Publications

2024

1. Poroelastic Response of a Fractured Rock to Hydrostatic Pressure Oscillations

   S. Chapman ,  S. Lissa ,  J. Fortin ,  and  B. Quintal

   Geophysical Research Letters, 2024

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   Abstract Poroelastic coupling between fractures and the surrounding rock is important to numerous applications in geosciences. We measure the in-situ fluid pressure and local strain response of a fractured carbonate sample to hydrostatic pressure oscillations. A linear poroelastic model that represents the rock sample is parameterized using X-ray imaging and ultrasonic wave transmission measurements. The numerical solution, based on Biot’s quasistatic equations, is consistent with the measured frequency dependent dispersion of the apparent bulk modulus of the background matrix and the in-situ pore pressure response, which is caused by fluid pressure diffusion from the compliant fractures into the stiffer matrix. The observed fluid pressure diffusion is causally related to the numerically quantified intrinsic attenuation at seismic frequencies, which is a major contributor to the dissipation of seismic waves. Our analysis supports the use of a simple approximation of fractures as compliant and planar inclusions in numerical simulations based on linear poroelasticity.

2. Pressure Dependence of Permeability in Cracked Rocks: Experimental Evidence of Non-Linear Pore-Pressure Gradients From Local Measurements

   G. Lin ,  S. Chapman ,  D. Garagash ,  J. Fortin ,  and  A. Schubnel

   Geophysical Research Letters, 2024

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   Abstract Understanding the coupling between rock permeability, pore pressure, and fluid flow is crucial, as fluids play an important role in the Earth’s crustal dynamics. We measured the distribution of fluid pressure during fluid-flow experiments on two typical crustal lithologies, granite and basalt. Our results demonstrate that the pore-pressure distribution transitions from a linear to a non-linear profile as the imposed pore-pressure gradient is increased (from 2.5 to 60 MPa) across the specimen. This non-linearity results from the effective pressure dependence of permeability, for which two analytical formulations were considered: an empirical exponential and a new micromechanics-based model. In both cases, the non-linearity of pore pressure distribution is predicted. Using a compilation of permeability versus Terzaghi’s effective pressure data for granites and basalts, we show that our micromechanics-based model has the potential to predict the pore pressure distribution over the range of effective pressures expected within the brittle crust.

3. Hydro-Mechanical Characterization of a Fractured Aquifer Using Groundwater Level Tidal Analysis: Effect of Pore Pressure and Seismic Dynamic Shear Stresses on Permeability Variations

   A. Thomas ,  J. Fortin ,  B. Vittecoq ,  H. Aochi ,  S. Violette ,  J. Maury ,  F. Lacquement ,  and  A. Bitri

   Journal of Geophysical Research: Solid Earth, 2024

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   Abstract Groundwater level tidal analysis is a powerful technique to monitor aquifer’s permeability and hence its change over time. Earthquakes are known to affect aquifer’s properties, in their vicinity through static stress changes but also further away through dynamic stresses. Most often changes are in the form of permeability increases, but sometimes decreases; the changes can be either permanent or transient. These observations are relatively well documented but the physical processes behind these changes are not well understood. By combining solid-earth and barometric tidal groundwater level responses in a borehole in a coherent poroelastic theoretical framework, and a bi-layer hydrogeological model, we recover a 15 years-long time series evolution of aquifer transmissivity and shear modulus. This study showcases the full potential of the tidal analysis method, coupling pore pressure diffusion and rock deformation, at the frontier of hydrogeology and rock physics. This unprecedented measurement of permeability and shear modulus evolution by tidal analysis reveals, during interseismic period, high sensitivity of this shallow aquifer to effective stress, and thus to pore pressure. Thanks to additional finite element simulation of seismic wave propagation, we explore the different mechanisms affecting permeability and shear modulus in the studied fractured andesite aquifer. This study confirms the predominant role of seismic dynamic stresses, and more precisely of dynamic shear stresses, in the change of permeability following an earthquake.

4. Compaction and pore-collapse of chalky limestones from Mururoa atoll

   J. Aubry ,  L. Bollinger ,  A. Schubnel ,  D. Deldicque ,  and  J. Fortin

   Comptes Rendus. Géoscience, 2024

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   Between 1975 and 1996, the Centre d’Expérimentation du Pacifique (CEP) carried out French underground nuclear tests under the atoll of Mururoa (French Polynesia). The deformation of its coral rim was extensively monitored in order to assess the stability of the outer slopes, in particular since a flank collapsed in 1979, triggering a landslide-generated tsunami. The atoll has attracted the attention of experts since the beginning of the nuclear tests because of the mechanical behavior of porous and weak chalky limestones at depth. In this study, samples of these rocks, which were extracted from the atoll’s rim through drilling, have been deformed in the laboratory. The implications of the experiments provide a new perspective on the deformation of the Mururoa atoll since the end of nuclear tests—and, by extension, on the micromechanics of chalks for several other geological contexts.

