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[1] During earthquakes, frictional heating on the fault plane induces a temperature rise and thus a pore pressure rise, which is known as thermal pressurization (TP). Coseismic mineral dehydrations may occur because of this temperature increase and are included within the TP framework. Dehydrations are modeled as a source term for pore pressure because of the total volume change and as a sink term for temperature because they are endothermic. The reaction occurs within the slipping zone when a threshold temperature T s is reached. Dehydration reaction kinetic is modeled using a first-order reaction rate. Using energy and fluid mass conservation, we derive analytically the equations of evolution of pore pressure, temperature, and reaction extent in the undrained, adiabatic case using a constant reaction rate. We investigate the values of the kinetic rate constant required to produce a significant effect, which are much higher than laboratory data reported in the literature on clay, serpentine, and phyllosilicate dehydration. We show, however, that such high values can be reached if the temperature dependency of the rate constant is taken into account. Next, we include fluid and heat transport and use an Arrhenius law to calculate the rate constant as a function of temperature. The subsequent set of differential equations is then solved numerically. The main effect of dehydration reactions is an increase of pore pressure and a stabilization of the temperature during slip. We explore a wide range of parameters in order to determine in which cases dehydration can be considered as a nonnegligible process. For high-permeability rocks (>10 −18 m 2 ) and when the amount of water that can be released is of the order of 10%, dehydration is an important mechanism as it delays the onset of melting, which would normally occur even within the TP framework. If the onset temperature is low compared to the initial temperature T 0 (T s − T 0 ] 150°C), overpressure can occur. If the reactions are highly endothermic and if their kinetic is fast enough, frictional melting would not occur unless the dehydration reactions are completed within the slipping zone.

Elastic wave velocity measurements in the laboratory are used to assess the evolution of the microstructure of shales under triaxial stresses, which are representative of in situ conditions. Microstructural parameters such as crack aperture are of primary importance when permeability is a concern. The purpose of these experiments is to understand the micromechanical behavior of the Callovo-Oxfordian shale in response to external perturbations. The available experimental setup allows for the continuous, simultaneous measurement of five independent elastic wave velocities and two directions of strain (axial and circumferential), performed on the same cylindrical rock sample during deformation in an axisymmetric triaxial cell. The main results are (1) identification of the complete tensor of elastic moduli of the transversely isotropic shales using elastic wave velocity measurements, (2) assessment of the evolution of these moduli under triaxial loading, and (3) assessment of the evolution of the elastic anisotropy under loading in terms of Thomsen’s parameters. This last outcome allows us to use the anisotropy of the elastic properties of this rock as an indicator of the evolution of its microstructure. In particular, [Formula: see text] in the dry case decreases from 0.5 (ambient pressure) toward 0.37 [Formula: see text], while [Formula: see text] and [Formula: see text] are almost insensitive to pressure. In the wet case, [Formula: see text] decreases from 0.3 (ambient pressure) toward 0.2 [Formula: see text]. Deviatoric stresses have a strong effect on [Formula: see text], [Formula: see text], and [Formula: see text] variations. In this case, [Formula: see text] drops (both for the dry and wet conditions) when failure is approached.

SUMMARY For the first time, a comprehensive and quantitative analysis of the domains of validity of popular wave propagation theories for porous/cracked media is provided. The case of a simple, yet versatile rock microstructure is detailed. The microstructural parameters controlling the applicability of the scattering theories, the effective medium theories, the quasi‐static (Gassmann limit) and dynamic (inertial) poroelasticity are analysed in terms of pores/cracks characteristic size, geometry and connectivity. To this end, a new permeability model is devised combining the hydraulic radius and percolation concepts. The predictions of this model are compared to published micromechanical models of permeability for the limiting cases of capillary tubes and penny‐shaped cracks. It is also compared to published experimental data on natural rocks in these limiting cases. It explicitly accounts for pore space topology around the percolation threshold and far above it. Thanks to this permeability model, the scattering, squirt‐flow and Biot cut‐off frequencies are quantitatively compared. This comparison leads to an explicit mapping of the domains of validity of these wave propagation theories as a function of the rock’s actual microstructure. How this mapping impacts seismic, geophysical and ultrasonic wave velocity data interpretation is discussed. The methodology demonstrated here and the outcomes of this analysis are meant to constitute a quantitative guide for the selection of the most suitable modelling strategy to be employed for prediction and/or interpretation of rocks elastic properties in laboratory–or field‐scale applications when information regarding the rock’s microstructure is available.

