Detection, analysis and monitoring of slope movements by high-resolution digital elevation models

Summary Detection, analysis and monitoring of slope movements by high-resolution digital elevation modelsSlope movements, such as rockfalls, rockslides, shallow landslides or debris flows, are frequent in many mountainous areas. These natural hazards endanger the inhabitants and infrastructures making it necessary to assess the hazard and risk caused by these phenomena. This PhD thesis explores various approaches using digital elevation models (DEMs) - and particularly high-resolution DEMs created by aerial or terrestrial laser scanning (TLS) - that contribute to the assessment of slope movement hazard at regional and local scales.The regional detection of areas prone to rockfalls and large rockslides uses different morphologic criteria or geometric instability factors derived from DEMs, i.e. the steepness of the slope, the presence of discontinuities, which enable a sliding mechanism, and the denudation potential. The combination of these factors leads to a map of susceptibility to rockfall initiation that is in good agreement with field studies as shown with the example of the Little Mill Campground area (Utah, USA). Another case study in the Illgraben catchment in the Swiss Alps highlighted the link between areas with a high denudation potential and actual rockfall areas.Techniques for a detailed analysis and characterization of slope movements based on high-resolution DEMs have been developed for specific, localized sites, i.e. ancient slide scars, present active instabilities or potential slope instabilities. The analysis of the site's characteristics mainly focuses on rock slopes and includes structural analyses (orientation of discontinuities); estimation of spacing, persistence and roughness of discontinuities; failure mechanisms based on the structural setting; and volume calculations. For the volume estimation a new 3D approach was tested to reconstruct the topography before a landslide or to construct the basal failure surface of an active or potential instability. The rockslides at Åknes, Tafjord and Rundefjellet in western Norway were principally used as study sites to develop and test the different techniques.The monitoring of slope instabilities investigated in this PhD thesis is essentially based on multitemporal (or sequential) high-resolution DEMs, in particular sequential point clouds acquired by TLS. The changes in the topography due to slope movements can be detected and quantified by sequential TLS datasets, notably by shortest distance comparisons revealing the 3D slope movements over the entire region of interest. A detailed analysis of rock slope movements is based on the affine transformation between an initial and a final state of the rock mass and its decomposition into translational and rotational movements. Monitoring using TLS was very successful on the fast-moving Eiger rockslide in the Swiss Alps, but also on the active rockslides of Åknes and Nordnesfjellet (northern Norway). One of the main achievements on the Eiger and Aknes rockslides is to combine the site's morphology and structural setting with the measured slope movements to produce coherent instability models. Both case studies also highlighted a strong control of the structures in the rock mass on the sliding directions. TLS was also used to monitor slope movements in soils, such as landslides in sensitive clays in Québec (Canada), shallow landslides on river banks (Sorge River, Switzerland) and a debris flow channel (Illgraben).The PhD thesis underlines the broad uses of high-resolution DEMs and especially of TLS in the detection, analysis and monitoring of slope movements. Future studies should explore in more depth the different techniques and approaches developed and used in this PhD, improve them and better integrate the findings in current hazard assessment practices and in slope stability models.Résumé Détection, analyse et surveillance de mouvements de versant à l'aide de modèles numériques de terrain de haute résolutionDes mouvements de versant, tels que des chutes de blocs, glissements de terrain ou laves torrentielles, sont fréquents dans des régions montagneuses et mettent en danger les habitants et les infrastructures ce qui rend nécessaire d'évaluer le danger et le risque causé par ces phénomènes naturels. Ce travail de thèse explore diverses approches qui utilisent des modèles numériques de terrain (MNT) et surtout des MNT de haute résolution créés par scanner laser terrestre (SLT) ou aérien - et qui contribuent à l'évaluation du danger de mouvements de versant à l'échelle régionale et locale.La détection régionale de zones propices aux chutes de blocs ou aux éboulements utilise plusieurs critères morphologiques dérivés d'un MNT, tels que la pente, la présence de discontinuités qui permettent un mécanisme de glissement ou le potentiel de dénudation. La combinaison de ces facteurs d'instabilité mène vers une carte de susceptibilité aux chutes de blocs qui est en accord avec des travaux de terrain comme démontré avec l'exemple du Little Mill Campground (Utah, États-Unis). Un autre cas d'étude - l'Illgraben dans les Alpes valaisannes - a mis en évidence le lien entre les zones à fort potentiel de dénudation et les sources effectives de chutes de blocs et d'éboulements.Des techniques pour l'analyse et la caractérisation détaillée de mouvements de versant basées sur des MNT de haute résolution ont été développées pour des sites spécifiques et localisés, comme par exemple des cicatrices d'anciens éboulements et des instabilités actives ou potentielles. Cette analyse se focalise principalement sur des pentes rocheuses et comprend l'analyse structurale (orientation des discontinuités); l'estimation de l'espacement, la persistance et la rugosité des discontinuités; l'établissement des mécanismes de rupture; et le calcul de volumes. Pour cela une nouvelle approche a été testée en rétablissant la topographie antérieure au glissement ou en construisant la surface de rupture d'instabilités actuelles ou potentielles. Les glissements rocheux d'Åknes, Tafjord et Rundefjellet en Norvège ont été surtout utilisés comme cas d'étude pour développer et tester les diverses approches. La surveillance d'instabilités de versant effectuée dans cette thèse de doctorat est essentiellement basée sur des MNT de haute résolution multi-temporels (ou séquentiels), en particulier des nuages de points séquentiels acquis par SLT. Les changements topographiques dus aux mouvements de versant peuvent être détectés et quantifiés sur l'ensemble d'un glissement, notamment par comparaisons des distances les plus courtes entre deux nuages de points. L'analyse détaillée des mouvements est basée sur la transformation affine entre la position initiale et finale d'un bloc et sa décomposition en mouvements translationnels et rotationnels. La surveillance par SLT a démontré son potentiel avec l'effondrement d'un pan de l'Eiger dans les Alpes suisses, mais aussi aux glissements rocheux d'Aknes et Nordnesfjellet en Norvège. Une des principales avancées à l'Eiger et à Aknes est la création de modèles d'instabilité cohérents en combinant la morphologie et l'agencement structural des sites avec les mesures de déplacements. Ces deux cas d'étude ont aussi démontré le fort contrôle des structures existantes dans le massif rocheux sur les directions de glissement. Le SLT a également été utilisé pour surveiller des glissements dans des terrains meubles comme dans les argiles sensibles au Québec (Canada), sur les berges de la rivière Sorge en Suisse et dans le chenal à laves torrentielles de l'Illgraben.Cette thèse de doctorat souligne le vaste champ d'applications des MNT de haute résolution et particulièrement du SLT dans la détection, l'analyse et la surveillance des mouvements de versant. Des études futures devraient explorer plus en profondeur les différentes techniques et approches développées, les améliorer et mieux les intégrer dans des pratiques actuelles d'analyse de danger et surtout dans la modélisation de stabilité des versants.