5. Towards a better comprehension of reactive transport coupling experimental and numerical approaches

   D. Bauer ,  T. Briolet ,  M. Adelinet ,  M. Moreaud ,  O. Sissmann ,  M. Pelerin ,  J. Fortin ,  and  E. Bemer

   Science and Technology for Energy Transition, 2024

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   In this work we focus on further understanding reactive transport in carbonate rocks, in particular limestones characterized by a bimodal pore size distribution. To this end, we performed injection experiments with CO 2 -saturated water on a sample of Euville limestone and monitored the experiments with a medical CT scanner. Microscanner imaging was performed before and after alteration. Experiments showed that permeability increased by nearly two decades due to the alteration process. This increase could be attributed to the formation of a preferential dissolution path visualized on the CT images. Microscanner images show that preferential dissolution areas are characterized by the presence of numerous enlarged macropores. The preferential dissolution path created therefore retains a porous structure and does not correspond to a wormhole-type channel. To provide further knowledge of the small-scale physics of reactive transport, we performed Lattice-Boltzmann simulations of flow in a numerically generated model 2D porous medium having geometrical and topological features designed to approach Euville limestone. We showed that the fluid velocity increased in nearly percolating paths of macropores. Considering the experiments, this means that the CO 2 -saturated water starts to enter high-velocity zones earlier than low-velocity zones, inducing an earlier onset of the alteration process and a more pronounced local dissolution. However, numerical results showed that the alteration of non-connected macropores leads to an increase of permeability much smaller than the experimentally observed one. To explain this fact we used effective medium modelling that permits predicting the variation in permeability as a function of the fraction of macropores and consequently as a function of alteration. It proved that as long as there is no alteration-induced percolating path consisting of macropores, the increase in permeability is relatively low as shown by the Lattice-Boltzmann simulations. An increase in permeability of several orders of magnitude is only observed when the macroporosity is close to the percolation threshold. This fact is in accordance with the experimentally observed results

2023

1. Earthquakes and Heavy Rainfall Influence on Aquifer Properties: A New Coupled Earth and Barometric Tidal Response Model in a Confined Bi-Layer Aquifer

   A. Thomas ,  J. Fortin ,  B. Vittecoq ,  and  S. Violette

   Water Resources Research, 2023

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   Abstract Among the impacts of earthquakes on aquifers, permeability change is one of the most challenging to quantify, since techniques to measure permeability evolution are scarce. The study of tidal response of boreholes is one of the most promising, yet complex to use in practice. We used 14 years of piezometric level measurements and two concurrent source signals, earth tidal strain and barometric pressure, for which we separated the respective contribution in a state-of-the-art tidal analysis. We developed a new general analytical hydrogeological model, based on geological observations of a confined bi-layer aquifer. It is able to match combined observations of earth and barometric tide phase lags which could not be explained by existing models. We demonstrate that its relative complexity can be overcome thanks to the results of tidal analysis, yielding a simpler model adapted to the Fond Lahaye site of the Martinique Island. The resulting evolution of diffusivity and loading efficiency, was validated independently with several pumping tests occurring all along the studied period. The transient diffusivity increases and decreases indicate which earthquakes impacted the aquifer, enabling to establish an empirical magnitude-distance relationship criterion. This criterion confirms the suspected dependence on dynamic stresses, which decrease as the square of the hypocentral distance. Additionally, we investigate two other factors of diffusivity changes: heavy rainfall events and aquifer withdrawals, which demonstrates the sensitivity of volcanic aquifers properties to environmental and anthropogenic influence.

2. Reconstruction of the Late Miocene to Pliocene continental succession of Samos Island: Palaeoenvironmental implications for the Eastern Aegean domain

   Y. Hamon ,  R. Deschamps ,  C. Gorini ,  D. Sakellariou ,  C. Bailly ,  T. Kernif ,  A. Christ ,  M. Adelinet ,  and  J. Fortin

   The Depositional Record, 2023

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   Abstract On the Island of Samos (East Aegean region, Greece), two sedimentary basins are filled by thick continental series dated to the Late Miocene to Early Pliocene. A multidisciplinary study has been performed including (1) the definition of 21 sedimentary facies, (2) a review of the biological components and (3) carbon, oxygen and strontium stable isotope analyses. The succession is characterised by various depositional settings and hydrochemical compositions. Five main stages of basin evolution have been identified: (1) The Late Serravallian is marked by the development of alluvial fans and fan delta; (2) during the Lower Tortonian, isolated shallow lakes with variable salinity, from fresh to brackish, developed under warm and relatively humid conditions; (3) the Middle to Upper Tortonian is marked by the development of a large and deep lake with saline and alkaline waters, under colder and drier conditions; (4) the Latest Tortonian to Messinian period is represented by an ephemeral alluvial system, developed under a dry climate; (5) during the Zanclean, a palustrine and paludal wetland system, dominated by tufa carbonates, developed under moderately humid conditions. This succession is of particular interest for the reconstruction of the palaeoenvironmental evolution of the transition zone between the Mediterranean domain, and the Paratethys and circum-Paratethys areas. The geochemical data and the presence of flora (diatoms) and fauna (gastropods) of marine affinity suggest transient ingressions of marine-related water or groundwater inflows as early as the Lower Tortonian. The Samos succession records the complex interaction between the regional geodynamics and climate. The extensional regime of the Eastern Aegean zone generates subsidence, interrupted in the mid-Tortonian (9 Ma) by a brief compressive event and a major exposure of the basins. Furthermore, the Late Miocene progressive aridification, followed by a change to a more humid climate (Pliocene) is also a major driver of the sedimentation.

