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We model in 2-D the formation and development of half-graben faults above a low-angle normal detachment fault. The model, based on a “sequential limit analysis” accounting for mechanical equilibrium and energy dissipation, simulates the incremental deformation of a frictional, cohesive, and fluid-saturated rock wedge above the detachment. Two modes of deformation, gravitational collapse and tectonic collapse, are revealed which compare well with the results of the critical Coulomb wedge theory. We additionally show that the fault and the axial surface of the half-graben rotate as topographic subsidence increases. This progressive rotation makes some of the footwall material being sheared and entering into the hanging wall, creating a specific region called foot-to-hanging wall (FHW). The model allows introducing additional effects, such as weakening of the faults once they have slipped and sedimentation in their hanging wall. These processes are shown to control the size of the FHW region and the number of fault-bounded blocks it eventually contains. Fault weakening tends to make fault rotation more discontinuous and this results in the FHW zone containing multiple blocks of intact material separated by faults. By compensating the topographic subsidence of the half-graben, sedimentation tends to slow the fault rotation and this results in the reduction of the size of the FHW zone and of its number of fault-bounded blocks. We apply the new approach to reproduce the faults observed along a seismic line in the Southern Jeanne d'Arc Basin, Grand Banks, offshore Newfoundland. There, a single block exists in the hanging wall of the principal fault. The model explains well this situation provided that a slow sedimentation rate in the Lower Jurassic is proposed followed by an increasing rate over time as the main detachment fault was growing.

International audience; Estimating the stress in reservoirs and their surroundings prior to the production is a key issue for reservoir management planning. In this study, we propose an integrated inverse method to estimate such initial stress state. The 3D stress state is constructed with the displacement-based finite element method assuming linear isotropic elasticity and small perturbations in the current geometry of the geological structures. The Neumann boundary conditions are defined as piecewise linear functions of depth. The discontinuous functions are determined with the CMA-ES (Covariance Matrix Adaptation Evolution Strategy) optimization algorithm to fit wellbore stress data deduced from leak-off tests and breakouts. The disregard of the geological history and the simplified rheological assumptions mean that only the stress field, statically admissible and matching the wellbore data should be exploited. The spatial domain of validity of this statement is assessed by comparing the stress estimations for a synthetic folded structure of finite amplitude with a history constructed assuming a viscous response.

Two modes of extensional collapse in a cohesive and frictional wedge of arbitrary topography, finite extent, and resting on an inclined weak decollement are examined by analytical means. The first mode consists of the gravitational collapse by the action of a half-graben, rooting on the decollement and pushing seaward the frontal part of the wedge. The second mode results from the tectonics extension at the back wall with a similar half-graben kinematics and the landward sliding of the rear part of the wedge. The predictions of the maximum strength theorem, equivalent to the kinematic approach of limit analysis and based on these two collapse mechanisms, not only match exactly the solutions of the critical Coulomb wedge theory, once properly amended, but generalizes them in several aspects: wedge of finite size, composed of cohesive material and of arbitrary topography. This generalization is advantageous to progress in our understanding of many laboratory experiments and field cases. For example, it is claimed from analytical results validated by experiments that the stability transition for a cohesive, triangular wedge occurs with the activation of the maximum length of the decollement. It is shown that the details of the topography, for the particular example of the Mejillones peninsula (North Chile) is, however, responsible for the selection of a short length-scale, dynamic instability corresponding to a frontal gravitational instability. A reasonable amount of cohesion is sufficient for the pressures proposed in the literature to correspond to a stability transition and not with a dynamically unstable state.

Listric normal faults are widespread in the extension of the upper crust. Despite major advances in understanding the formation of listric faults through various experiments, the mechanical conditions that allow their formation are highly debated. In particular, Anderson's faulting theory predicts that newly formed normal faults are planar and are dipping at least at 45 ∘ , and in practice, at 60–65∘ for most rock types. Here, we develop Limit Analysis to investigate the formation of a listric fault at the onset of slip linking a deep detachment to the topographic surface. We find that listric normal faults can occur in the brittle upper crust without appealing to viscous or ductile behaviours, nor to flexural stresses. The disequilibrium-compaction fluid pressures, typically observed in many sedimentary basins, are essential for the formation of listric faults. The fluid pressure is hydrostatic down to the fluid-retention depth Z F R D and sustains a higher gradient below this depth. Parametric studies show that the surface slope is also essential for the formation of listric faults even with a gently dipping surface slope ( ≤ 4 ∘ ) , whereas a flat topographic surface leads to a simple Andersonian geometry at the onset of slip. The method is applied to two field examples in order to determine fluid overpressures that best match the fault shapes interpreted from seismic data. For the offshore Niger Delta, the simulated normal faults match the observed listric faults with a very shallow Z F R D = 0.5–0.75 km, and below Z F R D the fluid pressure has a lithostatic gradient, consistent with the observed fluid-pressure profiles. To reproduce a series of listric faults joining on one common low-angle detachment in the NW Gulf of Mexico, we demonstrate that a shallow Z F R D = 0.7–1.1 km is required, below which the fluid pressure increases to the lithostatic pressure on the detachment, in agreement with the fluid-pressure observations.