Towards a consensus view on understanding nanomaterials hazards and managing exposure

The aim of this article is to present an overview of salient issues of exposure, characterisation and hazard assessment of nanomaterials as they emerged from the consensus-building of experts undertaken within the four year European Commission coordination project NanoImpactNet. The approach adopted is to consolidate and condense the findings and problem-identification in such a way as to identify knowledge-gaps and generate a set of interim recommendations of use to industry, regulators, research bodies and funders. The categories of recommendation arising from the consensual view address: significant gaps in vital factual knowledge of exposure, characterisation and hazards; the development, dissemination and standardisation of appropriate laboratory protocols; address a wide range of technical issues in establishing an adequate risk assessment platform; the more efficient and coordinated gathering of basic data; greater inter-organisational cooperation; regulatory harmonization; the wider use of the life-cycle approaches; and the wider involvement of all stakeholders in the discussion and solution-finding efforts for nanosafety.

The Quaternary Active Faults Database of Iberia (QAFI v.2.0)

The Quaternary Active Faults Database of Iberia (QAFI) is an initiative lead by the Institute of Geology and Mines of Spain (IGME) for building a public repository of scientific data regarding faults having documented activity during the last 2.59 Ma (Quaternary). QAFI also addresses a need to transfer geologic knowledge to practitioners of seismic hazard and risk in Iberia by identifying and characterizing seismogenic fault-sources. QAFI is populated by the information freely provided by more than 40 Earth science researchers, storing to date a total of 262 records. In this article we describe the development and evolution of the database, as well as its internal architecture. Aditionally, a first global analysis of the data is provided with a special focus on length and slip-rate fault parameters. Finally, the database completeness and the internal consistency of the data are discussed. Even though QAFI v.2.0 is the most current resource for calculating fault-related seismic hazard in Iberia, the database is still incomplete and requires further review.