3. Prediction of dispersion and attenuation on elastic wave velocities in partially saturated rock based on the fluid distribution obtained from three-dimensional (3D) micro-CT images

   C. Sun ,  J. Fortin ,  G. Tang ,  and  S. Wang

   Frontiers in Earth Science, 2023

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   Elastic wave attenuation in partially saturated porous rock is primarily due to wave-induced fluid flow, which arises from the contrast in compressibility between air and water and is influenced by the water distribution within the rock. We propose a method for constructing a numerical model that predicts mesoscopic dispersion and attenuation. Initially, we use fluid distribution data sourced from 3D X-ray Computed Tomography images to construct the numerical model, utilizing Biot’s poroelastic equations as the governing equations. Subsequently, we implement the finite element method to derive solutions for the numerical model. Our focus is centered on two key challenges: 1) reducing memory cost, and 2) efficiently handling element intersection during the meshing process. The solutions illustrate the evolution of fluid pressure distribution and the frequency-dependent advancement of the elastic moduli, coupled with their corresponding attenuation. Ultimately, we compare these numerical predictions with previously published experimental data from a study on partially saturated Indiana limestone. The considerable agreement between our numerical results and the experimental data confirms the validity of our method, which crucially incorporates the actual fluid distribution (captured from 3D CT images) as a vital input.

4. A numerical assessment of local strain measurements on the attenuation and modulus dispersion in rocks with fluid heterogeneities

   C. Sun ,  G. Tang ,  S. Chapman ,  H. Zhang ,  J. Fortin ,  S. Wang ,  D. Pan ,  and  J. Yue

   Geophysical Journal International, 2023

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   The forced oscillation method is widely used to investigate intrinsic seismic wave dispersion and attenuation in rock samples by measuring their dynamic stress–strain response. However, using strain gauges to locally measure the strains on samples surfaces can result in errors in determining the attenuation and moduli of rocks with mesoscopic scale heterogeneities. In this study, we developed a 3-D numerical model based on Biot’s poroelastic theory to investigate the effect of strain gauge location, number and size on attenuation and dispersion in response to wave-induced fluid flow. Our results show that increasing the strain gauge length, number, and size can reduce the error between local and bulk responses. In a homogeneous and isotropic rock with a quasi-fractal fluid heterogeneity at 12 per cent gas saturation, the relative error between local and bulk responses stays below 6 per cent when the strain gauge length surpasses 8.6 times the correlation length. As the gas saturation becomes larger, the ratio minimally changes non-monotonically, initially increasing and then decreasing. We also used the Monte Carlo method to demonstrate that local laboratory measurements can approximate the reservoir-scale response with a minimum relative error of 1.5 per cent as the sample number increases. Our findings provide guidance for (i) interpreting local low-frequency measurements in terms of bulk properties of rock and (ii) upscaling lab measurements to reservoir-scale properties.

5. Strain Amplitude Dependent Transition from Dynamic to Static Bulk Modulus in Rocks with and Without Pre-existing Cracks

   S. Chapman ,  J. Fortin ,  A. Gallagher ,  and  J. Borgomano

   Rock Mechanics and Rock Engineering, 2023

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   Numerous experimental studies show significant differences between the static and dynamic elastic moduli of rocks. These differences are commonly attributed to the presence of cracks and uncemented grain contacts that make rocks non-linear elastic materials with a sensitivity to strain amplitude. To investigate the impact of strain amplitude on the bulk modulus of different rock types, we performed hydrostatic oscillations to induce strain amplitudes from 10–6 to 10–4 on the samples at frequencies ≤ 0.04 Hz. In addition, we measured the dynamic bulk modulus from ultrasonic wave velocities and the static bulk modulus from hydrostatic pressure ramps. In five out of the six samples, we observe a transition from the dynamic to static modulus with increasing strain amplitude. With increasing effective pressure, the bulk moduli increase, and the strain amplitude dependence is reduced. In the oolitic Chauvingy limestone, in contrast, we observed neither a significant strain nor effective pressure dependence on the bulk modulus, which is interpreted as the absence of pre-existing cracks. In the reservoir carbonate samples, for strain amplitudes > 5 × 10–5 the stress–strain loops become non-linear hysteretic and the measured attenuation plateaus. The presence of additional harmonics in the strain and the absence of harmonics in the stress, indicate that the non-linearity is inherent to the samples. The transition from dynamic to static bulk modulus is explained at first order by slip at grain contacts.

