Laser scanning-based recognition of rotational movements on a deep seated gravitational instability: The Cinque Torri case (North-Eastern Italian Alps)

The Cinque Torri group (Cortina d'Ampezzo, Italy) is an articulated system of unstable carbonatic rock monoliths located in a very important tourism area and therefore characterized by a significant risk. The instability phenomena involved represent an example of lateral spreading developed over a larger deep seated gravitational slope deformation (DSGSD) area. After the recent fall of a monolith of more than 10 000 m3, a scientific study was initiated to monitor the more unstable sectors and to characterize the past movements as a fundamental tool for predicting future movements and hazard assessment. To achieve greater insight on the ongoing lateral spreading process, a method for a quantitative analysis of rotational movements associated with the lateral spreading has been developed, applied and validated. The method is based on: i) detailed geometrical characterization of the area by means of laser scanner techniques; ii) recognition of the discontinuity sets and definition of a reference frame for each set, iii) correlation between the obtained reference frames related to a specific sector and a stable external reference frame, and iv) determination of the 3D rotations in terms of Euler angles to describe the present settlement of the Cinque Torri system with respect to the surrounding stable areas. In this way, significant information on the processes involved in the fragmentation and spreading of a former dolomitic plateau into different rock cliffs has been gained. The method is suitable to be applied to similar case studies.

An introductory review on gravitational-deformation induced structures, fabrics and modeling

Recent studies have pointed out a similarity between tectonics and slope tectonic-induced structures. Numerous studies have demonstrated that structures and fabrics previously interpreted as of purely geodynamical origin are instead the result of large slope deformation, and this led in the past to erroneous interpretations. Nevertheless, their limit seems not clearly defined, but it is somehow transitional. Some studies point out continuity between failures developing at surface with upper crust movements. In this contribution, the main studies which examine the link between rock structures and slope movements are reviewed. The aspects regarding model and scale of observation are discussed together with the role of pre-existing weaknesses in the rock mass. As slope failures can develop through progressive failure, structures and their changes in time and space can be recognized. Furthermore, recognition of the origin of these structures can help in avoiding misinterpretations of regional geology. This also suggests the importance of integrating different slope movement classifications based on distribution and pattern of deformation and the application of structural geology techniques. A structural geology approach in the landslide community is a tool that can greatly support the hazard quantification and related risks, because most of the physical parameters, which are used for landslide modeling, are derived from geotechnical tests or the emerging geophysical approaches.

Detailed assessment of the deep-seated gravitational deformation at Stampa above Flåm, Norway

The unstable rock slope above the village of Flåm shows signs of active and postglacial gravitational deformation over an area of 11 km2. We performed detailed structural field mapping, annual differential Global Navigation Satellite System (GNSS) surveys, and generated a detailed topographic model based on airborne and terrestrial laser scanning. Kinematic analyses of the structural data indicates that deformation is complex and varies over the slope. Both sliding and toppling are locally feasible. Using differential GNSS, 18 points were measured annually over a period of up to 6 years. Two of these points show an average yearly movement of around 10 mm/year. They are located at the frontal cliff on almost completely detached blocks. Large fractures indicate deep-seated gravitational deformation of volumes up to 80 million m3, but the movement rates in these areas are below 2 mm/year. Based upon these combined observations, we interpret that small collapses of blocks along the frontal cliff will be more frequent. Larger collapses of free-standing blocks along the cliff with volumes >100,000 m3, thus large enough to reach the fjord, cannot be ruled out. A large collapse involving more than 10 million m3, however, is of very low likelihood at present.

Flow-R, a model for susceptibility mapping of debris flows and other gravitational hazards at a regional scale: some case studies

Every year, debris flows cause huge damage in mountainous areas. Due to population pressure in hazardous zones, the socio-economic impact is much higher than in the past. Therefore, the development of indicative susceptibility hazard maps is of primary importance, particularly in developing countries. However, the complexity of the phenomenon and the variability of local controlling factors limit the use of processbased models for a first assessment. A debris flow model has been developed for regional susceptibility assessments using digital elevation model (DEM) with a GIS-based approach.. The automatic identification of source areas and the estimation of debris flow spreading, based on GIS tools, provide a substantial basis for a preliminary susceptibility assessment at a regional scale. One of the main advantages of this model is its workability. In fact, everything is open to the user, from the data choice to the selection of the algorithms and their parameters. The Flow-R model was tested in three different contexts: two in Switzerland and one in Pakistan, for indicative susceptibility hazard mapping. It was shown that the quality of the DEM is the most important parameter to obtain reliable results for propagation, but also to identify the potential debris flows sources.