Quaternary active tectonic structures in the offshore Bajo Segura basin (SE Iberian Peninsula Mediterranean Sea).

The Bajo Segura fault zone (BSFZ) is the northern terminal splay of the Eastern Betic shear zone (EBSZ), a large left-lateral strike-slip fault system of sigmoid geometry stretching more than 450 km from Alicante to Almería. The BSFZ extends from the onshore Bajo Segura basin further into the Mediterranean Sea and shows a moderate instrumental seismic activity characterized by small earthquakes. Nevertheless, the zone was affected by large historical earthquakes of which the largest was the 1829 Torrevieja earthquake (IEMS98 X). The onshore area of the BSFZ is marked by active transpressive structures (faults and folds), whereas the offshore area has been scarcely explored from the tectonic point of view. During the EVENT-SHELF cruise, a total of 10 high-resolution single-channel seismic sparker profiles were obtained along and across the offshore Bajo Segura basin. Analysis of these profiles resulted in (a) the identification of 6 Quaternary seismo-stratigraphic units bounded by five horizons corresponding to regional erosional surfaces related to global sea level lowstands; and (b) the mapping of the active sub-seafloor structures and their correlation with those described onshore. Moreover, the results suggest that the Bajo Segura blind thrust fault or the Torrevieja left-lateral strike-slip fault, with prolongation offshore, could be considered as the source of the 1829 Torrevieja earthquake. These data improve our understanding of present deformation along the BSFZ and provide new insights into the seismic hazard in the area.

An active zone characterized by slow normal faults, the northwestern margin of the València trough (NE Iberia): a review

The northwestern margin of the Valencia trough is an area of low strain characterized by slow normal faults and low to moderate seismicity. Since the mid 1990s this area has been the subject of a number of studies on active tectonic which have proposed different approaches to the location of active faults and to the calculation of the parameters that describe their seismic cycle. Fifty-six active faults have been found and a classification has been made in accordance with their characteristics: a) faults with clear evidence of large paleo-, historic or instrumental earthquakes (2/56); b) faults with evidence of accumulated activity during the Plio-Quaternary and with associated instrumental seismicity (7/56); c) faults with evidence of accumulated activity during the Plio-Quaternary and without associated instrumental seismicity (17/56); d) faults with associated instrumental seismicity and without evidence of accumulated activity during the Plio-Quaternary (30/56), and e) faults without evidence of activity or inactive faults. The parameters that describe the seismic cycle of these faults have been evaluated by different methods that use the geological data obtained for each fault except when paleoseismological studies were available. This classification can be applied to other areas with low slip faults because of the simplicity of the approaches adopted. This study reviews the different approaches proposed and describes the active faults located, highlighting the need a) to better understand active faults in slow strain zones through paleoseismological studies, and b) to include them in seismic hazard studies.

Caracterização e classificação quanto ao risco ambiental do estéril da mina de cromita do município de Andorinha, Bahia

The mineral waste studied was host rock from a chromite mine located in Andorinha/Bahia, extracted and stockpiled in yards without specific application. Host rock was submitted to chemical analysis, XRD, SEM-EDS, IR and TGA and classified according to ABNT standards for solid waste classification. Analyses confirmed that this host rock, classified as ultrabasic, consists mainly of dolomite, calcite and diopside. Hazard assessment results showed this host rock should be classified as class II B - inert waste, important for its potential application in agriculture as a soil acidity correction agent.

Dam safety guide

A new Dam Safety Act (494/2009) came into force on 1st October 2009 and a Government Decree on Dam Safety (319/2010) on 5th May 2010. This Dam Safety Guide replaces the Dam Safety Code of Practice (Publication of the Ministry of Agriculture and Forestry 7/1997), removed from circulation on 1st October 2009. The Dam Safety Guide is not binding on the dam owner; the purpose is to complement and elucidate the relevant law and and decree through examples and descriptions. The Guide takes up questions concerning dam design, for instance hydrological dimensioning and technical safety requirements, dam construction and use, the dam break hazard analysis and the dam owner’s emergency action plan, maintenance, use, monitoring as well as the annual and periodic inspections. Dams are classified according to the hazard they pose into class 1, 2 or 3 dams. The classification is not needed, if, according to the dam safety authority, the dam poses no danger. The owner of a classified dam must prepare a monitoring programme, to be approved by decision of the dam safety authority. To establish the hazard caused by a dam, the owner of a class 1 dam must prepare an analysis of the dam hazard to humans and property as well as to the environment. The dam safety authority may also require a dam break hazard analysis for a dam other than class 1 dam if deemed necessary for classification. The owner of a class 1 dam must prepare a plan of measures in case of emergency or operational failure. The plan shall present the dam owner’s state of preparedness to act on their own initiative in the situations described above. In each case, the rescue authorities make a separate assessment for the need to prepare a plan as set out in the Rescue Act. The dam owner must provide the information specified in the Dam Safety Decree to be entered into the dam safety information system. The dam safety authority and the owner of the dam must keep up-to-date printouts in their own dam safety files from the information system for each dam as well as other important documents connected with dam safety to ensure that these are readily available in case of disturbance.

