Rozprawy doktorskie na temat „LIMIT EQUILIBRIUM METHOD (LEM)”

This thesis reports a detailed investigation into the use of the Shear Strength Reduction (SSR) method to determine factor of safety values in discontinuum models using the Universal Distinct Element Code. The SSR method depends on the definition of failure within the model and two different criteria were compared: the numerical unbalanced force definition and a more qualitative displacement-monitoring based method. A parametric study was first undertaken, using a simple homogeneous rock slope, with three different joint networks representing common kinematic states. Lessons learned from this study were then applied to a more complex case history used for validation of the SSR method. The discontinuum models allow for the failure surface to propagate based on constitutive models that better idealize the rockmass than simpler methods such as limit equilibrium (e.g. either method of slices or wedge solutions) and even numerical continuum models (e.g. finite difference, finite element). Joints are explicitly modelled and can exert a range of influences on the SSR result. Simple elasto-plastic models are used for both the intact rock and joint properties. Strain-softening models are also discussed with respect to the SSR method. The results presented highlight several important relationships to consider related to both numerical procedures and numerical input parameters. The case history was modelled similar to how a typical forward analysis would be undertaken: i.e. simple models with complexities added incrementally. The results for this case generally depict a rotational failure mode with a reduced factor of safety due to the presence of joints within the rockmass when compared to a traditional limit equilibrium analysis. Some models with large persistence of steeply dipping joints were able to capture the actual failure surface. Softening models were employed in order to mimic the generation and propagation of joints through the rockmass in a continuum; however, only discontinuum models using explicitly defined joints in the model were able to capture the correct failure surface.

Limits of slope stability, limit equilibrium methods, and of the finite element code FEADAM are reached in the application of these methods to the problem of cracked dams constructed on collapsing soils.

Main goal of thesis entitled "Landslide remediation design" is - based on acquired knowledge and submitted documents about the problematic of landslides - to determine the causes of the landslides on II. class road between villages Koryčany and Jestřabice and to propose optimal redevelopment.

A pesquisa voltada para a retroanálise de taludes de mineração está se tornando cada vez mais importante. As dimensões das atuais cavas de mineração visam sempre obter a melhor relação entre custo, benefício e segurança. Isso exige que por vezes o trabalho ocorra próximo destes limites. Neste trabalho o estudo de retroanálise consiste em um talude misto composto por aluvião e rocha em uma mineração de carvão localizada no município de Arroio dos Ratos, RS. O objetivo foi realizar um estudo de retroanálise onde se utilizou dois métodos de análise método dos Elementos Finitos (MEF) e o método do Equilíbrio Limite (EL). A metodologia adotada foi dividida em três fases: uma etapa de campo, para coleta do material e dados geométricos do talude, uma etapa de laboratório para caracterizar todo o material e a última etapa computacional onde foram gerados os modelos e simulações numéricas através dos softwares comerciais da empresa RocScience, sendo eles o SLIDE e o RS2. Os resultados encontrados mostraram que a porção do talude composta por aluvião apresentava seis camadas intercaladas de areias bem graduadas e argilas de média a alta plasticidade. Em relação as simulações, observou uma diferença entre o MEF e EL devido ao grande número de camadas presentes no talude e a interação entre elas. Foram criados quatro diferentes cenários para observar o comportamento do talude, com presença e ausência de água. O MEF mostrou uma superfície de ruptura próxima a encontrada porem com a presença de água o Fator de Segurança (FS) sofreu uma grande depreciação. O EL considerou uma superfície de ruptura satisfatória, nas simulações com presença de água FS sofreu uma depreciação mínima mesmo com máxima saturação de água no talude. Apesar das diferenças ambos os métodos são confiáveis mas devem ser usados de forma adequado ao tipo de problema existente. Situações mais simples e com taludes mais homogêneos o EL trona-se mais indicado, para problemas de maior complexidades e interações entre camadas o MEF se mostrou satisfatório e com boa resposta. O resultados através do MEF se aproximaram mais da situação real encontrada em campo.
