O método dos elementos de contorno (MEC) surgiu como uma poderosa alternativa ao método dos elementos finitos (MEF) principalmente em casos como problemas de concentração de tensões ou onde o domínio se estende para o infinito. Em virtude das potencialidades já identificadas do MEC para a solução de problemas da geotecnia, em especial para problemas de túneis, este trabalho tem como objetivo desenvolver um programa que seja capaz de analisar as variáveis envolvidas na construção de túneis profundos através de um modelo numérico bidimensional baseado no MEC, implementando técnicas numéricas tais como: subelementação, técnica da sub-região e modelagem de inclusão e enrijecedores. O modelo numérico bidimensional foi calibrado para considerar o efeito tridimensional do problema de túneis no que se refere ao avanço da frente de escavação, para dois casos a saber: i) túneis sem suporte e ii) túneis com suporte. Os resultados mostraram grande precisão quando comparados com os resultados analíticos mesmo utilizando um número pequeno de elementos, provocando uma redução significativa no tempo de processamento se comparado com outros métodos. A técnica da subelementação produziu uma suavização nos resultados dos pontos internos localizados muito próximos do contorno. A técnica da sub-região, bem como a modelagem de inclusão e enrijecedores apresentaram resultados consistentes dando ao programa uma versatilidade maior. Na calibração dos parâmetros para a consideração do efeito tridimensional na escavação de túneis sem suporte, foi proposto o método da redução do carregamento com a construção do perfil de deformação longitudinal do túnel - LDP (Longitudinal Deformation Profile). Para a escavação de túneis com suporte foram propostos quatro métodos de análise: i) método da redução do carregamento sobre o túnel, ii) método da redução de rigidez do suporte, iii) método do acréscimo do carregamento sobre o túnel e iv) método do alívio de carga sobre o suporte. Todos esses métodos foram desenvolvidos a partir do modelo Kappa (\'kapa\'), elaborado neste trabalho a partir dos resultados encontrados na simulação numérica tridimensional realizado nos programas BEFE e BEFE++, e comparado com o modelo de Schwartz e Einstein. Por fim, o método para a construção do gráfico de deslocamento radial para túneis circulares suportados, considerando o atraso na instalação do suporte, utilizando um método numérico ou resultado analítico do estado plano de deformação se mostra como uma alternativa simples para análise do efeito tridimensional contido no problema de túneis. / The boundary element method (BEM) has appeared as a powerful alternative to the finite element method (FEM) mainly in the cases where a good accuracy is required, as for problems with strain or stress concentration and problems with domain extending to infinite. The objective of this work is to develop a formulation and the corresponding computational code to analyse the variables in a design of deep tunnels, using a improved BEM two-dimensional numerical model, in which the following techniques were implemented: sub-elementation, sub-region technique, reinforcements introduced by modifying locally the domain rigidity. The two-dimensional model was calibrated to take into account the three-dimensional effects appearing around the tunnel face advance for two cases: i) tunnel without support and ii) tunnel with support. The results showed good accuracy when compared with analytical results even when obtained by using coarse discretizations and therefore requiring less computer time in comparison with other numerical procedures. The sub-elementation technique has smoothed the results for internal points near the boundary. The sub-region technique and the reinforcement inclusions lead to accurate making the computer code reliable. For the parameter calibration to take into account the three-dimensional effects applied to non lined tunnels the method of loading reductions was proposed obtaining a tunnel longitudinal deformation profile - LDP. For the excavation of lined tunnels four methods of analysis were proposed: i) load reduction model, ii) reduction support stiffness model, iii) additional load model, and iv) decrease of lining load model. All these methods were developed from the kappa (\'kapa\') model, developed in this work using three-dimensional results obtained by using the computational systems BEFE and BEFE++ and compared with the Schwartz-Einstein method. Finally the method used to build the radial displacement graphic for lined circular tunnels, taking into account the support insertion delay, using either a numerical method or plane strain analytical solutions, was developed.