We analyze the mechanical properties needed to account for the large shallow slip during the 2011 Tohoku-Oki earthquake and the activation of landward normal faulting within the forearc. We show that the morphology and internal structure of the forearc follows closely the prediction of the critical Coulomb wedge in horizontal compression, implying a high internal pore pressure ratio (λ = 0.7 + 0.14/ – 0.48) and a low effective basal friction (μ^(eff)_b = 0.14 + 0.18/ – 0.04). We then show that the activation of the normal fault requires a lower effective basal friction beneath the outer wedge than beneath the inner wedge (μ_outer ≤ 0.015), possibly due to transient dynamic weakening associated to the seismic rupture. Forearc normal faults could be considered as evidence for very efficient dynamic weakening along the megathrust and typify megathrust with high tsunamigenic potential.

International audience; The objective is to capture the 3D spatial variation in the failure mode occurring in accretionary wedges and their analog experiments in the laboratory from the sole knowledge of the material strength and the structure geometry. The proposed methodology relies on the maximum strength theorem which is in- herited from the kinematic approach of the classical limit analysis. It selects the optimum virtual velocity field which minimizes the tectonic force. These velocity fields are constructed by interpolation thanks to the spatial discretization conducted with ten-noded tetra- hedra in 3D and six-noded triangles in 2D. The re- sulting, discrete optimization problem is first presented emphasizing the dual formalism found most appropri- ate in the presence of nonlinear strength criteria, such as the Drucker-Prager criterion used in all reported examples. The numerical scheme is first applied to a perfectly triangular 2D wedge. It is known that fail- ure occurs to the back for topographic slope smaller than and to the front for slope larger than a critical slope, defining subcritical and supercritical slope stabil- ity conditions, respectively. The failure mode is char- acterized by the activation of a ramp, its conjugate back thrust, and the partial or complete activation of the décollement. It is shown that the critical slope is captured precisely by the proposed numerical scheme, the ramp, and the back thrust corresponding to regions of localized virtual strain. The influence of the back- wall friction on this critical slope is explored. It is found that the failure mechanism reduces to a thrust rooting at the base of the back wall and the absence of back thrust, for small enough values of the friction angle. This influence is well explained by the Mohr construction and further validated with experimental results with sand, considered as an analog material. 3D applications of the same methodology are presented in a companion paper.

The motivation of the study is to demonstrate that geometrical constructions of fault‐related folds can be mechanically balanced according to the theory of limit analysis assuming that materials are cohesive and frictional. The advantage of the proposed methodology is to remain simple in terms of geometry and to introduce explicitly the various discontinuities such as the ramps which compose the geological structure. The main outcome of such mechanically balanced cross section construction is the availability of the stress field history which is fundamental to estimate the fracture pattern. These fracture predictions could be compared and benchmarked with data from outcrops. The proposed methodology is presented with the help of the field example of the Nerthe duplex, South‐Est France, with two horses, each well described with the classical fault‐bend fold geometry. The results highlight the role of erosion in the tectonic history of the folds and try to answer why early, inherited, fracture networks have not been reactivated during folding