A research focus on retro analysis on mine slopes is becoming increasingly important. The dimensions of current mining caves aim to always obtain the best cost benefit ratio as well as the highest safety level. This demands that the work sometimes is done within these limits. In this paper the study of retro analysis is made up of a mixed slope composed of alluvial and rocks, in a coal mine in Arroio dos Ratos, RS. The goal was to carry out a retro analysis study using two analysis methods: The Finite Element Method (FEM) and Limit Equilibrium analysis (LE). The methodology adopted was split into three phases: a field stage for the sample collection and slopes geometric , a laboratory stage to classify all the material and a final computacional stage were model and numerical simulations were created by way of commercial software, Slide and RS2, by RocScience. The results showed that the portion of the slope composed of alluvium had six layers interspersed with well graded sands and high plasticity clays. The simulations observed a difference between the FEM and LE due to the number of layers present in the slope and the interaction among them. Four different scenarios were created in order to observe the behavior of the slope. The FEM presents surface failure similar to one found in the field. The LE always takes into consideration the overall critical surface which is not observed in the field, it also show high security factor levels above one 1.3 that does not reflect a real situation since the slope is collapsed. In spike of the differences, both methods are reliable but they must be used according to the existing problems. For simpler situations with homogeneous slopes LE is recommended while move complex problems and interactions among lawyers calls for FEM.

La presente tesis de investigación fue elaborada con la finalidad de contribuir con el estudio de la construcción de rampas de acceso a excavaciones mediante el análisis de los taludes provisionales sin sostenimiento que garanticen la estabilidad global en el Conglomerado de Lima. Las rampas de acceso son estructuras provisionales cuya construcción no se rige bajo normativas o indicaciones establecidas, además no contempla un estudio, se basa en la experiencia del responsable en obra. La ciudad de Lima se emplaza sobre un suelo gravoso el cual contribuye a que sea posible optimizar el grado de inclinación de los taludes provisionales. El alcance de este trabajo consiste en modelar una rampa de acceso en el conglomerado típico de Lima aplicando las sobrecargas existentes de la maquinaria y realizar un análisis de estabilidad global frente a condiciones estáticas y pseudodinámicas. Mediante la técnica de retroanálisis basándose en el método de Equilibrio Límite en Slide se estimarán los parámetros de resistencia mínimos característicos de la grava de Lima, el parámetro de cohesión y ángulo de fricción. A partir de ello se procederá a la optimización de los taludes, evaluando los diferentes grados de inclinación, y se estimarán las deformaciones producidas en los taludes a través del programa Plaxis, basado en Elementos Finitos. Finalmente se exponen las conclusiones obtenidas de la presente tesis de investigación, además de brindar recomendaciones para futuras investigaciones relacionadas a este tema.
This research thesis was developed with the purpose of contributing to the study of the construction of access ramps to building’s excavations by unsupported provisional slopes analysis to guarantee the global stability factor in the Lima Conglomerate. The access ramps are provisional structures whose construction is not governed by norms or established indications, in addition it does not include a study, it is based on the experience of the person responsible for the work. The city of Lima is located on a gravelly ground which helps to optimize the degree of inclination of the provisional slopes. The scope of this work is to model an access ramp in the typical conglomerate of Lima applying the existing machinery overloads and perform an analysis of global stability against static and pseudodynamic conditions. The minimum resistance parameters characteristic of the Lima gravel, the cohesion parameter and friction angle will be estimated using the retro-analysis technique based on the Limit Equilibrium method in Slide. From this, the slopes will be optimized, evaluating the different degrees of inclination, and the deformations produced in the slopes will be estimated through the Plaxis program, based on Finite Elements. Finally, the conclusions obtained from this research thesis are presented, as well as providing recommendations for future research related to this topic.
