Brittle-ductile coupling : Role of ductile viscosity on brittle fracturing

International audienceLocalized or distributed deformations in continental lithosphere are supposed to be triggered by rheological contrasts, and particularly by brittle-ductile coupling. A plane-strain 2D finite-element model is used to investigate the mechanical role of a ductile layer in defining the transition from localized to distributed fracturing in a brittle layer. The coupling is performed through the shortening of a Von Mises elasto-visco-plastic layer rimed by two ductile layers. By increasing the viscosity of the ductile layers by only one order of magnitude, the fracturing mode in the brittle layer evolves from localized (few faults) to distributed (numerous faults), defining a viscosity-dependent fracturing mode. This brittle-ductile coupling can be explained by the viscous resistance of the ductile layer to fault motion, which limits the maximum displacement rate along any fault connected to the ductile interface. An increase of the viscosity will thus make necessary new faults nucleation to accommodate the boundary shortening rate

Localisation de la déformation et fracturation associée. Etude expérimentale et numérique sur des analogues de la lithosphère continentale

Thèse publiée dans la collection des Mémoires de Géosciences Rennes (ISSN 1240-1498) : Mémoire n° 117 (ISBN 2-914375-33-6)The study of localisation of deformation in brittle/ductile media aims to understand from a mechanical point of view the development of multi-scales fracture patterns, which are characteristic of intra-continental deformation. Experimental modelling of collision at lithospheric scale allows to reproduce and follow with time the fracturation process. The obtained fault patterns have statistical properties similar to the ones of natural fault patterns. Detailed analysis of deformation and fracture organisation provides meaningful information on the system evolution and on the localisation of deformation at large scale. The deformation in an analogue of continental lithosphere is characterized by three factors: the brittle/ductile coupling G, the Argand number Ar and the boundary conditions. G, bound to brittle/ductile coupling, controls the localisation of deformation. Ar characterizes the role of the gravity forces on the expression of the modes of deformation (compression, strike-slip or extension). The boundary conditions influence the spatial distribution of the deformation modes. Through analysis of the deformation fields, the localisation process is divided in two stages: the pre-localisation stage and the post-localisation stage. The pre-localisation stage corresponds to an increase with time of the average deformation according to a power law, which exponent is independent of the rheology of the media. This stage is characterized by a progressive organisation of the deformation, with an increase of the correlation length. It takes place on a time period that is apparently independent of the rheology and the deformation mode. It ends in the development of the fault pattern. The post-localisation stage is characterized by the organisation of deformation according to scaling laws, which fractal dimension depends on the rheology of the media. Despite the stabilisation of the average deformation and of the correlation length (equal to the system size), the system is still dynamic, as proven by the fluctuations of the active faults mass or of the post-localisation correlation dimension. Since the mechanics of the brittle/ductile coupling cannot be explained by the experiments, numerical simulations have been developed. The role of the ductile media viscosity on the localized or distributed mode of fracturation is particularly studied. Results notably shows that a viscosity variation of one order magnitude is sufficient to observe a transition between the localised fracturing mode and the distributed one.L'étude de la localisation de la déformation dans un milieu fragile/ductile s'inscrit dans la compréhension mécanique du développement des réseaux de fractures multi-échelles, caractéristiques de la déformation intra-continentale. Une approche expérimentale, simulant un contexte de collision à l'échelle lithosphérique, a été mise en oeuvre. Elle permet de décrire et de suivre dans le temps un mode de rupture, dans lequel les réseaux de failles obtenus présentent des propriétés statistiques similaires à celles des réseaux naturels. Une analyse détaillée de l'organisation des hétérogénéités et des déformations dans ces expériences permet d'obtenir des informations importantes sur l'évolution de ces systèmes et sur la localisation de la déformation à grande échelle. La déformation d'un analogue de la lithosphère continentale peut ainsi être caractérisée par trois facteurs : le paramètre fragile/ductile G, le nombre d'Argand Ar et les conditions aux limites. G, lié au couplage fragile/ductile, contrôle le degré de localisation de la déformation. Ar caractérise le rôle des forces gravitaires sur l'expression du mode de déformation dominant (compressif, décrochant ou extensif). Les conditions aux limites influent sur la répartition spatiale de ces modes de déformation. A partir de l'analyse des champs de déformation, le processus de localisation est découpé en deux phases : la phase pré-localisation et la phase post-localisation. La phase pré-localisation se traduit par une augmentation de la déformation moyenne avec le temps selon une loi de puissance, dont l'exposant est indépendant de la rhéologie du milieu. Elle se caractérise par une organisation progressive des déformations, qui s'accompagne d'une augmentation de la longueur de corrélation. Cette phase pré-localisation semble se faire sur une période de temps indépendante de la rhéologie du milieu comme du mode de déformation. Elle aboutit au développement du réseau de failles. La phase post-localisation est caractérisée par une organisation des déformations selon des lois d'échelles, dont la dimension fractale est fonction de la rhéologie du milieu. Bien que la déformation moyenne et la longueur de corrélation (de la taille du système) soient stabilisées, le système reste dynamique, comme en témoignent les fluctuations observées au niveau de la masse des failles actives ou de la dimension de corrélation. Dans la mesure où la mécanique du couplage fragile/ductile ne peut être expliquée à partir des expériences, celle-ci est abordée au travers de simulations numériques. Le rôle de la viscosité du milieu ductile sur le caractère localisé ou diffus de la fracturation dans le milieu fragile y est plus particulièrement étudié. Les résultats montrent notamment qu'une variation d'un ordre de grandeur de la viscosité permet de passer d'un mode de fracturation diffus à localisé

