolesche Funktionen, die auch unter dem Namen branching program bekannt ist. In ordered binary decision diagrams (OBDDs) müssen die Tests einer festen Variablenordnung genügen. In free binary decision diagrams (FBDDs) darf jede Variable höchstens einmal getestet werden. Die Effizienz neuer Varianten des BDD-Konzepts wird gewöhnlich anhand spektakulärer (worst-case) Beispiele aufgezeigt. Wir verfolgen einen anderen Ansatz und vergleichen die Darstellungsgrößen für fast alle Booleschen Funktionen. Während I. Wegener bewiesen hat, daß für die `meisten' n die erwartete OBDD-Größe einer zufälligen Booleschen Funktion von n Variablen gleich der worst-case Größe bis auf Terme kleinerer Ordnung ist, zeigen wir daß dies nicht der Fall ist für n innerhalb von Intervallen konstanter Länge um die Werte n = 2h + h. Ferner gibt es Bereiche von n, in denen minimale FBDDs fast immer um mindestens einen konstanten Faktor kleiner sind als minimale OBDDs. Unsere Hauptsätze ha ben doppelt exponentielle Wahrschein- lichkeitsschranken (in n). Außerdem untersuchen wir die Entwicklung zufälliger OBDDs und ihrer worst-case Größe und decken dabei ein oszillierendes Verhalten auf, das erklärt, warum gewisse Aussagen im allgemeinen nicht verstärkt werden können. / Binary Decision Diagrams (BDDs) are a data structure for Boolean functions which are also known as branching programs. In ordered binary decision diagrams (OBDDs), the tests have to obey a fixed variable ordering. In free binary decision diagrams (FBDDs), each variable can be tested at most once. The efficiency of new variants of the BDD concept is usually demonstrated with spectacular (worst-case) examples. We pursue another approach and compare the representation sizes of almost all Boolean functions. Whereas I. Wegener proved that for `most' values of n the expected OBDD size of a random Boolean function of n variables is equal to the worst-case size up to terms of lower order, we show that this is not the case for n within intervals of constant length around the values n = 2h + h. Furthermore, ranges of n exist for which minimal FBDDs are almost always at least a constant factor smaller than minimal OBDDs. Our main theorems have doubly exponentially small probability bounds (in n). We also investigate the evolution of random OBDDs and their worst-case size, revealing an oscillating behaviour that explains why certain results cannot be improved in general.

Na prática de fundações por estacas helicoidais submetidas a esforços de tração (também conhecidas como ancoragens helicoidais) frequentemente são observadas discrepâncias entre valores de capacidade de carga previstos por métodos teóricos e medidos em provas de carga. Entre outros fatores, estas diferenças ocorrem pelo fato de nenhum dos métodos teóricos existentes considerarem adequadamente o efeito da instalação no comportamento deste tipo de ancoragem. Durante a penetração por rotação das hélices da estaca/ancoragem no terreno, os parâmetros de resistência e de rigidez do solo penetrado, e as tensões radiais em torno da estaca são modificados. O nível de degradação do solo que suportará as cargas aplicadas na ancoragem é dependente do tipo e características do solo, e do número e geometria das hélices. Diante deste cenário de incertezas provenientes do efeito da instalação, duas distintas abordagens probabilísticas são apresentadas nesta dissertação. A primeira abordagem tem o intuito de verificar o efeito da variabilidade de distintas variáveis influentes no comportamento de ancoragens helicoidais. Para este fim, foi utilizado o método de expansão em Polinômio de Caos, baseado na modelagem numérica de ancoragens helicoidais em areia, calibrada com os resultados medidos em modelos testados em centrifuga. Foi verificado nesta parte o nível de influência de cada parâmetro de entrada do solo no comportamento carga x deslocamento da ancoragem. No segundo enfoque, foi proposto e avaliado um modelo probabilístico para simular a curva carga x deslocamento, obtida em provas de carga. Nesta parte, foi realizada uma análise de confiabilidade para verificação do estado limite de serviço de ancoragens helicoidais baseada em resultados de provas de carga executadas no Brasil. São também apresentadas nesta análise as incertezas provenientes da variabilidade do fator de torque utilizado na verificação da capacidade de carga durante a instalação da ancoragem. / Discrepancies between predicted and measured results of uplift capacity of helical piles (or helical anchors) have been commonly observed in the practical experience. Among other factors, these differences occur because the existing theoretical methods do not consider adequately the installation effect on the behavior of this type of anchor. During the anchor installation, the penetration by rotation of the helical plates into the ground modifies the soil strength and stiffness parameters, and the radial stresses around the pile. The degradation degree of the soil penetrated is dependent on the type and characteristics of the soil, and also on the number and geometry of helices. Against this background of uncertainty due to the installation effect, two different probabilistic approaches are presented in this dissertation. The first approach is used to verify the effect of the variability of different influential variables on the behavior of helical anchors. For this purpose, the probabilistic method named Sparse Polynomial Chaos Expansion was used, based on the numerical modeling of helical anchors in sand, calibrated with measured results obtained from reduced models tested in centrifuge. As a result, the level of influence of each soil input parameter on the anchor load-displacement behavior is presented. In the second approach, a probabilistic model to simulate the load-displacement curve obtained in load tests was proposed and evaluated. For this part, a reliability analysis was performed to check the serviceability limit state of helical anchors, based on the results of field load tests performed in Brazil. In addition, the uncertainties arising from the variability of the torque factor were evaluated. The torque factor is frequently used to verify the uplift capacity of helical anchors during installation.