<div>Underground structures must be able to support static overburden loads, as well as to accommodate additional deformations imposed by seismic motions. Progress has been made in the last few years in understanding the soil-structure interaction mechanisms and the stress and displacement transfer from the ground to the structure during a seismic event. It seems well established that, for most tunnels, the most critical demand to the structure is caused by shear waves traveling perpendicular to the tunnel axis. Those waves cause distortions of the cross section (ovaling for a circular tunnel, and racking for a rectangular tunnel) that result in axial forces (thrusts) and bending moments. While all this has been well-studied for structures placed in linear-elastic ground, there is little information regarding the behavior of buried structures placed in nonlinear ground, especially under undrained conditions, i.e., when excess pore pressures generate and accumulate during the earthquake.</div><div><br></div><div><div>Two-dimensional dynamic numerical analyses are conducted to assess the seismic response of deep circular tunnels located far from the seismic source, under drained or undrained loading conditions. It is assumed that the liner remains elastic and that plane strain conditions apply. </div><div> A new cyclic nonlinear elastoplastic constitutive model is developed and verified, to simulate the nonlinear behavior and excess pore pressures accumulation with cycles of loading in the ground. The results of the numerical analyses show negligible effect of input frequencies on the normalized distortions of a tunnel for input frequencies smaller than 5 Hz (the distortions of the tunnel are normalized with respect to those of the free field); that is, for ratios between the wavelength of the seismic input and the tunnel opening larger than about eight to ten. The results also show that undrained conditions, compared with drained conditions, tend to reduce deformations for flexible liners and increase them for stiffer tunnels, when no accumulation of pore pressures with cycles of loading is assumed. However, when pore pressures increase with the number of cycles, the differences in distortions between drained and undrained loading are reduced, i.e., the normalized distortions increase for flexible and decrease for stiff tunnels, compared to those with drained conditions. </div></div><div><br></div><div><div>Undrained loading produces larger thrust in the liner than drained loading for stiff tunnels with flexibility ratio F ≤ 2.0.</div><div>For more flexible tunnels with F > 2.0, the behavior is the opposite, i.e., smaller axial forces are obtained for undrained loading than for drained loading. Including excess pore pressure accumulation does not introduce significant changes in the axial forces of the liner, irrespective of the flexibility of the tunnel, compared to those obtained from undrained loading without pore pressure accumulation.</div><div>The drainage loading condition (drained or undrained) or the magnitude of the free-field excess pore pressures during undrained loading do not affect the normalized bending moments for flexible tunnels, with F ≥ 2. For stiffer tunnels, with F < 2, the normalized bending moments increase from drained to undrained loading, and with the free field excess pore pressures.</div></div><div><br></div><div><div>It is found that the tunnel’s response is determined by the load on the liner, or by the distortions of the cross section, depending on the flexibility ratio. For stiff structures, with F ≤ 2.0, important axial forces and bending moments are produced in the structure, with larger magnitudes for the undrained case; while the distortions of the cross section are very small. When the tunnel becomes more flexible, the loading on the liner decreases, but the distortions of the cross section start to be important. For flexible structures with initial F ≥ 10 (for the cases investigated), the performance is largely determined by the distortions of the cross section, while the axial forces and bending moments are almost negligible. Such distortions are drastically affected by the drainage loading condition and by the magnitude of pore pressures in the free field. </div></div><div><br></div>

O presente trabalho de pesquisa aborda a aplicação de análise por elementos finitos a maciços escavados por túneis, revisando relevantes estudos sobre análise numérica deste tipo de obra e realizando modelagem numérica própria, bi e tridimensional, voltada ao caso do Túnel Paraíso do Metrô de São Paulo (obra com dados de instrumentação e de ensaios), com uso do consagrado programa de elementos finitos Imperial College Finite Element Program (ICFEP), desenvolvido nos últimos trinta anos no Imperial College de Londres. Dentre os modelos constitutivos adotados nestas análises, destaca-se o Cinemático com Duas Superfícies Modificado do Imperial College, modelo elasto-plástico com endurecimento cinemático e isotrópico, baseado no estado crítico, com grande capacidade de representar as características de rigidez de argilas sobreadensadas (como são as argilas da região do Túnel Paraíso), cujas principais características são levantadas através de revisão bibliográfica. Da observação da etapa de reprodução numérica de ensaios e dos resultados conseguidos com as análises da escavação do túnel, são feitas considerações sobre o desempenho de todos os modelos constitutivos adotados (além do Cinemático com Duas Superfícies Modificado, o Cam-Clay Modificado e o elasto perfeitamente plástico com critério de ruptura de Mohr-Coloumb), bem como sobre a performance dos modelos numéricos desenvolvidos. / This research approaches the application of finite element analysis to tunnel excavation, making a survey of some numerical relevant studies of this kind of construction and performing a range of plane-strain and three-dimensional analyses, focused on the Paraíso Tunnel from Sao Paulo Underground (with field instrumentation and lab tests), using a powerful finite element program, the Imperial College Finite Element Program (ICFEP), developed in the last thirty years at Imperial College London. Among the constitutive models adopted in those analyses, it is highlighted the Modified Two Surfaces Kinematic from Imperial College, a elasto-plastic model with kinematic and isotropic hardening, based on the critical state, with great ability to represent the pre-failure stiffness of overconsolidated clays (as are the clays around Paraíso Tunnel), whose main features are raised through a literature survey. From the results of numerical simulation of lab tests and from the predictions of the tunnelling analyses, it is discussed the performance of all constitutive models adopted (including Modified Cam-Clay and elastic perfectly plastic model with Mohr-Coloumb failure criterion) and of the numerical models developed.