Tesis

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
O perfeito entendimento de deslizamentos de terra tem sido objeto de grande interesse na engenharia geotécnica há muitos anos. Encostas naturais representam um desafio constante para os engenheiros, mais do que os taludes artificiais. Não é incomum que os escorregamentos causam perdas de vidas humanas e também danos materiais. As informações obtidas a partir de retro-análise de casos históricos, têm servido como uma ferramenta valiosa para a compreensão da estabilidade de taludes. Vale a pena notar que o primeiro método de cálculo de estabilidade de taludes, usando divisão de fatia, foi desenvolvido após um acidente na Noruega. Métodos de estabilidade por Equilíbrio Limite, desenvolvidos no século passado são atualmente utilizados na prática da engenharia. Apesar de suas deficiências, eles provaram ser confiáveis na determinação do Fator de Segurança. A geometria 2D e a abordagem completa da condição saturada são provavelmente as questões mais relevantes dos métodos atuais. A condição do solo não saturado está geralmente presente em taludes naturais e os métodos ignoram a influência da sucção do solo sobre a estabilidade do talude. O desenvolvimento de computadores no meio do século passado, tornaram os cálculos Equilíbrio Limite fáceis de serem executados. Por outro lado, eles não podem explicar a natureza do problema ou prever o comportamento do solo antes da ruptura. A década de 1960 marcou o início do desenvolvimento de programas de computador baseados em métodos numéricos que, entre outros, destaca-se, em geotecnia, a aplicação dos métodos de Elementos Finitos (FEM). Este método é ideal para muitos fins, uma vez que permite a simulação da sequência de construção e também a incorporação de diferentes modelos constitutivos. Este trabalho mostra a influência da sucção sobre a estabilidade de encostas naturais. Uma retroanálise de um escorregamento no Morro dos Cabritos, no Rio de Janeiro, foi feita através de um programa de análise de tensão (Plaxis 2D). Os resultados foram comparados com o FS obtido por programa de Equilíbrio Limite (Slide v5). O efeito de sucção do solo foi incorporada nas análises, através de sua influência sobre os parâmetros de resistência do solo e por diferentes possibilidades de infiltração de água na encosta. Este caso histórico foi estudado anteriormente por Gerscovich (1994), que na época, fez analise de fluxo e estabilidade utilizando um abordagem de Equilíbrio Limite 3D. Os resultados mostraram boa concordância entre a análise de Elementos Finitos e a simulação de Equilíbrio Limite, sem a presença de nível de água. Os resultados confirmaram que foi necessário haver pressões positivas para explicar a ruptura do talude.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Análises de estabilidade de taludes são predominantemente realizadas em duas-dimensões (2D) por métodos de equilíbrio limite. Os métodos convencionais de equilíbrio limite são alvos de muitas críticas pelo o uso do equilíbrio estático, pressuposições de forças na análise e por possuir o mesmo fator de segurança ao longo de toda a superfície de deslizamento. Para superar essas deficiências, o método proposto por Kulhawy (1969) incorpora o comportamento tensão-deformação do solo com tensões oriundas do Método de Elementos Finitos (FEM) e tem a mesma estrutura dos métodos de equilíbrio dos métodos de equilíbrio de equilíbrio limite clássicos. É também chamado de método aperfeiçoado. Devido à existência de taludes com geometrias complexas, a abordagem tridimensional (3D) é a única capaz de incorporar todos os aspectos geométricos do problema. Esta dissertação é dividida em dois artigos com o tema de estabilidade de taludes pelo o método de Kulhawy em abordagens 2D e 3D. O objetivo primário dessa dissertação é avaliar os principais fatores que influenciam a estabilidade de taludes. O primeiro artigo propôs geometrias variando de convexo a côncavo em um conjunto de propriedades típicas de solos. Duas trajetórias de geração de tensões in- situ foram utilizadas, i.e., construção e escavação. O método GLE foi calculado para fins de comparação. A superfície de deslizamento é muito dependente do histórico de tensão e da forma da face do talude. A diferença relativa no estado de tensões inicial típico alcançou 15% nas análises 2D e 34% nas análises 3D. A análise de sensibilidade do efeito do Poisson no fator de segurança mostrou-se muito relevante. A relação entre os fatores de segurança 2D e 3D são quase lineares independente do estado de tensões, das propriedades de resistência, formato da face do talude, na ordem de 30 a 40%. O segundo artigo propõe análises em barragens construídas em vales estreitos. Três abordagens de análises foram utilizadas: redução de resistência ao cisalhamento (SSR), métodos de Kulhawy e GLE. Condições típicas de fundações são muito variáveis como topografia e deformabilidade. A análise de sensibilidade do módulo de fundação de Young no fator de segurança foi insignificante em 2D e relevantes em 3D. A relação entre o comprimento do aterro (W) e a altura () é uma variável representativa do grau de estreitamento da barragem e na estabilidade de taludes. A análise de deformações planas tende a altas relações W/H e o oposto mostra elevados efeitos 3D. A inclinação da ombreira mostrou-se relevante no fator de segurança apenas em aterros em vales estreitos. Fundações mais rígidas são mais beneficias para o fator de segurança devido à produção de altos efeitos de arqueamento neste cenário. O método de Kulhawy provou-se ser vantajoso pela a incorporação do comportamento mecânico do solo, o uso de tensões mais realísticas nas análises e avaliação da estabilidade local na superfície de deslizamento. Isso aumenta a quantidade de informações úteis e confiáveis para o profissional de engenharia no projeto de taludes. Todas as análises foram realizadas usando o software SoilVision Systems, Saskatchewan, Canadá. Os módulos utilizados foram o SVLOPE, SVSOLID e o SVFLUX (SoilVision Systems Ltd., 2018). A análise de tensão para a simulação de trajetórias de escavação e construção utilizou do solucionador de Equações Diferenciais Parcias (PDE) o FlexPDE 6 (PDE Solutions Inc., 2014).