Influence of structural heterogeneities and of large scale topography on imbricate gravitational rock slope failures: New insights from 3-D physical modeling and geomorphological analysis

Initial topography and inherited structural discontinuities are known to play a dominant role in rock slope stability. Previous 2-D physical modeling results demonstrated that even if few preexisting fractures are activated/propagated during gravitational failure all of those heterogeneities had a great influence on mobilized volume and its kinematics. The question we address in the present study is to determine if such a result is also observed in 3-D. As in 2-D previous models we examine geologically stable model configuration, based upon the well documented landslide at Randa, Switzerland. The 3-D models consisted of a homogeneous material in which several fracture zones were introduced in order to study simplified but realistic configurations of discontinuities (e.g. based on natural example rather than a parametric study). Results showed that the type of gravitational failure (deep-seated landslide or sequential failure) and resulting slope morphology evolution are the result of the interplay of initial topography and inherited preexisting fractures (orientation and density). The three main results are i) the initial topography exerts a strong control on gravitational slope failure. Indeed in each tested configuration (even in the isotropic one without fractures) the model is affected by a rock slide, ii) the number of simulated fracture sets greatly influences the volume mobilized and its kinematics, and iii) the failure zone involved in the 1991 event is smaller than the results produced by the analog modeling. This failure may indicate that the zone mobilized in 1991 is potentially only a part of a larger deep-seated landslide and/or wider deep seated gravitational slope deformation.

Flow-R, a model for susceptibility mapping of debris flows and other gravitational hazards at a regional scale

The development of susceptibility maps for debris flows is of primary importance due to population pressure in hazardous zones. However, hazard assessment by processbased modelling at a regional scale is difficult due to the complex nature of the phenomenon, the variability of local controlling factors, and the uncertainty in modelling parameters. A regional assessment must consider a simplified approach that is not highly parameter dependant and that can provide zonation with minimum data requirements. A distributed empirical model has thus been developed for regional susceptibility assessments using essentially a digital elevation model (DEM). The model is called Flow-R for Flow path assessment of gravitational hazards at a Regional scale (available free of charge under www.flow-r.org) and has been successfully applied to different case studies in various countries with variable data quality. It provides a substantial basis for a preliminary susceptibility assessment at a regional scale. The model was also found relevant to assess other natural hazards such as rockfall, snow avalanches and floods. The model allows for automatic source area delineation, given user criteria, and for the assessment of the propagation extent based on various spreading algorithms and simple frictional laws.We developed a new spreading algorithm, an improved version of Holmgren's direction algorithm, that is less sensitive to small variations of the DEM and that is avoiding over-channelization, and so produces more realistic extents. The choices of the datasets and the algorithms are open to the user, which makes it compliant for various applications and dataset availability. Amongst the possible datasets, the DEM is the only one that is really needed for both the source area delineation and the propagation assessment; its quality is of major importance for the results accuracy. We consider a 10m DEM resolution as a good compromise between processing time and quality of results. However, valuable results have still been obtained on the basis of lower quality DEMs with 25m resolution.

Characterization of gravitational rock slope deformations at different spatial scales based on field, remote sensing and numerical approaches