(R~~ir~tl4 MUITII 1993) AESTRACI THE STABILITY OF il geological two-layer system composed of a frictional material layer of finite thickness. called the overburden, resting on a viscous half-space of lower density is investigated. The salient features of this study are a realistic description of the stiffness of the overburden and its state of (in sitzl) prestress. and the USC of the viscosity of the substratum to define a characteristic time for the stability analysis. A general variational formulation for the linearized. non-selfadjoint stability problem is prcsentcd, followed by asymptotic analyses for the cases of large and small perturbation wavelengths and by an analytical solution in the absence of gravity. Results obtained by a finite-element method are compared with the analytical and asymptotic predictions: they permit the detection of various modes of instability : interfaceand beam-type modes in the compressive range of deformation. and neck-type modes in the tensile ransc. It is found that the system’s stability is not only governed by geometry and density contrast. as expected from the conclusions of earlier studies on viscous and viscoelastic models, but is also scnsitivc to the state of in .viru stress. A complete parametric study reveals that the overburden material cohesion and workhardening properties have more influence on stability than the friction angle. Furthermore, it is found that critical stresses at neutral stability predicted by deformation theory. which is an appropriate model for studying the initiation of faulting in rocks. are smaller in magnitude than those obtained by the corresponding flow theory with a smooth yield surface. Implications of this work for the interpretation of various laboratory analogue model experiments pertaining to geological two-layer systems arc also discussed.

[1] The objective is to demonstrate that the equilibrium element method (EEM) provides the stress distribution in geometrical models of folds, relevant to fold-and-thrust belts as well as accretionary wedges. The core of the method, inherited from limit analysis, is the search for an optimum stress field that (1) is in equilibrium, (2) remains everywhere below or equal to the maximum strength of the rock, and (3) balances the largest possible applied tectonic force. This force and the associated stress field are interpreted as those at the onset of rupture. The method makes no appeal to the rock rheology nor to its elasticity, except for its maximum strength described here with the Coulomb criterion. The stress fields are discretized by elements covering the whole domain and allowing for discontinuities. The example chosen to illustrate the potential of the EEM and to validate our implementation is the thrusting of a rectangular sheet over a flat and weak decollement. The EEM reproduces the solution proposed by Hafner (1951) on the basis of linear elasticity, as long as the strength limit is not reached in the bulk of the domain. The EEM shows in addition that failure in the bulk prevents the activation of the decollement. The EEM is then applied to two fault-bend folds, with known ramp and flat decollement, with and without relief buildup. It is shown that the transition from the flat to the ramp hanging walls occurs through a narrow fan defining the back thrust. The predicted dip of this back thrust decreases with increase in the ramp friction angle, the relief buildup, as well as the ramp curvature. A sharp increase and then a sharp decrease in the magnitudes of the equivalent shear stress and of the mean stress are observed as one moves from the lower flat, through the back thrust up the ramp. If the ramp friction angle is too large, or the relief too important, the EEM predicts the initiation of a new thrust rooting at the back wall, instead of activating the proposed ramp. The application to detect the incipient thrust system within the toe of Nankai's accretionary wedge, southeast coast of Japan, is proposed in the auxiliary material.

International audience; The main objective is to determine the three stages of the life of a thrust in an accretionary wedge which are the onset of thrusting along its ramp, the development with the construction of the relief, and the arrest because of the onset of another thrusting event. A simple kinematics is proposed for the geometry of the developing thrust fold based on rigid regions separated by velocity discontinuities along which work is dissipated according to the Coulomb criterion. The evolution of the thrust fold satisfies mechanical equilibrium and is optimized at every time of the three stages to provide the least upper bound in tectonic force according to the maximum strength theorem. The development of the thrust or its arrest because of the initiation of another thrust is decided by selecting the event which leads to the least upper bound in tectonic force. The approach is first validated by proving that the critical slope angle a c for the classical triangular wedge is properly captured. It is shown that a perturbation, in the form of an extra relief in this perfectly triangular geometry, leads to the onset of thrusting with the ramp or the back thrust outcropping either at the back or to the front of the perturbation, respectively, for a range of slope dip close to the critical angle a c. The study of normal thrust sequences (from the rear to the front in the wedge toe) reveals that weakening of the ramp, accounted for by changing its friction angle from an initial to a smaller final value, is necessary for each thrust to have a finite life span. This life span is longer with a larger relief buildup for more pronounced weakening. Decreasing the décollement friction angle results in an increase in the number of thrusts in the sequence, each thrust creating milder relief. The normal sequence is ended with the first out of sequence thrust which occurs earlier for smaller weakening over the ramp. The proposed methodology is partly used to construct an inverse method proposed to assess the likeliness for the transfer of activity from the active to the incipient thrust in a section of Nankai's accretionary wedge. The inverse method provides the initial friction angle over the incipient ramp and the final friction angle over the fully active ramp, from the geometry of the corresponding thrusts, and the topography. It is shown that the friction angle over the incipient ramp is most likely to be larger then the one over the active ramp, justifying a key hypothesis needed to predict discrete sequences of thrusting.