Modelling the lava dome extruded at Soufrière Hills Volcano, Montserrat, August 2005–May 2006. Part I: Dome shape and internal structure

Lava domes comprise core, carapace, and clastic talus components. They can grow endogenously by inflation of a core and/or exogenously with the extrusion of shear bounded lobes and whaleback lobes at the surface. Internal structure is paramount in determining the extent to which lava dome growth evolves stably, or conversely the propensity for collapse. The more core lava that exists within a dome, in both relative and absolute terms, the more explosive energy is available, both for large pyroclastic flows following collapse and in particular for lateral blast events following very rapid removal of lateral support to the dome. Knowledge of the location of the core lava within the dome is also relevant for hazard assessment purposes. A spreading toe, or lobe of core lava, over a talus substrate may be both relatively unstable and likely to accelerate to more violent activity during the early phases of a retrogressive collapse. Soufrière Hills Volcano, Montserrat has been erupting since 1995 and has produced numerous lava domes that have undergone repeated collapse events. We consider one continuous dome growth period, from August 2005 to May 2006 that resulted in a dome collapse event on 20th May 2006. The collapse event lasted 3 h, removing the whole dome plus dome remnants from a previous growth period in an unusually violent and rapid collapse event. We use an axisymmetrical computational Finite Element Method model for the growth and evolution of a lava dome. Our model comprises evolving core, carapace and talus components based on axisymmetrical endogenous dome growth, which permits us to model the interface between talus and core. Despite explicitly only modelling axisymmetrical endogenous dome growth our core–talus model simulates many of the observed growth characteristics of the 2005–2006 SHV lava dome well. Further, it is possible for our simulations to replicate large-scale exogenous characteristics when a considerable volume of talus has accumulated around the lower flanks of the dome. Model results suggest that dome core can override talus within a growing dome, potentially generating a region of significant weakness and a potential locus for collapse initiation.

Brief communication. Rain effect on the load of tephra deposits

Accumulation of tephra fallout produced during explosive eruptions can cause roof collapses in areas near the volcano, when the weight of the deposit exceeds some threshold value that depends on the quality of buildings. The additional loading of water that remains trapped in the tephra deposits due to rainfall can contribute to increasing the loading of the deposits on the roofs. Here we propose a simple approach to estimate an upper bound for the contribution of rain to the load of pyroclastic deposits that is useful for hazard assessment purposes. As case study we present an application of the method in the area of Naples, Italy, for a reference eruption from Vesuvius volcano.

Técnicas de suavização aplicadas à caracterização de fontes sísmicas e à análise probabilística de ameaça sísmica

A avaliação de risco sísmico, fundamental para as decisões sobre as estruturas de obras de engenharia e mitigação de perdas, envolve fundamentalmente a análise de ameaça sísmica. Calcular a ameaça sísmica é o mesmo que calcular a probabilidade de que certo nível de determinada medida de intensidade em certo local durante um certo tempo seja excedido. Dependendo da complexidade da atividade geológica essas estimativas podem ser bas- tante sofisticadas. Em locais com baixa sismicidade, como é o caso do Brasil, o pouco tempo (geológico) de observação e a pouca quantidade de informação são fontes de muitas incer- tezas e dificuldade de análise pelos métodos mais clássicos e conhecidos que geralmente consideram, através de opiniões de especialistas, determinadas zonas sísmicas. Serão discutidas algumas técnicas de suavização e seus fundamentos como métodos al- ternativos ao zoneamento, em seguida se exemplifica suas aplicações no caso brasileiro.