2022

1. Controlling factors of acoustic properties in continental carbonates: Implications for high-resolution seismic imaging

   C. Bailly ,  T. Kernif ,  Y. Hamon ,  M. Adelinet ,  and  J. Fortin

   Marine and Petroleum Geology, 2022

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   Continental carbonates are characterized by multi-scale heterogeneous porous networks, making the geological interpretation of seismic imaging difficult. We investigate two sedimentary sections exhibiting a similar facies succession, combining geological characterizations and multi-scale acoustic measurements. Based on outcrop investigation and petrographic description, we define nine sedimentary facies displaying contrasted early diagenetic evolutions. According to the vertical facies variations, we develop a depositional model corresponding to a low gradient valley fed by freshwaters, subdivided into three main domains (alluvial plain, palustrine and paludal). To understand the acoustic properties of the studied sedimentary rocks while remaining representative of their multi-scale heterogeneity, we acquire acoustic measurements at two different scales: i) at log-scale, directly on the outcrop surfaces using a frequency of 250 kHz; and ii) at plug-scale as usually done in laboratory using a frequency of 500 kHz. Based on these multi-scale geophysical acquisitions, we link in-situ P-wave velocities with the different sedimentary facies while characterizing centimeter-scale Representative Elementary Volumes (REVs). Conversely, based on laboratory measurements and thin-section petrography, we define relationships between P-wave velocity, porosity, facies, and diagenesis, corresponding to millimeter-scale REVs. Using both in-situ P-wave velocity measurements and plug densities, we construct 1-D synthetic seismograms showing meter-scale seismic reflectors equivalent to crosswell seismic frequency ranges. This approach shows the following: i) high-amplitude seismic reflectors fit with facies changes associated to diagenetic contrasts (e.g. cemented versus uncemented carbonates); ii) reflection free-zones match with a succession of facies changes affected by diagenetic homogenization (e.g. intensely to pervasively recrystallized and cemented carbonates). Our work highlights the importance of relating an extensive geological description of carbonates (facies, depositional model, diagenesis) together with multi-scale acoustic measurements and synthetic seismic modelling to predict the high-resolution heterogeneities of subsurface reservoirs.

2. Understanding the Geodetic Signature of Large Aquifer Systems: Example of the Ozark Plateaus in Central United States

   S. Larochelle ,  K. Chanard ,  L. Fleitout ,  J. Fortin ,  A. Gualandi ,  L. Longuevergne ,  P. Rebischung ,  S. Violette ,  and  JP Avouac

   Journal of Geophysical Research: Solid Earth, 2022

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   The continuous redistribution of water involved in the hydrologic cycle leads to deformation of the solid Earth. On a global scale, this deformation is well explained by the loading imposed by hydrological mass variations and can be quantified to first order with space-based gravimetric and geodetic measurements. At the regional scale, however, aquifer systems also undergo poroelastic deformation in response to groundwater fluctuations. Disentangling these related but distinct 3D deformation fields from geodetic time series is essential to accurately invert for changes in continental water mass, to understand the mechanical response of aquifers to internal pressure changes as well as to correct time series for these known effects. Here, we demonstrate a methodology to accomplish this task by considering the example of the well-instrumented Ozark Plateaus Aquifer System (OPAS) in the central United States. We begin by characterizing the most important sources of groundwater level variations in the spatially heterogeneous piezometer dataset using an Independent Component Analysis. Then, to estimate the associated poroelastic displacements, we project geodetic time series corrected for hydrological loading effects onto the dominant groundwater temporal functions. We interpret the extracted displacements in light of analytical solutions and a 2D model relating groundwater level variations to surface displacements. In particular, the relatively low estimates of elastic moduli inferred from the poroelastic displacements and groundwater fluctuations may be indicative of aquifer layers with a high fracture density. Our findings suggest that OPAS undergoes significant poroelastic deformation, including highly heterogeneous horizontal poroelastic displacements.

3. Influence of Fluid Distribution on Seismic Dispersion and Attenuation in Partially Saturated Limestone

   C. Sun ,  J. Fortin ,  J. Borgomano ,  S. Wang ,  G. Tang ,  T. Bultreys ,  and  V. Cnudde

   Journal of Geophysical Research: Solid Earth, 2022

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   Quantitatively assessing attenuation and dispersion of elastic-wave velocities in partially saturated reservoir is difficult because of its sensitivity to fluid distribution. We conducted experiments on homogeneous Indiana limestone samples, partially saturated by two methods: drying and imbibition which lead to different fluid distribution for a given saturation. Forced oscillations (from 0.004 to 100 Hz) and ultrasonic (1 MHz) measurements were done under confining pressure to measure the change of elastic moduli with frequency and their attenuation. Our measurements show that compressional (P-)velocities are strongly sensitive to the sample’s saturation method. For high saturations (above 80%), obtained by drainage, compressional velocities are frequency dependent, and clear peaks of attenuation can be observed. However, at the same saturations obtained by imbibition, no dispersion or attenuation is observed. In addition, shear velocities show little variation with frequency, saturations, and fluid distribution. The dispersion and attenuation of P-velocities are shown to be influenced by the pore fluid distribution, which was investigated using micro-computer-assisted tomographic (CT) scans. Furthermore, a numerical model developed within the framework of poroelasticity’s theory predicts well the experimental results, using the fluid distribution obtained from CT as an input. Our results show that the velocity dispersion was related to wave-induced fluid flow at mesoscopic scale controlled by the geometry and distribution of the gas patches.