SUMMARY The very low water content of the granulitic unit of Holsnoy, in the Bergen Arcs, Norway, caused its partial metastable preservation throughout Caledonian burial end exhumation, leading to the observed mixture of completely eclogitized and uneclogitized rocks. The eclogitization of the granulite-facies protolith led to a density increase ∼10%, but also to a large rheological weakening that resulted in the localization of all deep ductile deformation in the eclogite fraction. We address the consequences on subduction dynamics of the concomitant evolution of large-scale density and rheology during progressive eclogitization of crust by comparing the behaviour of buried crust with various properties in the channel-flow model. Large-scale buoyancy and density are integrated in a single adimensional parameter, the ‘exhumation number’ α, which describes the capacity of the crust to exhume. For a crust whose eclogitization causes a very large viscosity decrease (‘burial resistant’ end-member), α goes through a maximum in the partially eclogitized zone, that is, there is a given proportion of eclogite for which the crust is strongly weakened but still significantly lighter than surrounding mantle. For this partially eclogitized crust with α max, the maximum possible downward flow is very low, this zone acts as a bottleneck and all incoming crust in excess is forced backwards and starts exhuming. This return flow zone is bounded downwards in the partially eclogitized zone by α max, while its upper limit propagates upwards at a constant rate. The curve α(eclogite fraction) controls the maximum proportion of eclogite of the crust that can be exhumed. We also demonstrate that large exhumation rates reached by certain UHP units are incompatible with any stationary flow regime, whatever the nature of subducted crust. The additional presence of a weak layer on top of the channel favours burial for narrow channels and exhumation for large ones, but does not qualitatively change the dynamics of the subduction channel. This study shows that deep crustal circulation in subduction zones and exhumation from large depths are controlled by the evolution of large-scale crustal properties with progressive eclogitization.

The northwestern part of Holsnøy island, in the Bergen Arcs, Norway, consists of a granulite-facies protolith partially transformed at depth in eclogite (700 °C, > 19 kbars) and amphibolite (650 °C, 8-10 kbars) facies during the Caledonian orogenesis. Eclogitized zones are mainly planar objects (fractures with parallel reaction bands and cm-to-100 m-scale shear zones). Eclogitic zones are distributed in two sets of orientations and the associated deformation can be described as 'bookshelf tectonics'. The major shear zones strike around N120 and dip to the North, and show consistent top-to-the-NE shear sense throughout the area. In the large-scale kinematic frame of Caledonian NW-dipping slab, eclogitic shear zones are interpreted as the way to detach crustal units from the subducting slab and to prevent their further sinking. As the retrograde amphibolitic deformation pattern is similar to the eclogitic one, the detached crustal units started their way up along these eclogitic shear zones. Radiometric ages of eclogitic and amphibolitic metamorphism and their comparison with the chronology of Caledonian orogenesis show that the deformation recorded on Holsnøy occurred in a convergent context. The mechanism we propose can thus account for the first steps of exhumation during collision.

Direct observation of peak pressure deformation in exhumed subduction channels is difficult because little evidence of this deformation survives later syn-exhumation deformation. Most ultrahigh-pressure parageneses are found in continental derived metamorphic rocks making continental subduction the best context to observe peak pressure deformation. Whereas many studies have enlightened the main driving parameters of exhumation such as buoyancy forces, low viscosity in the subduction channel, overburden removal by erosion and normal faulting, a basic question is seldom considered: why is a tectonic unit disconnected from the descending lithosphere and why does it start its way towards the surface? This event, seminal to exhumation processes, must involve some deformation and decoupling of the exhumed slice from the descending slab at peak pressure conditions or close to it. Our field observations in the Bergen arc show that Caledonian eclogitization and later amphibolitization of a granulitic terrane was achieved with a consistent component of simple shear compatible with the sense of the Caledonian subduction. Thus, the sequence of deformation preserved in the Bergen Arc documents the decoupling of subducted crustal material from the descending slab at the onset of exhumation. This observation suggests that deformation in the subduction channel is largely controlled by kinematic boundary conditions, i.e. underthrusting of the subducting slab. In this context of simple shear, metamorphic reactions assisted by fracturating, fluid infiltration and ductile deformation lower the resistance of rocks and allow the localisation of shear zones and the decoupling of buoyant tectonic units from the subducting slab. These tectonic units can then be incorporated into the channel circulation and start their upward travel.

