Bed thickness-dependent fracturing and inter-bed coupling define the nonlinear fracture spacing-bed thickness relationship in layered rocks: Numerical modeling

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The formation of tabular compaction-band arrays: Theoretical and numerical analysis

Journal of the Mechanics and Physics of Solids, v. 57, n. 5, p. 851-868, 2009. http://dx.doi.org/10.1016/j.jmps.2009.01.007International audienceThe bifurcation analysis of compaction banding is extended to the formation of a tabular discrete compaction-band array. This analysis, taken together with the results of finite-difference simulations, shows that the bifurcation results in the formation of intermittent loading (elastic–plastic) and unloading (elastic) bands. The obtained analytical solution relates the spacing parameter χ (the ratio between the band thickness to the band-to-band distance) to all constitutive and stress-state parameters. Both this solution and numerical models reveal strong dependence of χ on the hardening modulus h: χ increases with h reduction. The band thickness in the numerical models is mesh dependent, but in terms of mesh-zone-size varies only from ∼2 to 4 depending on the constitutive parameters and independently on the mesh resolution. The thickness of the “elementary” compaction bands in real granular materials is equal to a few grain sizes. It follows that one grid zone in the numerical models corresponds approximately to one grain in the real material. The numerical models reproduce both discrete and continuous propagating compaction banding observed in the rock samples. These phenomena were shown to be dependent on the evolution of h and the dilatancy factor with deformation

Numerical Simulation of True 3D Rock Tests with Classical and New Three-Invariant Constitutive Models Focusing on the End Effects

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Modélisation expérimentale de la fracturation d'un milieu sédimentaire

La modélisation de la déformation, de la rupture et de la fracturation des milieux rocheux représente un enjeu majeur dans de nombreux domaines scientifiques et pratiques, notamment pour l'exploitation des réservoirs fracturés. Cependant, cette modélisation se heurte à la mauvaise connaissance des lois constitutives, ce qui rend particulièrement importantes les approches expérimentales et en particulier la modélisation physique, qui est au coeur de ce travail. Nous avons développé une technique originale d une telle modélisation, basée sur un nouveau matériau Crack1 à l'échelle physique par rapport à une roche réservoir typique: le calcaire. Un programme étendu d'expérimentation avec les modèles de Crack1 a été réalisé avec un dispositif de chargement poly-tridimensionnel. Ce dispositif combine à la fois la simplicité et l efficacité des solutions réalisées pour la réduction et l élimination complète de la friction aux bords des modèles. Les résultats principaux peuvent être résumés de la façon suivante: Des réseaux de diaclases ont été reproduits pour la première fois dans des conditions de chargement homogènes. 1 Les diaclases se forment, dans nos expériences, sous une compression triaxiale. Elles ne sont donc pas des fractures en Mode I. 2 Les figures fractographiques visibles sur les surfaces des diaclases naturelles et celles obtenues dans les modèles sont très similaires, ce qui suggère que la similarité physique est assurée pas seulement à macro-échelle, mais aussi à micro-échelle. 3 L'espacement S entre les diaclases ne dépend pas de l'épaisseur du modèle , contrairement au concept de saturation largement adopté dans la littérature et les modèles de réservoirs. Il a été démontré que S est contrôlé par l'état des contraintes imposé et la déformation accumulée du modèle. 4 Nous avons pu également reproduire dans des modèles les couloirs fracturés dont la formation est contrôlée par la rigidité des contacts aux limites de l unité mécanique affectée par la fracturation. 5 L'augmentation de la pression moyenne appliquée au modèle résulte en un changement du style de la fracturation, qui évolue de manière continue des diaclases vers des fractures obliques conjuguées. 6 L'analyse des conditions de cette transition à partir de la théorie de la bifurcation de la déformation montre qu elle est associée à la réduction du facteur de dilatance b de Crack1 avec l'augmentation de la pression p (ce type de dépendance b (p) est également connu pour les roches réelles). Les résultats obtenus confirment donc que les lois constitutives contrôlent directement la fracturation. Des études expérimentales plus larges doivent désormais être menées pour contraindre ces lois dans toute leur complexité et avec une précision nécessaire.Modelling of deformation, rupture and fracturing of rocks is a major challenge in many scienti c and practical elds, especially for fractured reservoir production. However, this modelling is harmed by poor knowledge of the constitutive laws. Therefore experimental approaches, and in particular physical modelling, that is the subject of this work, are of great importance. We developed an innovative technique of such a modelling, based on a new material, Crack1 which is physically scaled to a typical reservoir rock, a limestone. An extensive experimental program has been conducted, using a polyaxial device. This device combines both simplicity and e ciency, in particular in reduction or complete removal of the friction along the model boundaries. The main results can be summarized as following : (1) Joints networks has been reproduced for the rst time under homogeneous loading. (2) Joints form under triaxial compression and therefore they are not Mode I fractures. (3) Fractographic patterns on natural and the model joint surfaces are similar, implying that the physical similarity is observed both at micro- and macro-scale. (4) Joint spacing S does not depend on the model thickness, contrary to the widely adopted saturation concept. S was shown to be controlled by the stress state and the accumulated deformation. (5) We also reproduced fracture corridors, whose formation is controlled by the rigidity contrast at the model boundaries. (6) The increase in the mean stress results in the change of the fracturing style, which changes continuously from jointing to shear fracturing. (7) Based on the bifurcation theory, it was demonstrated that this transition is controlled by the reductionof the dilatancy factor b with growing . These results thus con rm that constitutive laws directly control the fracturing. More extensive accurate investigation are now needed to better constrain these laws.NICE-BU Sciences (060882101) / SudocSudocFranceF