4. Seismic dispersion and attenuation in fractured fluid-saturated porous rocks: An experimental study with an analytic and computational comparison

   A. Gallagher ,  J. Fortin ,  and  J. Borgomano

   Rock Mechanics and Rock Engineering, 2022

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   Seismic waves are typically assumed to propagate fast enough through a porous rock saturated with multiple fluid phases such that the interaction between the fluids can be considered adiabatic, or thermodynamically unrelaxed. However, at low gas saturations and when the gas is present in the form of microscopic bubbles the fluid mixture may in fact be thermodynamically relaxed at seismic frequencies. The effective fluid is then significantly more compressible. A transition from a thermodynamically relaxed to unrelaxed state of the fluids will be accompanied by frequency dependent attenuation of the wave in response to heat and/or mass transfer. We conducted experiments on two partially saturated sandstone samples to measure frequency dependent attenuation and modulus dispersion at seismic frequencies (\<1000 Hz). For CO2 saturations of 0.1–0.2 per cent we observe significant attenuation and dispersion in the bulk and shear modulus, with an attenuation peak at ∼100 Hz. The bulk modulus was significantly lower than the prediction by Gassmann–Wood fluid substitution, which assumes that the fluids are thermodynamically unrelaxed. Numerical simulations in poroelastic media further indicate that a partially drained boundary condition does not adequately explain the observed attenuation and dispersion, particularly in the shear modulus. Numerical simulations at the microscopic scale support the notion that pore-scale heterogeneities could explain the observed shear attenuation and dispersion, since an external shear deformation can cause local compressions of the pore space. The observed attenuation and dispersion are interpreted to be predominantly due to a transition from a thermodynamically relaxed to unrelaxed state of the saturating fluids.

5. Mass transfer between fluids as a mechanism for seismic wave attenuation: experimental evidence from water–CO2 saturated sandstones

   S. Chapman ,  J. Borgomano ,  B. Quintal ,  S. Benson ,  and  J. Fortin

   Geophysical Journal International, 2022

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   Seismic waves are typically assumed to propagate fast enough through a porous rock saturated with multiple fluid phases such that the interaction between the fluids can be considered adiabatic, or thermodynamically unrelaxed. However, at low gas saturations and when the gas is present in the form of microscopic bubbles the fluid mixture may in fact be thermodynamically relaxed at seismic frequencies. The effective fluid is then significantly more compressible. A transition from a thermodynamically relaxed to unrelaxed state of the fluids will be accompanied by frequency dependent attenuation of the wave in response to heat and/or mass transfer. We conducted experiments on two partially saturated sandstone samples to measure frequency dependent attenuation and modulus dispersion at seismic frequencies (\<1000 Hz). For CO2 saturations of 0.1–0.2 per cent we observe significant attenuation and dispersion in the bulk and shear modulus, with an attenuation peak at ∼100 Hz. The bulk modulus was significantly lower than the prediction by Gassmann–Wood fluid substitution, which assumes that the fluids are thermodynamically unrelaxed. Numerical simulations in poroelastic media further indicate that a partially drained boundary condition does not adequately explain the observed attenuation and dispersion, particularly in the shear modulus. Numerical simulations at the microscopic scale support the notion that pore-scale heterogeneities could explain the observed shear attenuation and dispersion, since an external shear deformation can cause local compressions of the pore space. The observed attenuation and dispersion are interpreted to be predominantly due to a transition from a thermodynamically relaxed to unrelaxed state of the saturating fluids.

2021

1. Elastic properties of a reservoir sandstone: a broadband inter‐laboratory benchmarking exercise

   A. Ògúnsàmì ,  J. Jackson ,  J. Fortin ,  H. Sidi ,  A. Gerhardt ,  B. Gurevich ,  V. Mikhaltsevitch ,  and  M. Lebedev

   2021

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   Low‐frequency forced‐oscillation methods applied to a reservoir sandstone allowed determination of the Young’s modulus and Poisson’s ratio (from axial loading), bulk modulus (by oscillation of the confining pressure) and shear modulus (from torsional‐forced oscillations) for comparison with conventional ultrasonic data. All tests were performed on a common sandstone core sample from an oil reservoir offshore West Africa. The results show a steady increase in ultrasonic velocities and shear modulus of the dry specimen as functions of pressure, which suggests a progressive closure of the inter‐granular contacts. An increase of bulk and Young’s moduli and Poisson’s ratio is observed on decane saturation of the sample when tested with a sufficiently small dead volume. This observation, consistent with Gassmann’s theory, suggests that such measurements probe undrained (saturated isobaric) conditions. Diminution or absence of such fluid‐related stiffening for low‐frequency measurements with dead volumes comparable with the pore volume of the specimen indicates partially drained conditions and highlights the critical role of experimental boundary conditions. Directly measured bulk and shear moduli are consistent with those derived from Young’s modulus and Poisson’s ratio. These results of the inter‐laboratory testing using different measurement devices are consistent in terms of the effect of frequency and fluid saturation for the reservoir sandstone specimen. Such broad consistency illustrates the validity of forced‐oscillation techniques and constitutes an important benchmarking of laboratory testing of the elastic properties of a porous medium.