Present address : Institut des Sciences de la Terre d'Orléans UMR 7327, Université d'Orléans, CNRS/INSU, BGRM; International audience; Low-angle midcrustal ductile shear zones and the related microseismic activity recorded below regions of active extension are seen here as two consequences of strain localization. The feldspar-to-mica reaction which occurs once feldspar grains are fractured is the destabilizing mechanism selected to explain the strain localization. The model problem considered to substantiate these claims is solved by numerical means and combines the simple shear due to the rigid gliding of the upper crust (at the velocity of V s ) and the stretch resulting from the extension of the whole crust (at the velocity V e ). The rheological model accounts for dislocation creep of quartz, feldspar, and mica, the feldspar-to-mica reaction, and its prerequisite, which is the feldspar fracturing detected by the Mohr-Coulomb criterion. The one-dimensional (1-D) solution, which constrains shear bands to be horizontal, shows the depth partitioning in deformation mode between the simple shear of the low-viscosity deep crust and the stretching of the highly viscous midcrust. Strain localization occurs during rapid increase of the shearing velocity V s , corresponding to low values of the velocity ratio V e /V s . The 2-D solution (for V e /V s = 10−3) reveals the development of a periodic system of extensional shear bands, dipping at 30° toward the shearing direction at a depth of 12 to 14 km. Shear bands are formed after less than half a million years at the base of the reaction zone defined by the region where feldspar-to-mica reaction is completed. Shear bands do not propagate to greater depths because the pressure prevents the feldspar from fracturing and thus the reaction to occur. The periodic system of shear bands defines a midcrustal flat weakened zone within which the equivalent shear stress is enhanced by at least a factor of three at the shear band tips. Brittle fracture could thus occur within the midcrustal flat weakened zone, explaining therefore the microseismicity monitored at these depths in regions of active extension.

International audience; This chapter discusses sandstone compaction by intergranular pressure solution and presents the theoretical means for exploring problems of stress-sensitive dissolution and coupled macroscopic deformation and transport. The simple one-dimensional compaction model discussed in this chapter represents only a first exploratory study of the behavior of the proposed model. Despite carrying out a numerical study for only one-layer thickness and a single set of initial and boundary conditions, the results obtained for this case have yielded some basic insights into the behavior of the compaction model that can also point the way for future studies. When precipitation was inhibited, the exceedingly slow diffusive transport over 5,000 m of layer thickness was found to lead to the build-up of high (possibly unrealistic) supersaturations, approximately 1.5 times the equilibrium concentration, which slowed down intergranular dissolution to extremely low rates. However, because this low-rate limit in compaction behavior is likely to be attained only in the absence of any significant advective influx of undersaturated fluid through the base of the layer, the role of the prevailing hydrological regime in compacting sedimentary layers is immediately apparent. This observation suggests that in a sedimentary column that is open only at its top, macroscopic advection will be activated only if there exist local sinks—the free faces—on the grain scale, where the material at a nearby grain boundary can be deposited.

[1] Back thrusts and hinges are two types of transition between rigid sections of hanging walls observed in fold-and-thrust belts. Back thrusts are typical of frictional and homogeneous solids and hinges of creeping and layered materials. Our objective is to study the orientation of these transitions for the special case of a lower flat-ramp transition in a fault-bend fold with the following general two-step methodology. In the first step, the forces acting on the transition are determined using equilibrium of each rigid section. In the second step, the optimal dip of the transition is obtained by minimizing the total dissipation of the structure. The three sources of dissipation, of comparable magnitude, are at the transition, on the flat, and on the ramp. For frictional material flows, the back thrusts are velocity discontinuities with optimal dips always less than half the complementary ramp angle, leading to hanging wall thickening. The optimal dip agrees well with the results of physical analogue and numerical experiments. For creeping and layered materials, it is shown that a destabilizing deformation mechanism, selected to be flexural slip, is necessary for the strain to localize and the existence of hinges to be justified. Activation of flexural slip reduces dissipation at the transition and affects the optimal transition dip. The two-step methodology proposed here could be seen as a first attempt in producing mechanically balanced cross sections accounting for material rheology. This approach should complement the now classical kinematic models of folding.