Slope stability analyses are predominantly performed using the two-dimensional (2D) conventional limit equilibrium methods. Conventional limit equilibrium methods are targets of many criticisms for using static equilibrium, assumptions of forces in the analysis and the same factor of safety along the slip surface. In order to overcome these shortcomings, the method proposed by Kulhawy (1969) incorporates the stress-strain behavior of the soil with stresses from the Finite Element Method (FEM) with the same structure as limit equilibrium methods. It is also called enhanced method. Due to the existence of slopes with complex geometries, the three-dimensional (3D) approach is only able to incorporate all the geometric aspects of the problem. This thesis is divided into two papers with the subject of slope stability analyses by the Kulhawy’s method in 2D and 3D approaches. The primary objective of this thesis is to evaluate major factors that influence slope stability. The first paper proposed geometries ranging from convex to concave in a set of soil properties. Two stress paths were considered, i.e., construction and excavation. The GLE method was computed for comparison purposes. The slip surface is very dependent on the stress history and the shape of slope face. The relative difference in typical initial stress state reached 15% in 2D analyses and 34% in 3D analyses. Sensitivity analysis of effect of Poisson’s ratio on factor of safety was very relevant. The relationship between 2D and 3D factors of safety are nearly linear independent of stress state on order of 30 to 40%. The second paper propose analyses on embankment dams built in narrow valleys. Three approaches of slope stability were used: shear strength reduction (SSR), Kulhawy’s and GLE methods. The typical conditions of foundation sites are very variable as topography and deformability. Sensitivity analysis of Young’s modulus of foundation on factor of safety was insignificant in 2D and relevant in 3D analyses. The ratio between embankment length (W) and height (H) was very important on slope stability. The plane strain analysis tends to high W/H ratio and the opposite shows high 3D effects. The inclination of abutment showed to be relevant on factor of safety only in embankments in narrow valleys. Stiffer foundations are beneficial to the factor of safety due producing high arching effects in this scenario. The Kulhawy’s method proved to be advantageous by the incorporation of mechanical behavior of soil, more realistic stress and local stability evaluation on slip surface. It increases the amount of useful and reliable information to the engineering professional in design of slopes. All analyses were performed using SoilVision Systems suite software, Saskatchewan, Canada. The modules used were SVSLOPE, SVSOLID and SVFLUX (SoilVision Systems Ltd., 2018). The stress analysis for the simulation of excavation and construction trajectories used partial differential equation (PDE) solver, FlexPDE 6 (PDE Solutions Inc., 2014).

As the main topic this thesis describes the design and evaluation of selected reinforced concrete members of the prefabricated reinforced concrete industrial building with administration at ultimate limit state in accordance with applicable standards. Movable overhead crane with carrying capacity of 50 tons is the main distinction of the industrial hall. Lateral frame whit main structural parts which are roof prestressed girder, load-bearing column supporting the overhead crane and drilled pile transferring loads from the upper construction to the load bearing subsoil, is designed in particular. Furthermore, design of the Gerber beam which forms the slab construction in the administrational part of the building is elaborated. Structural design and evaluation of other structures of the building is not part of this thesis.