2. Seismic Wave Attenuation and Dispersion Due to Partial Fluid Saturation: Direct Measurements and Numerical Simulations Based on X-Ray CT

   S. Chapman ,  J. Borgomano ,  B. Quintal ,  S. Benson ,  and  J. Fortin

   Journal of Geophysical Research: Solid Earth, 2021

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   Quantitatively assessing seismic attenuation caused by fluid pressure diffusion (FPD) in partially saturated rocks is challenging because of its sensitivity to the spatial fluid distribution. To address this challenge we performed depressurization experiments to induce the exsolution of carbon dioxide from water in a Berea sandstone sample. In a first set of experiments we used medical X-ray computed tomography (CT) to characterize the fluid distribution. At an equilibrium pressure of approximately 1 MPa and applying a fluid pressure decline rate of approximately 0.6 MPa per minute, we allowed a change in saturation of less than 1%. The gas was heterogeneously distributed along the length of the sample, with most of the gas exsolving near the sample outlet. In a second set of experiments, at the same pressure and temperature, following a very similar exsolution protocol, we measured the frequency dependent attenuation and modulus dispersion between 0.1 and 1,000 Hz using the forced oscillation method. We observed significant attenuation and dispersion in the extensional and bulk deformation modes, however, not in the shear mode. Lastly, we use the fluid distribution derived from the X-ray CT as an input for numerical simulations of FPD to compute the attenuation and modulus dispersion. The numerical solutions are in close agreement with the attenuation and modulus dispersion measured in the laboratory. Our approach allows for accurately relating attenuation and dispersion to the fluid distribution, which can be applied to improving the seismic monitoring of the subsurface.

3. Porous and cracked rocks elasticity: Macroscopic poroelasticity and effective media theory

   J. Fortin ,  and  Y. Guéguen

   Mathematics and Mechanics of Solids, 2021

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   Macroscopic poroelasticity and effective medium theory are two independent approaches which can be used to analyze the role of pores, cracks, and fluid on elastic properties. Macroscopic poroelasticity belongs to the macroscopic framework of thermodynamics whereas effective medium theory expresses the medium properties in terms of microstructural characteristics (pore and crack shape, etc.) and component properties (fluid properties, solid grain properties, etc.). In this paper, we review the fundamental assumptions and results of both approaches, and show that they are complementary but do not apply over the same range of conditions. A compilation of data is reported, in various dry and saturated rocks, to show the validity of the Gassmann equation and the dispersion between unrelaxed modulus –where effective medium model applies- and relaxed modulus –where poroelasticity applies.

2020

1. Poroelastic Relaxation in Thermally Cracked and Fluid-Saturated Glass

   A. Ògúnsàmì ,  J. Borgomano ,  J. Fortin ,  and  I. Jackson

   Journal of Geophysical Research: Solid Earth, 2020

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   Abstract To test theoretical models of modulus dispersion and dissipation in fluid-saturated rocks, we have investigated the broadband mechanical properties of four thermally cracked glass specimens of simple microstructure with complementary forced-oscillation (0.004–100 Hz) and ultrasonic techniques ( 1 MHz). Strong pressure dependence of moduli (bulk, Young’s, and shear), axial strain, and ultrasonic wave speeds for dry conditions attests to essentially complete crack closure at a confining pressure of 15 MPa—consistent with ambient-pressure crack aspect ratios ≤2 × 10−4. Oscillation of the confining pressure reveals bulk modulus dispersion and a corresponding dissipation peak, near 0.002 Hz only at the lowest effective pressure (2.5 MPa)—attributed to the transition with increasing frequency from the drained to saturated-isobaric regime. The observations are consistent with Biot-Gassmann’s theory, with dispersion and dissipation adequately represented by Zener model. Above the draining frequency, axial forced-oscillation tests show dispersion of Young’s modulus and Poisson’s ratio, and an associated broad dissipation peak centered near 0.3 Hz, thought to reflect local “squirt” flow and adequately modeled with a continuous distribution of relaxation times over two decades. Observations of Young’s and shear moduli dispersion and dissipation from complementary flexural and torsional oscillation measurements for differential pressure ≤10 MPa provide supporting evidence of the transition with increasing frequency from the saturated-isobaric to the saturated-isolated regime—also probed by ultrasonic technique. These findings validate predictions from theoretical models of dispersion in cracked media and emphasize need for caution in the seismological application of laboratory ultrasonic data for cracked media.