Caracterização estatística de processos sísmicos via Distribuição Generalizada de Pareto. Estudo de caso: João Câmara-RN

The work is to make a brief discussion of methods to estimate the parameters of the Generalized Pareto distribution (GPD). Being addressed the following techniques: Moments (moments), Maximum Likelihood (MLE), Biased Probability Weighted Moments (PWMB), Unbiased Probability Weighted Moments (PWMU), Mean Power Density Divergence (MDPD), Median (MED), Pickands (PICKANDS), Maximum Penalized Likelihood (MPLE), Maximum Goodness-of-fit (MGF) and the Maximum Entropy (POME) technique, the focus of this manuscript. By way of illustration adjustments were made for the Generalized Pareto distribution, for a sequence of earthquakes intraplacas which occurred in the city of João Câmara in the northeastern region of Brazil, which was monitored continuously for two years (1987 and 1988). It was found that the MLE and POME were the most efficient methods, giving them basically mean squared errors. Based on the threshold of 1.5 degrees was estimated the seismic risk for the city, and estimated the level of return to earthquakes of intensity 1.5°, 2.0°, 2.5°, 3.0° and the most intense earthquake never registered in the city, which occurred in November 1986 with magnitude of about 5.2º

Correlação entre contexto morfoestrutural e sismicidade nas regiões de João Câmara e São Rafael (RN)

This MSc thesis describes brittle deformation in two seismic zones located in north-eastern Brazil: João Câmara and São Rafael, Rio Grande do Norte State. Both areas show seismogenic faults, Samambaia and São Rafael, indicated by narrow zones of epicentres with a strike of 040o, a lenght of 30 km and 4 km, and a depth of 1-12 and 0,5-4 km, respectively. The first seismological and geological studies suggested blind faults or faults that were still in the beginning of the nucleation process. The region is under E-W-oriented compression and is underlain by Precambrian terrains, deformed by one or more orogenic cycles, which generated shear zones generally marked by strong pervasive foliation and sigmoidal shapes. The crystalline basement is capped by the Cretaceous Potiguar basin, which is also locally capped by Pliocene continental siliciclastic deposits (Barreiras Formation), and Quaternary alluvium. The main aim of this study was to map epicentral areas and find whether there are any surface geological or morphotectonic expression related to the seismogenic faults. A detailed geological map was carried out in both seismic areas in order to identify brittle structures and fault-related drainage/topographic features. Geological and morphotectonic evidence indicate that both seismogenic faults take place along dormant structures. They either cut Cenozoic rocks or show topographic expression, i.e., are related to topographic heights or depressions and straight river channels. Faults rocks in the Samambaia and São Rafael faults are cataclasite, fault breccia, fault gouge, pseudotachylyte, and quartz veins, which point to reactivation processes in different crustal levels. The age of the first Samambaia and the São Rafael faulting movement possibly ranges from late Precambrian to late Cretaceous. Both fault cut across Precambrian fabric. They also show evidence of brittle processes which took place between 4 and 12 km deep, which probably have not occurred in Cenozoic times. The findings are of great importance for regional seismic hazard. They indicate that fault zones are longer than previously suggested by seismogenic studies. According to the results, the methodology used during this thesis may also be useful in other neotectonic investigation in intraplate areas

Could albumin level explain the higher mortality in hemodialysis patients with pulmonary hypertension?

Background: The pathogenesis of pulmonary hypertension (PH) in hemodialysis is still unclear. The aim of thisstudy was to identify the risk factors associated with the presence of PH in chronic hemodialysis patients and toverify whether these factors might explain the highest mortality among them.Methods: We conducted a retrospective study of hemodialysis patients who started treatment from August 2001to October 2007 and were followed up until April 2011 in a Brazilian referral medical school. According to theresults of echocardiography examination, patients were allocated in two groups: those with PH and those withoutPH. Clinical parameters, site and type of vascular access, bioimpedance, and laboratorial findings were comparedbetween the groups and a logistic regression model was elaborated. Actuarial survival curves were constructed andhazard risk to death was evaluated by Cox regression analysis.Results: PH > 35 mmHg was found in 23 (30.6%) of the 75 patients studied. The groups differed in extracellularwater, ventricular thickness, left atrium diameter, and ventricular filling. In a univariate analysis, extracellular waterwas associated with PH (relative risk = 1.194; 95% CI of 1.006 1.416; p = 0.042); nevertheless, in a multiple model,only left atrium enlargement was independently associated with PH (relative risk =1.172; 95% CI of 1.010 1.359;p = 0.036). PH (hazard risk = 3.008; 95% CI of 1.285 7.043; p = 0.011) and age (hazard risk of 1.034 per year of age;95% CI of 1.000 7.068; p = 0.047) were significantly associated with mortality in a multiple Cox regression analysis.However, when albumin was taken in account the only statistically significant association was between albuminlevel and mortality (hazard risk = 0.342 per g/dL; 95% CI of 0.119 0.984; p = 0.047) while the presence of PH lost itsstatistical significance (p = 0.184). Mortality was higher in patients with PH (47.8% vs 25%) who also had astatistically worse survival after the sixth year of follow up.Conclusions: PH in hemodialysis patients is associated with parameters of volume overload that sheds light on itspathophysiology. Mortality is higher in hemodialysis patients with PH and the low albumin level can explain thisassociation.© 2012 Greenfield et al.; licensee BioMed Central Ltd.