An approach was developed which allows for design studies of commercial aircraft using physics-based noise analysis methods while retaining the ability to perform the rapid tradeoff and risk analysis studies needed at the conceptual design stage. A prototype integrated analysis process was created for computing the total aircraft EPNL at the Federal Aviation Regulations Part 36 certification measurement locations using physics-based methods for fan rotor-stator interaction tones and jet mixing noise. The analysis process was then used in combination with design of experiments to create response surface equations (RSEs) for the engine and aircraft performance metrics, geometric constraints and takeoff and landing noise levels. In addition, Monte Carlo analysis was used to assess the expected variability of the metrics under the influence of uncertainty, and to determine how the variability is affected by the choice of engine cycle. Finally, the RSEs were used to conduct a series of proof-of-concept conceptual-level design studies demonstrating the utility of the approach. The study found that a key advantage to using physics-based analysis during conceptual design lies in the ability to assess the benefits of new technologies as a function of the design to which they are applied. The greatest difficulty in implementing the physics-based analysis proved to be the generation of design geometry at a sufficient level of detail for high-fidelity analysis.

Baigiamajame magistro darbe išnagrinėti STR ir EC 2 betono fizikinių ir mechaninių rodiklių nustatymo metodai bei šiose normose pateiktų įtempių nuostolių skaičiavimo modeliai. Aprašytas tikimybinis įtempių nuostolių vertinimo modelis. Atlikta atskirųjų ir suminių įtempių nuostolių analizė pagal STR ir EC 2 modelius, aprašyti šių modelių skirtumai. Išnagrinėta atskirų fizikinių faktorių lemiančių įtempių nuostolius įtaka. Atlikta iš anksto įtemptos gelžbetoninės sijos tikimybinė suminių įtempių nuostolių analizė. Darbe pateiktas kiaurymėtųjų perdangos plokščių suminių įtempių nuostolių skaičiavimo rezultatų pagal EC 2 ir STR modelius ir eksperimentinių įtempių nuostolių palyginimas. / Evaluation of different physical and mechanical factors of concrete according to STR and EC 2 models is considered in this master thesis. Probabilistic model for prestress loss determination is presented in this paper. The analysis of separate and total losses according to STR and EC 2 models was carried out. Some differencies of these models were described. The influence of several factors to the value of separate prestress loss has been studied in this thesis. The probabilistic analysis of long-term losses of post-tensioned RC beam has been carried out. The comparison of total prestress loss values of hollow core slabs according to EC 2, STR and experimental results is subjected in this master thesis.

Une question fondamentale qui surgit dans le cadre de l’analyse probabiliste du risque sismique est le choix des indicateurs de nocivité des signaux sismiques. En plus de réduire la variabilité de la réponse structurelle (ou non structurelle),un indicateur amélioré (i.e. capable de mieux capturer les caractéristiques de nocivité des mouvements sismiques, aussi bien que l’alea sismique) fournit des critères moins stricts pour la sélection des signaux sismiques.Deux nouveaux indicateurs sont proposés dans cette étude: le premier, nommé ASAR (i.e. Relative Average Spectral Acceleration), est conçu pour la prévision de la demande structurelle, le second, nommé E-ASAR (i.e.Equipment Relative Average Spectral Acceleration), vise à prévoir la demande des composants non structuraux. Les performances des indicateurs proposés sont comparées avec celles des indicateurs de la littérature, sur la base de: a)milliers d’enregistrements sismiques ; b) analyses numériques conduites avec des modèles représentants différents types de bâtiments; et c) analyses statistiques rigoureuses des résultats. Selon l'étude comparative, les indicateurs développés s'avèrent être plus “efficaces” que les indicateurs couramment utilisés. D'ailleurs, l’ASAR et l’E-ASAR ont montré au propre la caractéristique de la “suffisance” en ce qui concerne la magnitude, la distance source-site, et le type de sol (VS30). De plus, les deux indicateurs originaux peuvent être calculés simplement avec la connaissance de la fréquence fondamentale du bâtiment. Cette caractéristique rend l’ASAR et l’E-ASAR facilement exploitables dans les études probabilistes d’alea sismique.Par conséquent, en raison de leur efficacité, suffisance, robustesse et formulation simple, l’ASAR et l’E-ASAR peuvent être considérés comme des candidats prometteurs pour la définition de l’alea sismique dans les cadres de l'analyse probabiliste et déterministe du risque sismique. / A fundamental issue that arises in the framework of Probabilistic Seismic Risk Analysis is the choice of groundmotion Intensity Measures (IMs). In addition to reducing record-to-record variability, an improved IM (i.e. one able tobetter capture the damaging features of a record, as well as the site hazard) provides criteria for selecting input groundmotions to loosen restrictions.Two new structure-specific IMs are proposed in this study: the first, namely ASAR (i.e. Relative Average SpectralAcceleration), is conceived for Structural demand prediction, the second namely, E-ASAR (i.e. Equipment-RelativeAverage Spectral Acceleration), aims to predict Non-Structural components acceleration demand. The performance ofthe proposed IMs are compared with the ones of current IMs, based on: a) a large dataset of thousands recordedearthquake ground motions; b) numerical analyses conducted with state-of-the-art FE models, representing actualload-bearing walls and frame structures, and validated against experimental tests; and c) systematic statistical analysesof the results. According to the comparative study, the introduced IMs prove to be considerably more “efficient” withrespect to the IMs currently used. Likewise, both ASAR and E-ASAR have shown to own the characteristic of“sufficiency” with respect to magnitude, source-to-site distance and soil-type (Vs30). Furthermore, both the introducedIMs possess the valuable characteristics to need (in order to be computed) merely the knowledge of the building’sfundamental frequency, exactly as it is for the wide-spread spectral acceleration Spa(f1). This key characteristic makesboth ASAR and E-ASAR easily exploitable in Probabilistic Seismic Hazard Analysis.Therefore, due to their proven efficiency, sufficiency, robustness and applicable formulation, both ASAR and EASARcan be considered as worthy candidates for defining seismic hazard within the frameworks of both Probabilisticand Deterministic Seismic Risk Analysis.