Entre os principais problemas na execução de túneis metroviários e rodoviários estão a manutenção da posição (coordenadas) de pontos de uma poligonal aberta (sem pontos de controle), o monitoramento do alinhamento da escavação, o transporte da posição da superfície para níveis subterrâneos, a locação das cambotas e, como ferramenta para tudo isso, o controle de qualidade dos equipamentos, em especial a estação total na operação da medição de direções. Por isso, a presente pesquisa voltou-se para os métodos e procedimentos para a execução de poligonais subterrâneas, destinadas a escavação de túneis metroviários, rodoviários e assemelhados, focando a precisão e acurácia na medição de direções. Para conseguir o objetivo, foi estudada a precisão de diversas estações totais, na operação de medir direções. Foram feitas diversas campanhas e foi estabelecido um campo de provas que permite avaliar a precisão e acurácia dos equipamentos. Além disso, visando simular as condições de campo, os problemas e as precisões possíveis, implantou-se uma poligonal referente a um projeto geométrico de túnel na Raia Olímpica da USP com características semelhantes a um projeto metroviário. A Base Multipilar existente foi utilizada para o controle da poligonal ao longo do túnel simulado para verificar a precisão efetivamente alcançada com os equipamentos e metodologias. Outra contribuição foi o estabelecimento de um quadrilátero de controle, com ângulos conhecidos com desvio-padrão na ordem de 0,36\", servindo para verificar a precisão dos equipamentos (conjunto operador, equipamento e acessórios). Dos experimentos com diversos equipamentos surgiram propostas para serem incorporadas à norma de controle de qualidade da medição de direção. / Among the main problems in the implementation of subway and road tunnels are the maintenance of the correct position (coordinates) of points of an open traverse (without control points), the monitoring of the excavation alignment, the connection of the surface network with the points underground, the location of crankshafts and, as a tool for all this, the equipment quality control, particularly the total station in the direction measurement operation. Therefore, the current study is based on methods and procedures to implement underground traverse, intended to the excavation of subway and road tunnels and similar structures, focusing on the precision and accuracy in the measurement of directions. In order to achieve its aim, the precision of several total stations was studied in the operation of measuring directions. Several campaigns were made and a test field work was established allowing the assessment of the precision and accuracy of the equipment. Moreover, aiming to simulate the field conditions, the problems and possible precisions, a traverse was implemented referring to a tunnel geometrical project located at the University of São Paulo with similar characteristics to a subway project. The existing Multi-pillar Base was used to control the polygon along the simulated tunnel in order to verify the precision effectively reached with the equipment and methodology. Another contribution was the establishment of a control quadrangle, which the angles standard deviation is 0,36\", and it was used to verify the equipment precision. By testing several equipments some proposals arose to be incorporated to the direction measurement quality control.