Aplicação do Processo Analítico Hierarquico (AHP) Para Priorização de Obras de Intervenção em Áreas e Setores de Risco Geológico nos Municípios de Itapecerica da Serra e Suzano (SP)

Municipal Plans of Risk Reducing (PMRR's) were produced in settlements in the municipalities of Itapecerica da Serra (SP) and Suzano (SP), covering areas at risk of landslides and washouts of banks of streams. The development of PMRR's provided the delimitation of areas of risk, the indication of intervention works in order to eliminate and / or reduce risks, and consequently an indication of the areas and priority sectors for implementation of intervention works. The prioritization of areas and sectors that should receive the works of reducing or eliminating risk was performed by an expert involved in risk mapping. Despite the specialist's judgment exercise caution, the decision regarding the priority sites for implementation of alternative interventions is subjective. Since there is no way to eliminate this subjectivity, the use of decision-making techniques is important to evaluate whether the expert's reasoning is consistent. One of the first techniques developed for multiple criteria is the AHP (Analytic Hierarchy Process). This paper describes the results of a research carried out in order to assess whether the use of Analytic Hierarchy Process contributes to the results of the indication of the areas and priority sectors for implementation of interventions can be considered more consistent than in situations where the priority occurs without the use of decision making techniques. Results were compared between the prioritization of interventions for implementation contained in PMRR's of Itapecerica da Serra and Suzano and those obtained from the use of Analytic Hierarchy Process (AHP). It was concluded that such techniques permits an evaluation of the expert's judgment is logically coherent, thus contributing to produce results more technically based.

Longitudinal bar buckling behavior

Reinforced concrete columns might fail because of buckling of the longitudinal reinforcing bar when exposed to earthquake motions. Depending on the hoop stiffness and the length-over-diameter ratio, the instability can be local (in between two subsequent hoops) or global (the buckling length comprises several hoop spacings). To get insight into the topic, an extensive literary research of 19 existing models has been carried out including different approaches and assumptions which yield different results. Finite element fiberanalysis was carried out to study the local buckling behavior with varying length-over-diameter and initial imperfection-over-diameter ratios. The comparison of the analytical results with some experimental results shows good agreement before the post buckling behavior undergoes large deformation. Furthermore, different global buckling analysis cases were run considering the influence of different parameters; for certain hoop stiffnesses and length-over-diameter ratios local buckling was encountered. A parametric study yields an adimensional critical stress in function of a stiffness ratio characterized by the reinforcement configuration. Colonne in cemento armato possono collassare per via dell’instabilità dell’armatura longitudinale se sottoposte all’azione di un sisma. In funzione della rigidezza dei ferri trasversali e del rapporto lunghezza d’inflessione-diametro, l’instabilità può essere locale (fra due staffe adiacenti) o globale (la lunghezza d’instabilità comprende alcune staffe). Per introdurre alla materia, è proposta un’esauriente ricerca bibliografica di 19 modelli esistenti che include approcci e ipotesi differenti che portano a risultati distinti. Tramite un’analisi a fibre e elementi finiti si è studiata l’instabilità locale con vari rapporti lunghezza d’inflessione-diametro e imperfezione iniziale-diametro. Il confronto dei risultati analitici con quelli sperimentali mostra una buona coincidenza fino al raggiungimento di grandi spostamenti. Inoltre, il caso d’instabilità globale è stato simulato valutando l’influenza di vari parametri; per certe configurazioni di rigidezza delle staffe e lunghezza d’inflessione-diametro si hanno ottenuto casi di instabilità locale. Uno studio parametrico ha permesso di ottenere un carico critico adimensionale in funzione del rapporto di rigidezza dato dalle caratteristiche dell’armatura.