This contribution is concerned with the fundamental thermodynamic aspects of solid‐fluid phase transformations in stressed rocks, specifically in the context of pressure solution. We concentrate in particular on the formulation of a kinetic law governing the migration of stressed and curved solid‐fluid phase boundaries, an objective that is achieved by using the methods of the thermodynamics of irreversible processes. We then apply our result to the study of the geometrical evolution of a fluid‐filled cylindrical pore embedded in an isotropic, linear elastic solid that is subject to a hydrostatic remote stress, assuming that the interface kinetics controls the phase boundary migration and allowing for the effects of capillarity. On the basis of this investigation, we obtain an analytical expression for the pore's growth and show that phase equilibrium along the cylindrical solid‐fluid phase boundary is possible only when the pore pressure exceeds a critical value. The phase equilibrium is found to be kinetically unstable: when subjected to a small perturbation of its radius, the pore will either grow or shrink. The nature of this instability is further explored in the companion paper.
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.
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 ( ). 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.
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.
Abstract Two modes of extensional collapse in a cohesive and frictional wedge of arbitrary topography, finite extent, and resting on an inclined weak d collement are examined by analytical means. The first mode consists of the gravitational collapse by the action of a half‐graben, rooting on the d collement 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 d collement. 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.
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 α 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 α 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.
Gravity instabilities in offshore deltas often involve three structural domains in interaction by the weak detachment plane: an upslope extensional region, a transitional domain sliding seaward, and a downslope compressive region. We provide the fluid pressure conditions for the gravity instabilities due to the interaction of these three structural domains. For that purpose, we apply the kinematic approach of Limit Analysis which relies on the mechanical equilibrium and on the assumption that the onset of the instability is indeed triggered by the motion of the three domains if the Coulomb criterion is met on all slipping faults. The Limit Analysis predictions include the detachment activation length and the normal and thrust fault dips for any given topographic profile. The approach is validated by showing that our predictions match the experimental results on normal faulting triggered by air overpressure in sand analogues. For offshore wedges, the stabilizing effect of the frontal thrusting and of the transitional zone sliding requires large overpressures to reduce friction within the detachment and upslope sediment deposition to trigger the instability. As a consequence, the topographic slope is found to be several degrees larger than predicted with the Critical Coulomb Wedge (CCW) theory which does not account for the interaction of the three domains. The difference in predictions between the two theoretical approaches is important for length ratio less than 100, defined by the ratio of the detachment activated length to the downslope sediment thickness. Fitting our prototype to the offshore Niger Delta and estimating the above length ratio to be in the range of 30–70, it is found that, for cohesionless materials, the effective friction coefficient |$\mu ^{\prime }_{B}$| is less than 0.27 within the bulk material and |$\mu ^{\prime }_{D}$| is less than 0.017 in the detachment for the gravity instability to occur. These values are lower than those previously determined (|$\mu ^{\prime }_{B}=0.5{\rm -}0.9$|, |$\mu ^{\prime }_{D}=0.-0.2$|) by considering only the compressive domain and applying the CCW theory. These new values correspond to a pore-fluid pressure in the range of 80–90 per cent of the lithostatic pressure within the bulk material (Hubbert–Rubey fluid-pressure ratio 0.8–0.9), and in the range of 97–99 per cent of the lithostatic pressure within the detachment.