2. Pore pressure pulse migration in microcracked andesite recorded with fibre optic sensors

   A. Nicolas ,  G. Blöcher ,  C. Kluge ,  Z. Li ,  H. Hofmann ,  L. Pei ,  H. Milsch ,  J. Fortin ,  and  Y. Guéguen

   Geomechanics for Energy and the Environment, 2020

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   Pore pressure has a major influence on the effective stress and thus on the mechanical behaviour of rocks. In this study, we focus on the hydro-mechanical behaviour of a low porosity andesitic rock heat-treated to 930 °C to induce thermal cracks and increase the permeability of the samples. First, we show that permeability decreases from 8 × 10−16 m2 to 1.5 × 10−17 m2 with a confining pressure (Pc) increase from 2 MPa to 40 MPa (pore pressure being approximately 0.2 MPa). Then, we used fibre optic pressure sensors to monitor pore pressure diffusion at three points along the sample during the propagation of a pore pressure pulse under hydrostatic (Pc=40 MPa) and triaxial stresses (Pc=40 MPa, differential stress of 356 MPa). When the pore pressure pulse was applied, the fibre optic sensors showed a sudden pore pressure increase one after the other as a function of their location along the sample. Pore pressure increase downstream was very smooth under hydrostatic stress and almost zero after the duration of the experiment (50 min) under triaxial stresses. This lack of downstream pore pressure increase under triaxial stresses is due to the fact that a differential stress of 356 MPa decreased permeability from approximately 10−17m2 to approximately 10−19m2. Finally, the pore pressure diffusion process was modelled considering a uniform spatial distribution of permeability in the andesite sample and the dead volume attached at the downstream side.

3. An apparatus to measure elastic dispersion and attenuation using hydrostatic- and axial-stress oscillations under undrained conditions

   J. Borgomano ,  A. Gallagher ,  C. Sun ,  and  J. Fortin

   Review of Scientific Instruments, 2020

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   An experimental apparatus is described for the investigation of frequency dispersion, and related attenuation, of fluid-saturated rocks under confining pressure and undrained boundary conditions. The forced-oscillation method is performed on cylindrical samples. The measurement of stress and strain under hydrostatic oscillations allows the dynamic bulk modulus to be inferred, while axial oscillations give access to dynamic Young’s modulus and Poisson’s ratio. We present calibration measurements for dispersion and attenuation on standard materials such as glass, plexiglass, and gypsum. Results show that for strain amplitudes below 10−5, robust measurements can be achieved up to 1 kHz and 1.3 Hz, respectively, for axial and hydrostatic oscillations. A new experimental design of the endplatens (sample holders) allows control of drained or undrained boundary conditions using microvalves. The microvalves were tested on a porous Vosgian sandstone. In addition, numerical modeling confirms that the resonances of the apparatus only affect frequencies above 1 kHz, with little sensitivity to the sample’s stiffness.

4. Moisture-induced elastic weakening and wave propagation in a clay-bearing sandstone

   M. Tiennot ,  and  J. Fortin

   Géotechnique Letters, 2020

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   Long-term behaviour of a clay-bearing sandstone is investigated using elastic waves propagation coupled with strain measurements during moisture cycles. Adsorption and desorption are followed in a continuous way during several variations of relative humidity. Moisture adsorption is related to the solvation pressure and the measured elastic weakening during humidification is correlated with the clay minerals sensitivity.

5. Effect of pore collapse and grain crushing on the frequency dependence of elastic wave velocities in a porous sandstone

   C. Sun ,  J. Borgomano ,  and  W. ShangXu

   Rock Mechanics and Rock Engineering, 2020

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   A saturated Bleurswiller sandstone, of 25% porosity, was compacted by increasing the confining pressure over the critical pressure P* which characterizes the onset of pore collapse and grain crushing. The frequency-dependence of Young’s moduli were measured before and after the compaction using forced-oscillation method in a triaxial cell. For the intact and compacted samples, we observed one dispersive transition within the seismic band (0.01–100 Hz). The dispersion is consistent with crack-to-pore squirt flow, making the transition from the relaxed to the unrelaxed fluid-flow regime. The induced compaction shifted the critical frequency of the squirt-flow dispersion towards higher frequencies, thus moving it out of the seismic band and allowing Biot-Gassmann to fully apply. This result is a consequence of an increase in the crack aspect ratio after compaction. In addition, the dispersion of elastic modulus after compaction increases from about 25 to 30%, related to the increase of crack fraction.

6. Influence of hydrothermal alteration on the elastic behaviour and failure of heat-treated andesite from Guadeloupe

   A. Nicolas ,  L. Lévy ,  O. Sissmann ,  Z. Li ,  J. Fortin ,  B. Gibert ,  and  F. Sigmundsson

   Geophysical Journal International, 2020

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   Studies on the mechanical behaviour of rocks, including volcanic rocks, usually seek for unaltered and simple material: rocks without macroscopic defects. However, volcanic rocks are often naturally altered due to the circulation of hydrothermal fluids. This alteration may influence mechanical and physical properties. Here, we study the effect of hydrothermal alteration on the elasticity and failure properties of andesite. A homogeneous block of natural andesite was retrieved from a quarry. Three samples were first heat-treated and then artificially altered at different temperatures by soaking them in a brine for one month at a pressure of 20 MPa and temperatures of 80, 180 and 280 °C. Heat-treated unaltered and altered samples were hydrostatically loaded up to 50 MPa and unloaded, while strains and elastic wave velocities were recorded. Samples were also triaxially deformed to failure at a constant strain rate and a confining pressure of 15 MPa. At ambient pressure, increased alteration temperature resulted in increased wave propagation velocity, thus increased dynamic elastic moduli. During hydrostatic loading, volumetric deformation at a given effective pressure decreased with alteration temperature denoting increased static elastic moduli. During triaxial loading, the degree of alteration decreased elastic compaction and peak stress at failure. These observations are interpreted as the result of microcracks in-filling by alteration minerals, and in particular smectite, a swelling-clay mineral with a low friction coefficient. The mechanical behaviour of a volcanic rock subjected to triaxial loading was modelled with a damage model based on crack propagation from pre-existing flaws. A decreasing friction coefficient within the flanks of the cracks leads to a decrease of the peak stress and explains the experimental observations.