[1] Low-angle extensional shear zones, which often characterize the brittle–ductile transition of the continental crust, are seen here to result from strain localization. The potentially destabilizing deformation mechanism is assumed to be the progressive transformation of fractured coarse feldspar grains into white mica as observed in the East Tenda Shear Zone, Alpine Corsica. The coupling between microfracturing and feldspar-to-mica reaction is coeval with strain localization that occurred in that field case at a depth close to 15 km. This reaction is proposed as the main destabilizing factor responsible for the onset of localization, with feldspar having a stationary dislocation creep flow stress larger than mica. To test this hypothesis, a rheological model is constructed based on the field observations for a mixture of three phases—mica, quartz and feldspar—deforming at a common strain rate. The phase concentrations change with time according to the feldspar-to-mica reaction, which takes place only if feldspar grains are fractured, a condition detected with the Mohr–Coulomb criterion. The tendency for the strain to localize is assessed by numerical means for the structure composed of an upper crust gliding rigidly over the lower crust, which sustains an overall simple shear. The onset of strain localization is defined by an increase of at least two orders of magnitude in strain rate over part of the lower crust. The upper crust gliding velocity has to be increased by at least a factor of 5 for localization to occur. The time lapse for this velocity change determines the depth of the shear zone (15–17 km). The kinetics of the metamorphic reaction and the final amount of white mica control its width (1–4 km). The time of the shear zone formation is less than half a million years.

The model problem proposed to study the buckling of stratified geological layers consists of a linearly elastic plate, capable of accommodating finite rotations, resting over an inviscid and buoyant fluid. The Lyapunov–Schmidt–Koiter decomposition is applied to construct the bifurcated equilibrium solutions. The asymptotic analysis of the post-buckling reveals a decrease in the magnitude of the lateral compressive force during an overall shortening of the stratified structure. Buckling and post-buckling are not influenced by the presence of a vertical stress gradient in the elastic plate.

The fine structural motifs of sialic acids, a frequent terminal monosaccharide of glycans, seem to contain essential biological properties. To identify such subtle structural differences, a reliable method was developed for the qualitative and quantitative identification of sialic acids present in different tissues and fluids. This method involved, after liberation of sialic acids by mild acid hydrolysis, their methyl esterification using diazomethane in the presence of methanol and the formation of volatile derivatives using heptafluorobutyric anhydride. The derivatives were analyzed by gas chromatography coupled to mass spectrometry in the electron impact mode. This technique allowed the separation and identification of a large variety of sialic acids, including different O-acylated forms of N-acetyl and N-glycolyl neuraminic acids and of 3-deoxy-D-glycero-D-galacto-nonulosonic acid (Kdn). This method allowed also identifying 8-O-methylated and 8-O-sulfated derivatives, de-N-acetylated neuraminic acid, and 1,7-sialic acid lactones. Compounds present in very complex mixtures could be identified through their fragmentation patterns. Because of the stability of the heptafluorobutyrate derivatives, this method presents important improvements compared to the previous techniques, because it can be frequently applied on very small amounts of crude samples. This methodology will support progress in the field of the biology of sialic acids.

The overall compaction of porous rocks due to intergranular pressure solution (IPS) results from the dissolution of minerals within contact regions and the diffusive transport through the grain boundary of the dissolved species towards the fluid-filled pore space. The grain boundary structure can be imagined to be composed of dry contact zones, thin fluid films and fluid-filled cavities. The connectiveness and tortuosity of this structure determine the effective diffusivity of grain contacts and thus the potential of porous rock to compact by the action of IPS. The evolution in time of the grain-boundary structure, and thus of the effective diffusivity, is discussed here with the help of two 2D initial- and boundary-value problems which are solved by analytical and numerical means. The evolution of the solid–fluid interfaces within the grain boundary is governed by a phase transformation between the non-hydrostatically stressed elastic solid and the trapped fluid assumed in mechanical equilibrium. The characteristic time is provided by a linear kinetic law. The evolution of the structure away from a state of thermodynamic equilibrium during a loading normal to the grain boundary is found to occur in two steps. The first one consists of a diffuse morphology evolution in time and results in an enhancement of any initial stress concentration. The second step is characterized by a rapid and localized dissolution in the region of stress concentration. The latency period prior to localization is governed by the magnitude of the non-hydrostatic remote stress as well as the microstructural geometric factor responsible for the initial stress concentration at the solid–fluid interface. The localized dissolution is shown to provide a mechanism for the fluid to penetrate a previously dry contact region by marginal dissolution and thus to create a fluid film. However, the newly formed thin fluid layer is found to be unstable pointing to a possible repeated reorganization or dynamic evolution of the grain boundary internal structure during the action of IPS.