The stability analysis of natural slopes holds significant importance in geotechnical design. Both engineering consultancies and research organizations utilize various computer aided design software to address these slope stability problems. This approach provides the ability to precisely anticipate critical failure surfaces through diverse methodologies. This M.Tech thesis focuses on performing stability analysis of a natural slope located in Uzan Bazaar Guwahati Assam. There have been frequent and periodical occurrences of natural disasters in the State of Assam, viz. landslides, earthquake tremors, which not only caused lot of causalities and destruction of property, but also damage roads and infrastructures. The natural slope lies on left bank of mighty Brahmaputra River. Most of the Kharghulli Hill is covered with dense vegetation and soil cover including semi-consolidated to consolidated nature of slide cum slope debris material which consist of nala borne material second layer from top including highly to completely weathered, weak, jointed and fractured Gneisses/Schist is prone to slope failures. The Finite Element Method (FEM) based on the Shear Strength Reduction (SSR) technique offers several advantages. It enables the prediction of support elements' failure. The support elements such as micro-piles, ground anchors, geogrids, etc, as well as the calculation of factors of safety. This capability enables comprehensive analysis and assessment of the support elements, contributing to a more accurate understanding of their performance and potential failure modes. Despite these benefits, SSR has not been widely adopted for routine slope stability analysis, likely due to limited experience with the tool and the scarcity of published information regarding its accuracy. To tackle this issue, the objective of this thesis is to conduct its performance comparison with the widely employed conventional limit-equilibrium method. The findings indicate a favourable correlation between both these methods of analysis, establishing a strong level of agreement between the two approaches.

The LMVD Method of Planes has been used for many years by the New Orleans District of the U.S. Army Corps of Engineers to analyze the stability of flood control structures in the New Orleans hurricane protections system. The Method of Planes assumes a three-part, noncircular slip surface and generally does not satisfy any form of static equilibrium. In computing a factor of safety, the Method of Planes considers a balance of horizontal “resisting” and “driving” forces in computing a factor of safety. To better understand how the results of slope stability analyses with the Method of Planes compare with results from more rigorous procedures capable of analyzing slip surfaces with different shapes, a parametric study was performed by analyzing twenty earthen levee cross sections believed to represent the various levee configurations in southeastern Louisiana. Analyses were performed with a force equilibrium procedure that assumed a horizontal inclination for the interslice forces and Spencer’s (1967) procedure, and the results were compared with the solutions from the Method of Planes. The force equilibrium procedure with horizontal side forces was selected because the procedure is believed to yield results that are similar to results from the Method of Planes, and Spencer’s procedure was utilized because it is the only procedure considered in this study to completely satisfy static equilibrium. The analyses performed with the force equilibrium and Spencer’s procedures included analyses for the critical slip surfaces from the Method of Planes as well as analyses for critical circular and noncircular slip surfaces. It was shown with the results of the analyses that the shape of the assumed slip surface has a great effect on the differences in the factors of safety from Spencer’s procedure and the Method of Planes.
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The objective of this thesis was to identify the mechanisms associated with the recurrence of rock-slope instability along the R518 and R523 roads in Limpopo. Advanced geotechnical methods and ASTER imagery were used for the purpose while a predictive rockfall hazard rating matrix chart and rock slope stability charts for unsaturated sensitive clay soil and rock slopes were to be developed. The influence of extreme rainfall on the slope stability of the sensitive clay soil was also evaluated. To achieve the above, field observations, geological mapping, kinematic analysis, and limit equilibrium were performed. The latter involved toppling, transitional and rotational analyses. Numerical simulation was finally resorted to. The following software packages were employed: SWEDGE, SLIDE, RocData, RocFall, DIPS, RocPlane, and Phase 2. The simulation outputs were analyzed in conjunction with ASTER images. The advanced remote sensing data paved the way for landslide susceptibility analysis. From all the above, rockfall hazard prediction charts and slope stability prediction charts were developed. Several factors were also shown by numerical simulation to influence slope instability in the area of study, i.e. sites along the R518 and R523 roads in the Thulamela Municipality. The most important factors are extreme rainfall, steep slopes, geological features and water streams in the region, and improper road construction. Owing to the complexity of the failure mechanisms in the study area, it was concluded that both slope stability prediction charts and rock hazard matrix charts are very useful. They indeed enable one to characterize slope instability in sensitive clay soils as well as rockfall hazards in the study area. It is however recommended that future work is undertaken to explore the use of sophisticated and scientific methods. This is instrumental in the development of predictive tools for rock deformation and displacement in landslide events.