Rock slope instabilities such as rock slides, rock avalanche or deep-seated gravitational slope deformations are widespread in Alpine valleys. These phenomena represent at the same time a main factor that control the mountain belts erosion and also a significant natural hazard that creates important losses to the mountain communities. However, the potential geometrical and dynamic connections linking outcrop and slope-scale instabilities are often unknown. A more detailed definition of the potential links will be essential to improve the comprehension of the destabilization processes and to dispose of a more complete hazard characterization of the rock instabilities at different spatial scales. In order to propose an integrated approach in the study of the rock slope instabilities, three main themes were analysed in this PhD thesis: (1) the inventory and the spatial distribution of rock slope deformations at regional scale and their influence on the landscape evolution, (2) the influence of brittle and ductile tectonic structures on rock slope instabilities development and (3) the characterization of hazard posed by potential rock slope instabilities through the development of conceptual instability models. To prose and integrated approach for the analyses of these topics, several techniques were adopted. In particular, high resolution digital elevation models revealed to be fundamental tools that were employed during the different stages of the rock slope instability assessment. A special attention was spent in the application of digital elevation model for detailed geometrical modelling of past and potential instabilities and for the rock slope monitoring at different spatial scales. Detailed field analyses and numerical models were performed to complete and verify the remote sensing approach. In the first part of this thesis, large slope instabilities in Rhone valley (Switzerland) were mapped in order to dispose of a first overview of tectonic and climatic factors influencing their distribution and their characteristics. Our analyses demonstrate the key influence of neotectonic activity and the glacial conditioning on the spatial distribution of the rock slope deformations. Besides, the volumes of rock instabilities identified along the main Rhone valley, were then used to propose the first estimate of the postglacial denudation and filling of the Rhone valley associated to large gravitational movements. In the second part of the thesis, detailed structural analyses of the Frank slide and the Sierre rock avalanche were performed to characterize the influence of brittle and ductile tectonic structures on the geometry and on the failure mechanism of large instabilities. Our observations indicated that the geometric characteristics and the variation of the rock mass quality associated to ductile tectonic structures, that are often ignored landslide study, represent important factors that can drastically influence the extension and the failure mechanism of rock slope instabilities. In the last part of the thesis, the failure mechanisms and the hazard associated to five potential instabilities were analysed in detail. These case studies clearly highlighted the importance to incorporate different analyses and monitoring techniques to dispose of reliable and hazard scenarios. This information associated to the development of a conceptual instability model represents the primary data for an integrated risk management of rock slope instabilities. - Les mouvements de versant tels que les chutes de blocs, les éboulements ou encore les phénomènes plus lents comme les déformations gravitaires profondes de versant représentent des manifestations courantes en régions montagneuses. Les mouvements de versant sont à la fois un des facteurs principaux contrôlant la destruction progressive des chaines orogéniques mais aussi un danger naturel concret qui peut provoquer des dommages importants. Pourtant, les phénomènes gravitaires sont rarement analysés dans leur globalité et les rapports géométriques et mécaniques qui lient les instabilités à l'échelle du versant aux instabilités locales restent encore mal définis. Une meilleure caractérisation de ces liens pourrait pourtant représenter un apport substantiel dans la compréhension des processus de déstabilisation des versants et améliorer la caractérisation des dangers gravitaires à toutes les échelles spatiales. Dans le but de proposer un approche plus globale à la problématique des mouvements gravitaires, ce travail de thèse propose trois axes de recherche principaux: (1) l'inventaire et l'analyse de la distribution spatiale des grandes instabilités rocheuses à l'échelle régionale, (2) l'analyse des structures tectoniques cassantes et ductiles en relation avec les mécanismes de rupture des grandes instabilités rocheuses et (3) la caractérisation des aléas rocheux par une approche multidisciplinaire visant à développer un modèle conceptuel de l'instabilité et une meilleure appréciation du danger . Pour analyser les différentes problématiques traitées dans cette thèse, différentes techniques ont été utilisées. En particulier, le modèle numérique de terrain s'est révélé être un outil indispensable pour la majorité des analyses effectuées, en partant de l'identification de l'instabilité jusqu'au suivi des mouvements. Les analyses de terrain et des modélisations numériques ont ensuite permis de compléter les informations issues du modèle numérique de terrain. Dans la première partie de cette thèse, les mouvements gravitaires rocheux dans la vallée du Rhône (Suisse) ont été cartographiés pour étudier leur répartition en fonction des variables géologiques et morphologiques régionales. En particulier, les analyses ont mis en évidence l'influence de l'activité néotectonique et des phases glaciaires sur la distribution des zones à forte densité d'instabilités rocheuses. Les volumes des instabilités rocheuses identifiées le long de la vallée principale ont été ensuite utilisés pour estimer le taux de dénudations postglaciaire et le remplissage de la vallée du Rhône lié aux grands mouvements gravitaires. Dans la deuxième partie, l'étude de l'agencement structural des avalanches rocheuses de Sierre (Suisse) et de Frank (Canada) a permis de mieux caractériser l'influence passive des structures tectoniques sur la géométrie des instabilités. En particulier, les structures issues d'une tectonique ductile, souvent ignorées dans l'étude des instabilités gravitaires, ont été identifiées comme des structures très importantes qui contrôlent les mécanismes de rupture des instabilités à différentes échelles. Dans la dernière partie de la thèse, cinq instabilités rocheuses différentes ont été étudiées par une approche multidisciplinaire visant à mieux caractériser l'aléa et à développer un modèle conceptuel trois dimensionnel de ces instabilités. A l'aide de ces analyses on a pu mettre en évidence la nécessité d'incorporer différentes techniques d'analyses et de surveillance pour une gestion plus objective du risque associée aux grandes instabilités rocheuses.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Inheritance of ductile and brittle structures in the development of large rock slope instabilities: Examples from western Norway