Localized shear zones along low-angle normal faults have been identified in regions of extension at the brittle–ductile transition of the continental crust. The possibility of the strain localizing at a depth of 10 km is interpreted here as a consequence of an increase in the equivalent shear stress applied to the flow of the lower crust. This enhancement of the flow stress is seen as a prerequisite for the triggering of brittle deformation mechanisms leading to strain localization. The lower crust rheology used to examine this stress increase is strain-rate, temperature and grain-size dependent, due to the coupling of dislocation and diffusion creep. The model structure proposed consists of a top layer, the upper crust, gliding rigidly above a bottom layer, the lower crust, which deforms in simple shear. During a short time interval (1400 years), the equivalent shear stress is found to increase by a factor of up to 3 (67 MPa for anorthite and 17 MPa for quartz). For anorthite, this stress could explain the activation of a Mohr-Coulomb failure with a friction coefficient of 0.2, which is reasonable at the depth of 10 km. Dislocation creep is activated during a rapid change in the prescribed velocity, whereas diffusion creep dominates if the velocity is held constant, highlighting the importance of grain-size sensitivity for lower crustal rheology.

International audience; This article is concerned with the development and application of a simple continuum theory for rocks that may contain both randomly as well as preferentially oriented plane discontinuity surfaces. The theory stipulates that displacement discontinuities are independently activated on these surfaces as soon as an appropriate yield criterion is fulfilled; these displacement jumps account for the irreversible, ‘plastic’ part of the bulk deformation. In stress space, the critical conditions for the activation of discontinuous slip or opening displacements define an overall yield envelope that could be initially anisotropic, reflecting for example a weakness of certain orientations due to pre-existing joint sets. For the yield conditions studied in this paper, essentially a Coulomb-type friction law and a simple fracture opening condition, the inferred stress-strain response under typical triaxial loading conditions reveals the sensitivity of the two discontinuous deformation modes to the confining pressure. The incipient growth of a geological fold in such a material is modelled as a problem of plate bending. The slip- and opening-modes of deformation are found to be activated typically in the fold intrados and extrados, respectively. Under certain conditions, both modes will be activated simultaneously at the same locality and contribute to the total deformation. Field observations on a well exposed sandstone anticline are reported here, which support this conclusion. The present plasticity model for discontinua can clearly be explored in more detail for realistic distributions of faults and joints taken from field observations. It could also be improved in various ways in its description of the underlying deformation mechanisms. Apart from its interest as a mechanical constitutive model, it can also serve as a point of departure for studies of stress-sensitive, anisotropic permeability distributions in fractured formations.

This study deals with the stability of a stratified structure composed of a cohesive and frictional overburden, a viscous substratum, and a rigid basement. That structure should be seen as a prototype for various salt tectonics and lithospheric plates stability analyses. The destabilizing factors are the density contrast, the tectonic compressive stress, and the possible erosion and deposition at the top surface. The overburden stiffness, a nonlinear function of in situ stress, has a stabilizing role. Two solutions are extracted from the variational formulation of the stability problem previously proposed [Leroy and Triantafyllidis, 1996]: the first is analytical and is obtained by disregarding gravity, and the second is numerical and is based on the finite element method. The latter is used to assess the validity of the previously presented asymptotic solution. It is shown that the asymptotic solution is accurate even for values of the small parameter, defined as the perturbation wavenumber times the overburden thickness, as large as 0.4. Furthermore, the possibility for the cohesive material in the overburden to accommodate part of the deformation by slip along a population of small pervasive faults is accounted for by the introduction of a deformation theory of plasticity. Stability predictions based on this theory indicate that structural modes, such as folding, and localized faulting modes are triggered for similar stress magnitudes. The parametric study presented includes the previously undetected influences of the stress gradient with depth and of the work hardening properties of the competent overburden. The role of erosion and deposition in destabilizing shallow overburdens, regardless of the magnitude of the tectonic stress, is also established. The stability predictions are then applied to a folded section through the Campos basin, offshore Brazil, revealing that the deformation theory of plasticity is necessary to explain the buckling that occurred during the Albian.

The influence of the mixed mechanical boundary condition, defined by a linear relation between velocity at the boundary and stress, on the non-linear stability of steady states and on the localization of the deformation is investigated by numerical means. This mixed boundary condition is known to prevail during a torsional Kolsky bar test and depends on the geometry of the incident bar and of the specimen. It is shown that the coefficient which enters the mixed condition governs the evolution of the flow from a perturbed, unstable steady state towards a stable attractor. The same coefficient is found to have little influence on the nominal strain at initiation of the localization which appears to be governed by the total energy dissipated. However, the rate at which the stress drops during the development of the localization is affected by the mixed boundary condition.