Electrical and Mining Engineering

The objective of this thesis was to identify the mechanisms associated with the recurrence of rock-slope instability along the R518 and R523 roads in Limpopo. Advanced geotechnical methods and ASTER imagery were used for the purpose while a predictive rockfall hazard rating matrix chart and rock slope stability charts for unsaturated sensitive clay soil and rock slopes were to be developed. The influence of extreme rainfall on the slope stability of the sensitive clay soil was also evaluated. To achieve the above, field observations, geological mapping, kinematic analysis, and limit equilibrium were performed. The latter involved toppling, transitional and rotational analyses. Numerical simulation was finally resorted to. The following software packages were employed: SWEDGE, SLIDE, RocData, RocFall, DIPS, RocPlane, and Phase 2. The simulation outputs were analyzed in conjunction with ASTER images. The advanced remote sensing data paved the way for landslide susceptibility analysis. From all the above, rockfall hazard prediction charts and slope stability prediction charts were developed. Several factors were also shown by numerical simulation to influence slope instability in the area of study, i.e. sites along the R518 and R523 roads in the Thulamela Municipality. The most important factors are extreme rainfall, steep slopes, geological features and water streams in the region, and improper road construction. Owing to the complexity of the failure mechanisms in the study area, it was concluded that both slope stability prediction charts and rock hazard matrix charts are very useful. They indeed enable one to characterize slope instability in sensitive clay soils as well as rockfall hazards in the study area. It is however recommended that future work is undertaken to explore the use of sophisticated and scientific methods. This is instrumental in the development of predictive tools for rock deformation and displacement in landslide events.
Electrical and Mining Engineering
D. Phil. (Mining Engineering)

Η παρούσα διατριβή επανεξετάζει την οριακή ανάλυση ευστάθειας των λίθινων αψίδων. Η οριακή ανάλυση ευστάθειας χρησιμοποιείται σήμερα ως το βασικό εργαλείο αποτίμησης της ευστάθειας τόξων και θολωτών κατασκευών από τοιχοποιία, όπως ακριβώς συνέβαινε και τους τελευταίους τέσσερις αιώνες. Παρά την τόσο μακρόχρονη ιστορία της μεθόδου, δεν έχουν πλήρως διασαφηνιστεί στην επιστημονική κοινότητα θεμελιώδης έννοιες και δεν έχουν σαφώς απαντηθεί ερωτήματα όπως: Ποιες είναι οι φυσικά πραγματοποιήσιμες γραμμές ώθησης και ποιες όχι; Ποια είναι η επίδραση της στερεοτομίας ενός τόξου στην οριακή του ευστάθεια; Ποιος είναι ο ρόλος της αλυσοειδούς καμπύλης και κατά πόσο αυτή είναι μία φυσικά αποδεκτή γραμμή ώθησης; Τι σχέση υπάρχει ανάμεσα στην κλίση της συνισταμένης θλιπτικής δύναμης και στην κλίση της γραμμής ώθησης στο σημείο εφαρμογής της; Η παρούσα διατριβή αναζητά απαντήσεις στα ερωτήματα αυτά, και έχει ως στόχο τη βαθύτερη κατανόηση της οριακής ανάλυσης ευστάθειας των τόξων, με παράλληλη ανάδειξη νέων υπολογιστικών διαδικασιών. Η δομή της παρουσιάζεται συνοπτικά παρακάτω. Στο πρώτο κεφάλαιο γίνεται ιστορική ανάλυση της μεθόδου μέσα από παρουσίαση και σχολιασμό των εργασιών με τη σημαντικότερη συμβολή, από τα μέσα του 17ου αιώνα μέχρι σήμερα. Στο δεύτερο κεφάλαιο επανεξετάζεται ένα από τα πιο κλασικά προβλήματα της μηχανικής: ποιο είναι το ελάχιστο επιτρεπτό πάχος ενός ημικυκλικού τόξου υπό τη δράση του ιδίου βάρους του για να είναι ευσταθές. Παράλληλα απαντώνται τα ερωτήματα που τέθηκαν παραπάνω αναπτύσσοντας νέες κλειστές μαθηματικές εκφράσεις των γραμμών ώθησης μέσω γεωμετρικής προσέγγισης, αλλά και μέσω του λογισμού των μεταβολών. Στο τρίτο κεφάλαιο χρησιμοποιείται παρόμοια διαδικασία για την ανάλυση της γενικής περίπτωσης των ελλειπτικών τόξων, οποιουδήποτε γεωμετρικού λόγου ύψος προς βάση, καθώς δεν είναι διαθέσιμα αναλυτικά αποτελέσματα στη διεθνή βιβλιογραφία, όπως συμβαίνει για τα κυκλικά τόξα. Στο τέταρτο κεφάλαιο εξετάζεται η οριακή ευστάθεια κυκλικών τόξων