La modélisation expérimentale tridimensionnelle thermo mécanique de la subduction continentale et l'exhumation des roches de ultra haute pression/basse température

La distribution spatiale des massifs UHP/BT montre que leur exhumation est un phénomène 3D qui a lieu uniquement dans des zones particulières des chaînes de montagnes caractérisées par une complexité structurale et/ou géométrique. Dans les expériences de modélisation thermo mécanique 2D de la subduction continentale en régime de faible compression, nous obtenons l'exhumation de roches HP depuis des profondeurs d'environs 70 km. La croûte continentale subduite plus profondément dans l'asthenosphere devient trop chaude (peu résistante). Elle se détache du manteau continental subduit, flue verticalement et se sous plaque sous la plaque chevauchante. La subduction continentale en régime de forte compression peut provoquer la rupture de la plaque chevauchante dans l'arc volcanique ou le bassin arrière arc aboutissant à la subduction du bloc avant arc ou de la plaque d'arc. La croûte continentale subduite avec ces unités peut atteindre 200 km de profondeur en étant guidée par ces unités et le manteau continental subduit. Dans ces conditions, la croûte est soumise aux conditions UHP/BT, mais elle ne peut pas être exhumé dans un contexte 2D. Nous montrons numériquement en 3D, que la subduction le long d'une frontière de plaques convexe entraîne localement dans la plaque chevauchante une extension horizontale parallèle à la frontière qui provoque localement le retrait du front de cette plaque et la réduction de la pression inter plaque. En imposant cette déformation extensive à la plaque chevauchante dans un modèle expérimental thermo mécanique 3D nous avons obtenus l'exhumation locale des roches UHP/BT et avons pu étudier en détails son mécanisme.Spatial distribution of UHP/LT terrains evidences that their exhumation is essentially a 3-D process that takes place in specific sites of the mountain belt characterised by structural and/or geometrical complexities. In 2-D thermo-mechanical laboratory experiments of continental subduction in the low compressional regime, we obtained exhumation of HP rocks from depth limited by the overriding plate thickness (~70 km). Deeper subducted crust becomes too hot and hence weak. It flows up and underplates the overriding lithosphere. In 2-D experiments corresponding to highly compressional regime, the continental margin subduction causes failure of the overriding plate resulting in subduction of the fore-arc block or arc plate. The continental crust subducts to more than 200 km-depth, being sandwiched between the subducting "cold" block/plate and the subducted continental mantle. This crust thus meets UHP/LT conditions. It is still very weak but cannot flow up in this 2-D context, being blocked between the indicated rigid units. We show numerically that subduction along a convex plate boundary generates locally within the overriding plate along-boundary extension that produces local retreat of this plate front and thereby reduction of interplate pressure. Such a reduction is necessary to allow exhumation. By applying this extension to the overriding plate in a 3-D thermo mechanical model we do obtained local exhumation of UHP/LT and investigated in detail its mechanism.NICE-BU Sciences (060882101) / SudocSudocFranceF

Dependence of rock properties on the Lode angle: Experimental data, constitutive model, and bifurcation analysis