Na prática de fundações por estacas helicoidais submetidas a esforços de tração (também conhecidas como ancoragens helicoidais) frequentemente são observadas discrepâncias entre valores de capacidade de carga previstos por métodos teóricos e medidos em provas de carga. Entre outros fatores, estas diferenças ocorrem pelo fato de nenhum dos métodos teóricos existentes considerarem adequadamente o efeito da instalação no comportamento deste tipo de ancoragem. Durante a penetração por rotação das hélices da estaca/ancoragem no terreno, os parâmetros de resistência e de rigidez do solo penetrado, e as tensões radiais em torno da estaca são modificados. O nível de degradação do solo que suportará as cargas aplicadas na ancoragem é dependente do tipo e características do solo, e do número e geometria das hélices. Diante deste cenário de incertezas provenientes do efeito da instalação, duas distintas abordagens probabilísticas são apresentadas nesta dissertação. A primeira abordagem tem o intuito de verificar o efeito da variabilidade de distintas variáveis influentes no comportamento de ancoragens helicoidais. Para este fim, foi utilizado o método de expansão em Polinômio de Caos, baseado na modelagem numérica de ancoragens helicoidais em areia, calibrada com os resultados medidos em modelos testados em centrifuga. Foi verificado nesta parte o nível de influência de cada parâmetro de entrada do solo no comportamento carga x deslocamento da ancoragem. No segundo enfoque, foi proposto e avaliado um modelo probabilístico para simular a curva carga x deslocamento, obtida em provas de carga. Nesta parte, foi realizada uma análise de confiabilidade para verificação do estado limite de serviço de ancoragens helicoidais baseada em resultados de provas de carga executadas no Brasil. São também apresentadas nesta análise as incertezas provenientes da variabilidade do fator de torque utilizado na verificação da capacidade de carga durante a instalação da ancoragem. / Discrepancies between predicted and measured results of uplift capacity of helical piles (or helical anchors) have been commonly observed in the practical experience. Among other factors, these differences occur because the existing theoretical methods do not consider adequately the installation effect on the behavior of this type of anchor. During the anchor installation, the penetration by rotation of the helical plates into the ground modifies the soil strength and stiffness parameters, and the radial stresses around the pile. The degradation degree of the soil penetrated is dependent on the type and characteristics of the soil, and also on the number and geometry of helices. Against this background of uncertainty due to the installation effect, two different probabilistic approaches are presented in this dissertation. The first approach is used to verify the effect of the variability of different influential variables on the behavior of helical anchors. For this purpose, the probabilistic method named Sparse Polynomial Chaos Expansion was used, based on the numerical modeling of helical anchors in sand, calibrated with measured results obtained from reduced models tested in centrifuge. As a result, the level of influence of each soil input parameter on the anchor load-displacement behavior is presented. In the second approach, a probabilistic model to simulate the load-displacement curve obtained in load tests was proposed and evaluated. For this part, a reliability analysis was performed to check the serviceability limit state of helical anchors, based on the results of field load tests performed in Brazil. In addition, the uncertainties arising from the variability of the torque factor were evaluated. The torque factor is frequently used to verify the uplift capacity of helical anchors during installation.