The velocity field in the wake of a small scale flexible parachute canopy was measured using two-dimensional particle image velocimetry. The experiments were performed in a water tunnel with the Reynolds number ranging from 3.0-6.0 x 104. Both a fully inflated canopy and the inflation phase were investigated in a constant freestream (i.e. an infinite mass condition). The fully inflated canopy experienced a cyclic“breathing" which corresponded to the shedding of a vortex ring from the canopy. The normalized breathing frequency had a value of 0.56 +/- 0.03. The investigation of the canopy inflation showed that during the early stages of the inflation, the boundary layer on the canopy surface remains attached to the canopy while the canopy diameter increases substantially. The boundary layer begins to separate near the apex region when the diameter is ~68% of the fully inflated diameter. The separation point then progresses upstream from the canopy apex region toward the canopy skirt. During this time period, the force rapidly increases to its maximum value while the separation point of the boundary layer moves upstream towards the skirt. The force then declines rapidly and the separated boundary layer rolls-up into a large vortex ring near the canopy skirt. At the same time, the canopy is drawn into an over-expanded state after which the cyclic breathing initiates. The unsteady potential force was estimated from the rate of change of the canopy volume. It contributed no more than 10% of the peak opening force and was only significant during the early stages of inflation. The majority of the opening force was the result of the time rate of change of the fluid impulse. It accounts for approximately 60% of the peak opening force. This result shows that the formation of the viscous wake is the primary factor in the peak drag force of the canopy.

O dimensionamento e verificação estrutural de túneis envolve diversos parâmetros geotécnicos e o controle de diversas variáveis estruturais como, por exemplo, a convergência (fechamento) da cavidade, a pressão atuante no revestimento e o nível de descompressão do maciço. O campo de deformações e tensões que se desenvolve no entorno do túnel dependerá da profundidade, da geometria da seção, da distribuição de cargas na superfície, da heterogeneidade e distribuição das camadas de solo, do comportamento mecânico conjunto do maciço e do revestimento, bem como do processo de escavação e colocação do revestimento. Esse trabalho trata de simulações numéricas do comportamento a longo prazo em túneis revestidos com concreto, incluindo túneis gêmeos. Portanto, o maciço foi considerado com uma lei de comportamento viscoplástica, com superfície de cedência de von-Mises acoplada no modelo reológico de Perzyna, e para o concreto, foi considerada uma lei viscoelástica através das formulações de fluência e retração constantes no CEB-MC90 adaptadas à teoria da solidificação de Bazant & Prasannan (1989ª, 1989b). Para esse estudo foram construídos scripts de modelos bidimensionais axissimétricos e tridimensionais no software ANSYS. A implementação do modelo do concreto é feita através do recurso de customização do material que o ANSYS disponibiliza: a subrotina UserMat. O processo de escavação e colocação do revestimento é simulado através do recurso de ativação e desativação dos elementos finitos considerando uma velocidade de avanço constante. Além da validação do modelo do concreto, é feita a validação dos modelos dos túneis em elasticidade, plasticidade e viscoplasticidade sem e com revestimento elástico através de expressões analíticas e o software GEOMEC91 desenvolvido por Bernaud (1991), demonstrando excelente conformidade. Nos exemplos testados, a influência da viscoelasticidade do concreto pode aumentar as deformações em até 40% em comparação com o revestimento elástico, e a proximidade dos túneis longitudinais em cerca de 15% (fazendo com que o campo de deformações deixe de ser puramente radial). Também é estudada a influência de galerias transversais. / The structural desing and verification of tunnels involves several geotechnical parameters and the control of several structural variables, such as the convergence (closure) of the cavity, the pressure over the linning and the level of decompression of the rockmass. The field of deformations and stresses developed around the tunnel will depend of the depth, section geometry, surface load distribution, mechanical behavior of the rockmass and linning, as well as the process of excavation and placement of the linning. This dissertation deals with numerical simulations of long-term behavior in concrete lined tunnels, including twin tunnels. Therefore, for the rockmass it was considered a viscoplastic behavior law, with von-Mises yield surface coupled in the rheology model of Perzyna, and for concrete, it was considered a viscoelastic law through creep and shrinkage formulations in the CEB-MC90 adapted to the solidification theory of Bazant & Prasannan (1989a, 1989b). For this study, scripts were constructed for two-dimensional axissimetric and three-dimensional models in the ANSYS software. The implementation of concrete model is done through the material customization capabilities that ANSYS makes available: the UserMat subroutine. The process of excavation and placement of the linning is simulated through the activation/deactivation of finite elements considering a constant speed of advance of tunnel. The models are validated in elasticity, plasticity and viscoplasticity without and with elastic linning through analytical expressions and the software GEOMEC91 developed by Bernaud (1991), demonstrating excellent conformity. In the examples tested, the influence of viscoelastictity of the concrete can increase the deformations by up to 40% compared to the elastic linning, and the proximity of the longitudinal tunnels by about 15% (making the strain field no longer purely radial). The influence of transverse galleries is also studied.