International audienceThe overwhelming majority of experimental tests on rocks have only been conducted for a single value of the Lode angle θθ corresponding to the axisymmetric compression (AC). There are now sufficiently extensive data sets from both AC and axisymmetric extension (AE) tests (corresponding to two extreme θθ values) for two materials (synthetic rock analog GRAM1 and Solnhofen Limestone). These data cover a wide range of the confining pressure (from brittle faulting to ductile flow). Very recently the data from true 3-D tests (for different θθ) also covering both brittle and ductile fields were published for Castlegate and Bentheim Sandstone as well. The results from all these tests summarized and processed in this paper constitute a solid basis which allows general conclusions to be drawn about the dependence of rock behavior on θθ. In all cases, the yield/failure envelopes were shown to be θθ-dependent so that the material strength at low mean stress σσ is smaller under AE than under AC, while at high σσ, it is the opposite. The brittle-ductile transition under AE occurs at σσ ~1.5 times greater than under AC, meaning that under AE the material is more prone to fracture development. The angle between the most compressive stress and the forming deformation localization bands is systematically higher for AE than for AC for the same σσ. Based on these data we formulate a new three-invariant constitutive model with convex and concave yield functions (YFs) which is used for the bifurcation analysis. The results of this analysis agree with the experimental data (for both YFs) and reveal that the θ -dependence of rock properties encourages the strain localization. The major factors defining this dependence are the θθ-dependence of the YFs but also of the dilatancy factor which is greater for AE than for AC. The theoretical results show that the failure (deformation band) plane can deviate from the intermediate stress direction and can become parallel to the maximum compressive stress at high σσ for the concave YF

Numerical modeling of the opening mode fracturing emanating from deformation localization in layered rocks

International audienceIt is known that rock fracture includes inelastic straining or damage that should localize at a certain loading stage and result in fracture initiation. The details of this process are not clear, and it is frequently omitted in the models by imposing the initial microcracks (seeds) with certain lengths and orientations. Here we investigate 2-D systems of three layers in finite-difference models. The layers subjected to the horizontal extension are separated by cohesive-frictional interfaces and have contrasted properties typical of sedimentary piles. Fractures are initiated in a more brittle central layer in the vicinity of the interfaces with the adjacent layers. It starts with the initially distributed inelastic straining, which then localizes into narrow bands. The damage within these bands is strongly accelerated, resulting in complete material failure locally. Short initial fractures corresponding to narrow bands of failed material are normal to the least local stress. They then propagate from the interfaces to the layer center with further extension. We carefully investigate the impact of different regularization procedures, the grid geometry, and structure on all stages of the fracture process and define the optimal conditions that can be applied for fracture modeling in different structural and loading configurations

Evolution of compactive shear localization bands: geological data and numerical models

International audienceCompactive shear bands with different ratio of compactive to shear inelastic deformation were recently studied in detail in different regions within the porous rocks. Among them are nicely exposed networks of conjugate cataclastic bands formed in a single tectonic event in the "Bassin du Sud-Est" (Provence, France) in Cretaceous sandstones. Microanalysis of the material within the bands shows that they underwent mainly thrust-sense shearing with a minor compactive component. The most striking feature of the evolution of these bands is their thickening at the flanks by incorporation of the intact host rock into the deformation bands and formation of new strands. This feature as well as the general band pattern was reproduced in 2-D finite-difference models where the hardening modulus h grew with inelastic deformation. This growth causes strengthening of the material within the initial bands (resulting from deformation bifurcation) and considerably slows down its inelastic deformation after it reaches a maximal value defined by all the constitutive parameters and most of all by the rate of increase in h. The strengthening above a certain level results in the band widening due to the accretion at its edges of material not yet deformed as it becomes involved in compactive shearing. The inelastic deformation is therefore the most rapid along the band flanks, while the thickening with time of the band core part mainly undergoes elastic unloading starting from some stage. The initial band spacing depends on the initial h value h0 and increases with h0 in accordance with predictions from bifurcation theory. During deformation, the spacing reduces due to the propagation of bands that largely saturate the model/layer, resulting in a band pattern that resembles the natural band networks. The increase of h imposed in the models appears therefore as both an important and realistic property that can also be derived from available experimental rock testing data. On the other hand, it is difficult to constrain with sufficient AGU Abstract Browser http://abstractsearch.agu.org/meetings/2011/FM/sections/T/sessions/T... 1 sur 3 05/01/2015 19:08 precision the evolution of h with deformation based only such data. Therefore the adjustment/calibration of the constitutive models based on the reproduction of natural deformation patterns in numerical simulations appears as an important tool

Evolution of compactive shear deformation bands: Numerical models and geological data,