οποιασδήποτε γωνίας εναγκαλισμού, υπό την ταυτόχρονη δράση του ιδίου βάρους τους και σταθερής οριζόντιας εδαφικής επιτάχυνσης, ενώ υπολογίζεται με ακρίβεια η μορφή που θα έχει ο επικείμενος μηχανισμός κατάρρευσης μαζί με το οριακό πάχος, συναρτήσει της σεισμικής φόρτισης. Τα αποτελέσματα της μαθηματικής ανάλυσης (Κεφ. 2-4) επιβεβαιώνουν την ακρίβεια του λογισμικού που αναπτύχθηκε για τις ανάγκες της διατριβής, καθώς και τα αποτελέσματα που προκύπτουν από εμπορικό λογισμικό της μεθόδου των διακριτών στοιχείων. Στο πέμπτο κεφάλαιο γίνεται εφαρμογή και σύγκριση των πιο αντιπροσωπευτικών υπολογιστικών μεθόδων που απαντώνται σήμερα στη βιβλιογραφία για την αποτίμηση της ευστάθειας και φέρουσας ικανότητας της υπόγειας Θολωτής Διόδου του Σταδίου της Αρχαίας Νεμέας, ενώ η οριακή ανάλυση ευστάθειας αναδεικνύεται ως ένα μοναδικό εργαλείο για την κατανόηση της αλληλεπίδρασης της κατασκευής με το περιβάλλον έδαφος. Επιπλέων των συμπερασμάτων στο τέλος κάθε κεφαλαίου (Κεφ. 2 έως 5), στο έκτο κεφάλαιο παρουσιάζονται τα πιο σημαντικά συμπεράσματα και η συνεισφορά της παρούσας διατριβής.
This doctoral thesis revisits the limit equilibrium analysis of masonry arches. Limit equilibrium analysis is used today as the main analysis method for the assessment of the stability of masonry arches and vaulted structures, and is the outcome of important contributions that happened during the last four centuries. Although this method has a long history and a rich literature, there are still fundamental concepts that have not been thoroughly clarified, such as: What are the physically admissible thrust lines of an arch? How the stereotomy of an arch affects its limit stability? What is the role of the catenary curve (the alysoid)? Is the catenary curve a physically admissible thrust line? What is the relation between the direction of the thrust force and the slope of the thrust line at the point of application of the force? This thesis investigates these questions and aims to a better understanding of the limit equilibrium analysis of masonry arches, and at the same time, to present innovative methodologies and new analysis tools. Chapter 1 presents the work of other authors that have contributed the most to the stability analysis of masonry arches and vaulted structures over the last centuries. Chapter 2 revisits one of the most classical problems of Mechanics—what is the minimum thickness of a semicircular masonry arch subjected to its own weight. At the same time, the analysis presented in this chapter answers to the aforementioned questions through the development of closed-form expressions of the thrust line and the application of calculus of variation. Chapter 3 is focused on the limit equilibrium state of elliptical masonry arches, using the same approaches that were used in Chapter 2. This analysis was motivated from the fact that numerical results have been available in literature only for circular and not for elliptical masonry arches. Chapter 4 computes the location of the imminent hinges and the minimum thickness of circular masonry arches, for every given embrace angle, which can just sustain their own weight, together with a given level of horizontal ground acceleration. The numerical results presented in Chapters 2 to 4 confirm the accuracy of the in-house software that was developed for the needs of this thesis and the results obtained with a representative, commercially available software of the distinct element method. Chapter 5 present a comprehensive structural analysis of the Tunnel-Entrance to the Stadium of Ancient Nemea which ranges from the thrust line limit analysis and the discrete element method, to a 3-dimensional finite-element analysis. Limit equilibrium analysis emerges as a unique analysis method for the assessment of the stability of the structure and its interaction with the surrounding soil. While at the end of every chapter (Chapters 2 to 5) are presented detailed comments and conclusions, Chapter 6 is focused on outlining the most important conclusions and the main contribution of this thesis.