This paper is concerned with the experimental identification of the whole dynamic elastic stiffness tensor of a transversely isotropic clayrock from a single cylindrical sample under loading. Measurement of elastic wave velocities (pulse at 1 MHz), obtained under macroscopically undrained triaxial loading conditions are provided. Further macroscopic (laboratory scale) interpretation of the velocity measurements is performed in terms of (i) dynamic elastic parameters ; and (ii) elastic anisotropy. Experiments were performed on a Callovo-Oxfordian shale, Jurassic in age, recovered from a depth of 613 m in the eastern part of Paris basin in France.Moreover, a physically-based micromechanical model is developed in order to quantify the damaged state of the shale under loading through macroscopic measurements. This model allows for the identification of the pertinent parameters for a general transversely isotropic orientational distribution of microcracks, superimposed on the intrinsic transverse isotropy of the rock. It is directly inspired from experimental observations and measurements. At this stage, second-and fourthrank tensors α ij and β ijkl are identified as proper dammage parameters. However, they still need to be explicited in terms of micromechanical parameters for the complex case of anisotropy. An illustration of the protocole of this microstructural data recovery is provided in the simpler case of isotropy. This microstructural insight includes cavities geometry, orientation and fluid-content.

Anisotropy of velocity in shaly overburden is known to cause significant problems for geophysical interpretation, including depth conversion and fluid identification. In addition, mechanical and dynamic elastic shale behavior is not well understood because few tests have been performed on well-preserved samples. Multiple stage triaxial tests were performed upon horizontal core plugs of a shale from the Norwegian Sea with a view to evaluating rock strength and the evolution of ultrasonic response during rock deformation. In addition, standard rock physical properties were characterized as well as composition. The shale microfabric is seen to be strongly laminated, with alternating thick clay-rich laminae and thin silt-rich laminae. Occasional microfractures are also noted parallel to these laminations. The shale has low friction coefficient and cohesive strength, and shows anisotropy of these parameters when the maximum principal stress is oriented parallel to and at 45° to the microfabric. The orientation of the maximum principal stress parallel to the intrinsic fabric and microcracks was seen to significantly impact on velocity normal to the fabric as stress parallel to the fabric increased. S-wave anisotropy was significantly affected by the increasing stress anisotropy. Stress orientation with respect to fabric orientation was therefore found to be an important control on the degree of anisotropy of dynamic elastic properties in this shale.

We experimentally assess the impact of microstructure, pore fluid, and frequency on wave velocity, wave dispersion, and permeability in thermally cracked Carrara marble under effective pressure up to 50 MPa. The cracked rock is isotropic, and we observe that (1) P and S wave velocities at 500 kHz and the low‐strain (<10−5) mechanical moduli at 0.01 Hz are pressure‐dependent, (2) permeability decreases asymptotically toward a small value with increasing pressure, (3) wave dispersion between 0.01 Hz and 500 MHz in the water‐saturated rock reaches a maximum of ~26% for S waves and ~9% for P waves at 1 MPa, and (4) wave dispersion virtually vanishes above ~30 MPa. Assuming no interactions between the cracks, effective medium theory is used to model the rock's elastic response and its permeability. P and S wave velocity data are jointly inverted to recover the crack density and effective aspect ratio. The permeability data are inverted to recover the cracks' effective radius. These parameters lead to a good agreement between predicted and measured wave velocities, dispersion and permeability up to 50 MPa, and up to a crack density of ~0.5. The evolution of the crack parameters suggests that three deformation regimes exist: (1) contact between cracks' surface asperities up to ~10 MPa, (2) progressive crack closure between ~10 and 30 MPa, and (3) crack closure effectively complete above ~30 MPa. The derived crack parameters differ significantly from those obtained by analysis of 2‐D electron microscope images of thin sections or 3‐D X‐ray microtomographic images of millimeter‐size specimens.

This study was devoted to the interpretation of the evolution of elastic wave velocities in anisotropic shales that are subjected to deformation experiments in the laboratory. A micromechanical model was used to describe the macroscopic effective elastic properties and anisotropy of the rock in terms of its microscopic features, such as intrinsic anisotropy and crack/pore geometry. The experimental data (reported in Part 1) were compared quantitatively with the micromechanical model predictions to gain some insight into the microstructural behavior of the rock during deformation. The inversion of the experimental data using the micromechanical model was carried out by means of a numerical minimization of the least-squares distance between data and model in terms of effective compliances. Under isotropic mechanical loading, the overall behavior of the dry shale is consistent with the closure of crack-like pores, which are aligned in theplane of symmetry of the transversely isotropic background matrix. Those cracks represent a low fraction of the total porosity, but they have a strong effect on elastic wave velocities. The data are consistent with an initial (horizontal) crack density of 0.07. Crack closure also is evidenced at early stages of axial loading applied perpendicular to the shale bedding plane, whereas crack density increases significantly as axial stress is increased. Interpretation of the wet experiment is less straightforward, although some preliminary conclusions could be drawn. Under isotropic stress, crack closure also is evidenced, whereas crack density remains constant at the early stages of deviatoric loading. When axial peak stress is approached, crack density increases drastically, which likely indicates onset and development of vertical cracking. Wet experiments probably are more complex because water is likely to be expelled from crack-like pores toward equant pores in response to the mechanical loading.