The high density of slope failures in western Norway is due to the steep relief and to the concentration of various structures that followed protracted ductile and brittle tectonics. On the 72 investigated rock slope instabilities, 13 were developed in soft weathered mafic and phyllitic allochthons. Only the intrinsic weakness of such rocks increases the susceptibility to gravitational deformation. In contrast, the gravitational structures in the hard gneisses reactivate prominent ductile or/and brittle fabrics. At 30 rockslides along cataclinal slopes, weak mafic layers of foliation are reactivated as basal planes. Slope-parallel steep foliation forms back-cracks of unstable columns. Folds are specifically present in the Storfjord area, together with a clustering of potential slope failures. Folding increases the probability of having favourably orientated planes with respect to the gravitational forces and the slope. High water pressure is believed to seasonally build up along the shallow-dipping Caledonian detachments and may contribute to destabilization of the rock slope upwards. Regional cataclastic faults localized the gravitational structures at 45 sites. The volume of the slope instabilities tends to increase with the amount of reactivated prominent structures and the spacing of the latter controls the size of instabilities.

Bimodal magmatism as a consequence of the post-collisional readjustment of the thickened Variscan continental lithosphere (Aiguilles Rouges - Mont Blanc Massifs, Western Alps)

High Precision U-Pb zircon and monazite dating in the Aiguilles Rouges-Mont Blanc area allowed discrimination of three short-lived bimodal magmatic pulses: the early 332 Ma Mg-K Pormenaz monzonite and associated 331 Ma peraluminous Montees Pelissier monzogranite; the 307 Ma cordierite-bearing peraluminous Vallorcine and Fully intrusions; and the 303 Fe-K Mont Blanc syenogranite. All intruded syntectonically along major-scale transcurrent faults at a time when the substratum was experiencing tectonic exhumation, active erosion recorded in detrital basins and isothermal decompression melting dated at 327-320 Ma. Mantle activity and magma mixing are evidenced in all plutons by coeval mafic enclaves, stocks and synplutonic dykes. Both crustal and mantle sources evolve through time, pointing to an increasingly warm continental crust and juvenile asthenospheric mantle sources. This overall tectono-magmatic evolution is interpreted in a scenario of post-collisional restoration to normal size of a thickened continental lithosphere. The latter re-equilibrates through delamination and/or erosion of its mantle root and tectonic exhumation/erosion in an overall extensional regime. Extension is related to either gravitational collapse or back-are extension of a distant subduction zone.

Analyzing complex rock slope deformation at Stampa, western Norway, by integrating geomorphology, kinematics and numerical modeling