A method is proposed which aims at enhancing the performance of general classes of elements in problems involving strain localization. The method exploits information concerning the process of localization which is readily available at the element level. A bifurcation analysis is used to determine the geometry of the localized deformation modes. When the onset of localization is detected, suitably defined shape functions are added to the element interpolation which closely reproduce the localized modes. The extra degrees of freedom representing the amplitudes of these modes are eliminated by static condensation. The proposed methodology can be applied to 2-D and 3-D problems involving arbitrary rate-independent material behavior. Numerical examples demonstrate the ability of the method to resolve the geometry of localized failure modes to the highest resolution allowed by the mesh.

The first objective of this thesis is to contribute to the development of quantitative tools for an objective interpretation, based on mechanical equilibrium and material strength, of kink-folds and fault-related folds which are potential oil reservoirs. The second objective is to improve the prediction of fracture distributions in layered sequenceswhich control the permeability. Experiments and analytical results are presented on the onset, the development and the arrest of kink-folds and fault-propagation folds. The experiments, with a sequence of paraffin layers under compression, show the relation between the fracture distribution, the formation of damaged hinges and the development of kink-folds. The analytical results are obtained by combining simple geometrical rules with the application of the maximum strength theorem (limit analysis). It is shown how compaction bands, reverse faults and kinks are competing at the onset of a kink fold, depending on the initial dip of the layered structure and the burial depth. The same methodology is applied to the development of the fault-propagation fold which is shown to be potentially interrupted by thrusting, depending on the frictional properties of the various hinges. The second part presents experimental, numerical and analytical results on the extension of a block, composed of an analogue material (compacted gypsum), resulting from the stretching of its foundation. A linear relation between the bed thickness and the fracture spacing is observed at saturation. Saturation is linked to the delamination of the interface between the block and its foundation. The finite-elements calculations, based on plasticity theory, to produce strain localisation, confirms the competition between the delamination and the fracture process. The analytical approach, based again on the maximum strength theorem, provides a simple criterion to decide on the dominant mode of failure as well as a new relation for the fracture spacing. The last part of this thesis presents a new experimental device to create bending fractures. It is shown that layer thickness does not influence the fracture spacing under bending. To the contrary, this influence is remarkable if a combination of bending and stretching is applied., Le premier but de cette thèse est de développer une méthode objective pour l'interprétation de profils sismiques et des structures qui sont susceptibles d'être des réservoirs pétroliers. Le deuxième but est l'amélioration de la prévision des fractures dans les roches laminées, qui déterminent la perméabilité. Les expériences et les résultats analytiques montrent l'initiation, l'évolution et l'arrêt d'un kink et d'un pli de propagation de rampe (PPR). Les expériences avec paraffine multicouches établissent la relation entre la distribution des fractures, la formation des charnières endommagées et l'évolution d'un pli de kink. Les résultats analytiques se fondent sur des règles géométriques combinées à l'approche externe de l'analyse limite. Les bandes de compaction, les failles et les plis sont en concurrence à l'initiation du kink. Le mode dominant dépend de l'inclinaison des couches et de la profondeur d'enfouissement de la structure. Les résultats sont présentés dans une carte de mécanismes dominant dans l'espace des enfouissements et l'inclinaison des couches. La même approche est utilisée pour étudier le PPR dont l' évolution se termine à cause de l'initiation d'une faille. Parmi tous les paramètres, c'est l'angle de friction dans les charnières qui contrôle cette transition. La deuxième partie de cette thèse présente les résultats expérimentaux, numériques et analytiques sur les fractures. Une couche composée de gypse compacté, est en extension par sa base et se fracture en mode I. La relation entre la distance entre les fractures et l'épaisseur d'une couche est linéaire, quand la structure est saturée en fractures. Cette saturation est liée à un décollement de la base de la couche. La méthode des éléments finis et la théorie de la plasticité permettent de valider ces résultats. L'approche analytique (analyse limite) a donné un critère simple pour prédire si un décollement ou une fracture va se former. Un nouveau critère pour la distance entre deux fractures est proposé. Dans la dernière partie de cette thèse, un nouveau dispositif expérimental est présenté afin d'étudier les fractures en flexion. L'épaisseur d'une couche n'influence pas la distance entre les fractures si il y a seulement une flexure. Cette influence est par contre grande si la couche est cintrée et en extension.