Tunnelling in urban areas causes short-term and long-term ground movements under existing buildings. Finite element analysis provides a useful option for assessing the likely extent of damage induced in these buildings. Although finite element analysis is suggested to be used in the later phases of the building damage assessment procedures employed in practice, only the effect of short-term ground movements is typically considered and there are no detailed guidelines on the specification and complexity of the modelling. This thesis addresses the tunnel-soil-building interaction problem and the effect of long-term consolidation, as well as demonstrating the application of 3D finite element analysis with appropriate simplifications for practical assessment purposes. Finite element models are developed to quantify the effect of shallow tunnelling on an example masonry building founded on strip footings, considering both single- and twin-tunnel scenarios in a typical London soil profile. Total stress and effective stress analyses are adopted with specific modelling procedures to focus on the short-term and long-term response respectively. The analyses use a non-linear model for the masonry, and allow slippage and gapping at the soil-footing interface. Two advanced constitutive models for the soil (the extended Mohr-Coulomb model and the modified two-surface kinematic hardening model) are implemented with customized stress update schemes. The finite element results present the interaction between the soil and the building by comparing with the greenfield ground response. The horizontal coupling between the foundation and the ground is shown to be relatively weak. The dominant deformation mode of the building varies with the tunnel configuration (i.e. single or twin tunnels) and the tunnel eccentricity. Strain localization is found around the explicitly modelled window and door openings. The long-term consolidation is sensitive to the permeability of the tunnel lining. The building response to long-term ground movements is further affected by the tunnel-tunnel interaction in the case of twin-tunnel configuration. Performing 3D analysis of a single facade and foundation provides useful damage predictions, without the need to model a complete building. The proposed result processing methods such as characteristic strain and damage bar chart are practical tools for assessment. The study highlights some limitations of the elastic beam assessment method, which is often adopted in the early phase of the damage assessment process.

Les systèmes fixes par aspersion d'eau sont souvent cités comme un moyen pour améliorer le niveau de sécurité dans les tunnels routiers. Cependant, leurs effets sur un incendie en tunnel et les interactions possibles avec le système de ventilation sont encore mal connus. Le travail présenté ici vise à étudier l'action de ces systèmes par une approche phénoménologique de l'évaporation et l'utilisation d'un modèle CFD tridimensionnel. L'emploi d'un code CFD incluant des modèles diphasiques repose sur la simulation de deux situations expérimentales : une expérience académique de spray évaporant et des essais d'incendie avec aspersion dans un tunnel à échelle réduite. Les résultats obtenus sont relativement satisfaisants, en utilisant une modélisation Euler-Lagrange pour l'écoulement diphasique. L'influence du système d'aspersion sur la propagation de la couche de fumée est plus particulièrement étudiée. Cependant, ce type de modélisation nécessite des données d'entrée d'un niveau difficilement accessible sans avoir recours à une expérience de caractérisation des buses. Une approche plus phénoménologique, à intégrer dans un modèle unidimensionnel, est envisagée comme alternative.

In the last three decades, seismic performance assessment of buried structures has evolved through the following stages : i) buried structures are not prone to seismically-induced damages, thus no need for detailed investigations, ii) eliminating soil-structure-earthquake interaction and use of seismically-induced free field ground deformations directly as the basis for seismic demand, thus producing conservative results, and finally iii) soil-structure and earthquake interaction models incorporating both kinematic and inertial interactions. As part of soil-structure and earthquake interacting models, simplified frame analysis established the state of practice and is widely used. Within the confines of this thesis, the results of simplified frame analysis based response of buried structures are compared with those of 2-D finite element dynamic analyses. For the purpose, 1-D dynamic and 2-D pseudo-dynamic analyses of free field and buried structural systems are performed for a number of generic soil, structure and earthquake combinations. The analyses results revealed that, in general, available closed form solutions are in pretty good agreement with the results of finite element analyses. However, due to the fact that dynamic analyses can model both kinematic and inertial effects / it should be preffered for the design of critical structures.

Συγκριτική θεώρηση των συστημάτων ταξινόμησης βραχομάζας rmr gsi και rmi σε υδροηλ/κες σήραγγες στη θέση Παλιούρης Ν. Ιωαννίνων / The comparison of rockmass classification systems, rmr, gsi, rmi in hydrological tunnels at Paliouris Ioanninon