Scaling laws during localization of brittle/ductile systems

1 p.Complex multiscale fracture patterns are found to develop during fracturing process, as a consequence of strength and heterogeneities enhanced by fracture-to-fracture interactions. This spatial complexity was found to be ubiquous in geological environments. Statistical analysis on these systems demonstrates that it can be quantified, at the 1st-order, by both basic scaling laws: a fractal correlation between fault positions, and a power-law distribution of fault lengths. The scaling exponents are varying according to the nature of the fracturing process (jointing or faulting), and/or to the stress context (body forces vs. tectonic forces; compression vs. extension vs. strike-slip). The rationale of these basic observations still remains an issue. Our view on these basic processes is mainly based on some sandbox experiments where the deformation is applied to a thin brittle-ductile plate whose strength is of the order of gravity forces. The work is also motivated by having a better understanding of lithosphere deformation in continental collision. At the macroscopic level, deformation results in a large-scale localization whose deformation regime (compressional, wrenching or extensional) depends on the balance between gravity forces and layer strengths. At finer level, large-scale shear bands are actually made up of a series of faults - actually shear bands that develop in the sand layer with geometrical properties similar to tectonic faults -, whose geometrical complexity is primarily dependent on the brittle-to ductile strength ratio . is a function of the compression velocity, silicone viscosity, layer thicknesses and densities was found to well quantify the main transition between a pure ductile regime where no large fault develops, to a pure-brittle regime where localization takes place in a few very large faults. In between (0.5< <10), faults organize in a complex multi-scale pattern that progressively leads to large-scale localization in two main conjugate shear bands densely fractured. A fine analysis of the deformation field highlights the very nature of the localization process. Thanks to high-resolution measures of displacement, a scaling analysis of the average deformation intensity was performed to highlight the coalescence of locally deformed zone into a large-scale structure. This analysis reveals two additional modes of localization in the intermediate brittle regime (0.5< <10), which differs in the scaling of the mean deformation intensity at small scales: a "ductile-but-localizing" regime where the deformation intensity becomes scale-independent at small scales, and a "brittle" regime where the deformation intensity increases continuously when decreasing scale. The latter regime directly addresses the issue of the homogenization of local heterogeneities since the basic notion of mean deformation is not univocally defined. In the former regime, the viscosity of the underlying ductile layer introduces a correlation length scale below which strain heterogeneities are smoothed. Localization occurs from structures whose size is large enough to become insensitive to viscosity effects. The large-scale localization rate is a function of . Finally we discuss the relationship between the characteristics of the fault patterns (length, density) as a function of , and of the strain field

Brittle-ductile coupling : Role of ductile viscosity in the pattern of brittle fracturing

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Mechanics of the transition from localized to distributed fracturing in layered brittle­ductile systems

International audienceThe mechanical coupling between brittle and ductile layers in the continental lithosphere produces rheological contrasts, which are supposed to trigger localized or distributed mode of faulting. A plane-strain 2D finite-element model is used to highlight the mechanical role of the brittle­ductile coupling in defining the patterns of fracturing. The coupling is performed through the shortening of a Von Mises elastoviscoplastic layer rimmed by two ductile layers behaving as Newtonian incompressible fluids. By varying the viscosity of the ductile layers or the amount of softening in the brittle layer, the fracturing mode evolves from localized to distributed. The mechanics of brittle­ductile coupling is explained by the limitation of the fault displacement rate imposed by both brittle and ductile rheologies. On these bases, an analytical approach is presented in order to estimate the maximum velocity along each fault permitted by both brittle and ductile media. This velocity is then compared to the velocity required by the boundary shortening rate. If the velocity in the fault is not large enough, the development of new faults is necessary. From this analysis, we define four fracturing modes in a brittle­ductile media: the localized mode with the onset of a few large faults, the distributed mode with very dense fault patterns, and finally, the ductile-control mode and the brittle-control mode, where the number of faults increases with an increase in the ductile viscosity and a decrease in the brittle softening respectivel

Inversion of calcite twin data for paleostress orientations and magnitudes: A new technique tested and calibrated on numerically-generated and natural data

The inversion of calcite twin data is a powerful tool to reconstruct paleostresses sustained by carbonate rocks during their geological history. Following Etchecopar's (1984) pioneering work, this study presents a new technique for the inversion of calcite twin data that reconstructs the 5 parameters of the deviatoric stress tensors from both monophase and polyphase twin datasets. The uncertainties in the parameters of the stress tensors reconstructed by this new technique are evaluated on numerically-generated datasets. The technique not only reliably defines the 5 parameters of the deviatoric stress tensor, but also reliably separates very close superimposed stress tensors (30° of difference in maximum principal stress orientation or switch between σ3 and σ2 axes). The technique is further shown to be robust to sampling bias and to slight variability in the critical resolved shear stress. Due to our still incomplete knowledge of the evolution of the critical resolved shear stress with grain size, our results show that it is recommended to analyze twin data subsets of homogeneous grain size to minimize possible errors, mainly those concerning differential stress values. The methodological uncertainty in principal stress orientations is about ± 10°; it is about ± 0.1 for the stress ratio. For differential stresses, the uncertainty is lower than ± 30%. Applying the technique to vein samples within Mesozoic limestones from the Monte Nero anticline (northern Apennines, Italy) demonstrates its ability to reliably detect and separate tectonically significant paleostress orientations and magnitudes from naturally deformed polyphase samples, hence to fingerprint the regional paleostresses of interest in tectonic studies

Is EBSD a more efficient tool than universal stage to collect calcite twin data as used in calcite twin inversion for stress?

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