International audienceNetworks of localized compactive and isovolumetric shear bands were generated in 2-D finite-difference models. They reproduce the most striking feature of the evolution of natural deformation bands characterized by compactive (or non-dilatant) inelastic volumetric deformation, i.e., the band thickening from the flanks by incorporation of the initially intact host rock. Such a thickening was obtained in the models where the hardening modulus h grew with inelastic deformation. This growth causes strengthening of the material within the initial bands resulting from deformation bifurcation. The strengthening above a certain level causes band widening due to the accretion to its edges of a not yet deformed material as it becomes involved in compactive shearing. The inelastic deformation is therefore the most rapid along the band flanks, while the band core part mainly undergoes elastic unloading and thickens due to the incorporation of new strands of sheared and compacted material. The initial band spacing depends on the initial h value and grows with it in accordance with predictions from bifurcation theory. During the post bifurcation deformation, the spacing reduces due to both the formation of new and propagation of the existent bands. The band pattern in a layer is also shown to be dependent on the properties and thickness of the adjacent layers, causing acceleration of deformation localization, reduction of the band spacing, and a periodic clustering of the bands of different orientation groups. The band patterns generated resemble the natural band networks. The increase of h imposed in the models appears thus as both an important and realistic property. Therefore the adjustment/calibration of the constitutive models based on the reproduction of natural deformation patterns in numerical simulations represents an important too

Étude du rôle des hétérogénéités structurales et de l'altération sur la déstabilisation des massifs rocheux par une approche couplée de modélisation physique et numérique

Les déformations et ruptures gravitaires sont des phénomènes communs à tout massif rocheux, et se produisant à différentes échelles. Il est largement accepté que ces processus sont influencés par différents facteurs parmi lesquels les hétérogénéités structurales préexistantes (hérités de l histoire géologique du massif) et les processus d altération physico-chimique sont de premier ordre. Cependant, l influence respective de ces paramètres reste floue. Pour avancer dans ce domaine, nous avons utilisé une approche couplée de modélisation physique et numérique en deux et trois dimensions, en se basant sur deux analogues de terrain bien documentés que sont le glissement de La Clapière (Alpes Maritimes, France) et les écroulements de Randa (canton du Valais, Suisse). Le premier objectif de cette thèse a été l amélioration de la technique de modélisation physique existante afin de pouvoir d une part introduire un grand nombre de discontinuités (fractures et failles) dans des modèles physiques, et d autre part afin de produire des modèles en trois dimensions présentant une topographie réaliste issue de modèles numériques de terrain. Un protocole expérimentale de modélisation numérique a ensuite été développé afin d étudier l effet de l altération physico-chimique sur la perte de stabilité des versants rocheux et ce, à grande échelle. Les résultats ont montré, au travers de l application de la méthode couplée de modélisation physique et numérique (en deux et trois dimensions) que les failles et fractures affectant un massif rocheux (et héritées de son histoire géologique) sont des structures influençant fortement la cinématique des déstabilisations gravitaires et notamment au travers des paramètres propres de ces structures (géométrie, persistance et densité). Il a également été montré que la topographie tridimensionnelle (de premier et de second ordre) ainsi que les propriétés mécaniques à grande échelle (incluant l altération) ont une grande influence sur le volume mobilisé lors des déstabilisations de versant.Gravitational slope failures are common phenomena involving all rock slopes, at various scales. It is widely accepted that different factors exert an influence on those gravitational process. Among these, structural heterogeneities (inherited from the geological story of the massif) and alteration/weathering process are of first order. However, the relative influence of those parameters is still poorly constraint. To tackle this question, a coupled physical and numerical modelling approach has been developed, considering both two and three dimensional models based on two natural examples : The La Clapière landslide (Alpes Maritimes, France) and the 1991 Randa rockslides (Valais, Suitzerland). The first goal of this PhD Thesis was to improve the existing physical modelling technique. On the one hand in order to introduce a wide/realistic number of discontinuities in physical models, and on the other hand to performed 3-D physical models based on realistic topographies (using DTM data). Then a numerical experimental process has been carried out in order to study the influence of large scale alteration on gravitational slope failure. Results have shown that faults and joints, affecting rock structures, have a strong influence on gravitational failure kinematics and especially through their geometry, persistence and density. It has also been shown that 3-D topography (of first and second order), and large scale mechanical properties (including alteration process) have a great influence on mobilized volume during slope destabilisation.NICE-BU Sciences (060882101) / SudocSudocFranceF