The unstable rock slope, Stampa, above the village of Flåm, Norway, shows signs of both active and postglacial gravitational deformation over an area of 11 km2. Detailed structural field mapping, annual differential Global Navigation Satellite System (GNSS) surveys, as well as geomorphic analysis of high-resolution digital elevation models based on airborne and terrestrial laser scanning indicate that slope deformation is complex and spatially variable. Numerical modeling was used to investigate the influence of former rockslide activity and to better understand the failure mechanism. Field observations, kinematic analysis and numerical modeling indicate a strong structural control of the unstable area. Based on the integration of the above analyses, we propose that the failure mechanism is dominated by (1) a toppling component, (2) subsiding bilinear wedge failure and (3) planar sliding along the foliation at the toe of the unstable slope. Using differential GNSS, 18 points were measured annually over a period of up to 6 years. Two of these points have an average yearly movement of around 10 mm/year. They are located at the frontal cliff on almost completely detached blocks with volumes smaller than 300,000 m3. Large fractures indicate deep-seated gravitational deformation of volumes reaching several 100 million m3, but the movement rates in these areas are below 2 mm/year. Two different lobes of prehistoric rock slope failures were dated with terrestrial cosmogenic nuclides. While the northern lobe gave an average age of 4,300 years BP, the southern one resulted in two different ages (2,400 and 12,000 years BP), which represent most likely multiple rockfall events. This reflects the currently observable deformation style with unstable blocks in the northern part in between Joasete and Furekamben and no distinct blocks but a high rockfall activity around Ramnanosi in the south. With a relative susceptibility analysis it is concluded that small collapses of blocks along the frontal cliff will be more frequent. Larger collapses of free-standing blocks along the cliff with volumes > 100,000 m3, thus large enough to reach the fjord, cannot be ruled out. A larger collapse involving several million m3 is presently considered of very low likelihood.

Space-time within general relativity : a structural realist understanding

ABSTRACT This dissertation investigates the, nature of space-time as described by the theory of general relativity. It mainly argues that space-time can be naturally interpreted as a physical structure in the precise sense of a network of concrete space-time relations among concrete space-time points that do not possess any intrinsic properties and any intrinsic identity. Such an interpretation is fundamentally based on two related key features of general relativity, namely substantive general covariance and background independence, where substantive general covariance is understood as a gauge-theoretic invariance under active diffeomorphisms and background independence is understood in the sense that the metric (or gravitational) field is dynamical and that, strictly speaking, it cannot be uniquely split into a purely gravitational part and a fixed purely inertial part or background. More broadly, a precise notion of (physical) structure is developed within the framework of a moderate version of structural realism understood as a metaphysical claim about what there is in the world. So, the developement of this moderate structural realism pursues two main aims. The first is purely metaphysical, the aim being to develop a coherent metaphysics of structures and of objects (particular attention is paid to the questions of identity and individuality of these latter within this structural realist framework). The second is to argue that moderate structural realism provides a convincing interpretation of the world as described by fundamental physics and in particular of space-time as described by general relativity. This structuralist interpretation of space-time is discussed within the traditional substantivalist-relationalist debate, which is best understood within the broader framework of the question about the relationship between space-time on the one hand and matter on the other. In particular, it is claimed that space-time structuralism does not constitute a 'tertium quid' in the traditional debate. Some new light on the question of the nature of space-time may be shed from the fundamental foundational issue of space-time singularities. Their possible 'non-local' (or global) feature is discussed in some detail and it is argued that a broad structuralist conception of space-time may provide a physically meaningful understanding of space-time singularities, which is not plagued by the conceptual difficulties of the usual atomsitic framework. Indeed, part of these difficulties may come from the standard differential geometric description of space-time, which encodes to some extent this atomistic framework; it raises the question of the importance of the mathematical formalism for the interpretation of space-time.

Characterization and monitoring of the Åknes landslide using terrestrial laser scanning

Terrestrial laser scanning (TLS) provides high-resolution point clouds of the topography and new TLS instruments with ranges exceeding 300 m or even 1000 m are powerful tools for characterizing and monitoring slope movements. This study focuses on the 35 million m3 Åknes rockslide in Western Norway, which is one of the most investigated and monitored rockslides in the world. The TLS point clouds are used for the structural analysis of the steep, inaccessible main scarp of the rockslide, including an assessment of the discontinuity sets and fold axes. TLS acquisitions in 2006, 2007 and 2008 provide information on 3-D displacements for the entire scanned area and are not restricted like conventional survey instruments to single measurement points. The affine transformation matrix between two TLS acquisitions precisely describes the rockslide displacements and enables their separation into translational components, such as the displacement velocity and direction, and rotational components, like toppling. This study shows the ability of TLS to obtain reliable 3-D displacement information over a large, unstable area. Finally, a possible instability model for the upper part of Åknes rockslide explains the measured translational and rotational displacements by a combination of southward planar sliding along the gneiss foliation, gravitational vertical settlement along the complex, stepped basal sliding surface and northward toppling toward the opened graben structure.