7. Initial effective stress controls the nature of earthquakes

   F. X Passelègue ,  M. Almakari ,  P. Dublanchet ,  F. Barras ,  J. Fortin ,  and  M. Violay

   Nature Communications, 2020

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   Modern geophysics highlights that the slip behaviour response of faults is variable in space and time and can result in slow or fast ruptures. However, the origin of this variation of the rupture velocity in nature as well as the physics behind it is still debated. Here, we first highlight how the different types of fault slip observed in nature appear to stem from the same physical mechanism. Second, we reproduce at the scale of the laboratory the complete spectrum of rupture velocities observed in nature. Our results show that the rupture velocity can range from a few millimetres to kilometres per second, depending on the available energy at the onset of slip, in agreement with theoretical predictions. This combined set of observations bring a new explanation of the dominance of slow rupture fronts in the shallow part of the crust or in areas suspected to present large fluid pressure.

8. Dispersion and Attenuation of Elastic Wave Velocities: Impact of Microstructure Heterogeneity and Local Measurements

   C. Sun ,  G. Tang ,  J. Fortin ,  J. Borgomano ,  and  S. Wang

   Journal of Geophysical Research: Solid Earth, 2020

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   Abstract The variation of the seismic properties with frequency of a brine-saturated sandstone sample with a porosity of 22% was measured using a forced oscillation apparatus. Two pairs of orthogonal biaxial strain gauges were pasted at different locations at the length center of the sample. In the frequency range of 1–300 Hz, using these two pairs of strain gauges, we observed experimentally the same global flow but different local flows (squirt flow). Therefore, the observation of the local flow is influenced by the position of the strain gauges in contrast to the global flow. Indeed, local flow is strongly influenced by the microstructure (structure of the grain contacts and microcracks). In particular, we show that although the sample is homogeneous in terms of porosity and crack density, it is not the case in terms of crack aspect ratio, which may slightly vary along the sample. A 3D diffusion model coupled with a simple squirt model was built to further interpret the data. These results show that the wave-induced fluid flows occur at different scales and controls the dispersion and attenuation of saturated rocks.

9. Earthquakes and extreme rainfall induce long term permeability enhancement of volcanic island hydrogeological systems

   B. Vittecoq ,  J. Fortin ,  J. Maury ,  and  S Violette

   Scientific Reports, 2020

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   Earthquakes affect near-surface permeability, however temporal permeability evolution quantification is challenging due to the scarcity of observations data. Using thirteen years of groundwater level observations, we highlight clear permeability variations induced by earthquakes in an aquifer and overlaying aquitard. Dynamic stresses, above a threshold value PGV > 0.5 cm s−1, were mostly responsible for these variations. We develop a new model using earth tides responses of water levels between earthquakes. We demonstrate a clear permeability increase of the hydrogeological system, with the permeability of the aquifer increasing 20-fold and that of the aquitard 300-fold over 12 years, induced by fracture creation or fracture unclogging. In addition, we demonstrate unprecedented observations of increase in permeability due to the effect of extreme tropical deluges of rainfall and hurricanes. The water pressure increase induced by the exceptional rainfall events thus act as piston strokes strong enough to unclog congested fractures by colloids, particles or precipitates. Lastly, an analysis of regional permeabilities also highlights a permeability increase over geological timeframes (× 40 per million years), corroborating the trend observed over the last decade. This demonstrates that permeability of aquifers of andesitic volcanic islands, such as the Lesser Antilles, significantly evolve with time due to seismic activity and extreme rainfall.

2019

1. Seismic Dispersion and Attenuation in Fluid-Saturated Carbonate Rocks: Effect of Microstructure and Pressure

   J. Borgomano ,  L. Pimienta ,  J. Fortin ,  and  Y. Guéguen

   Journal of Geophysical Research: Solid Earth, 2019

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   Abstract The frequency dependence of seismic properties of fully saturated rocks can be related to wave-induced fluid flows at different scales. The elastic dispersion and attenuation of four fluid-saturated carbonate rocks, with different microstructures, have been measured over a broad frequency range in the laboratory. The selected rocks were a presalt coquina from offshore Congo, an Urgonian limestone from Provence (France), and an Indiana limestone either intact or thermally cracked. The selected samples present a variety of pore types characteristic of carbonates, and their link with potential squirt flow dispersion was investigated. To cover a broad frequency range, forced oscillations (0.004 to 100 Hz) and ultrasonic (1 MHz) measurement techniques were performed in a triaxial cell, at various differential pressures, on the samples saturated by fluids of different viscosity. Both hydrostatic and axial oscillations were applied in order to get the different dynamic moduli. For all our samples, the drained/undrained transition and the squirt flow mechanisms were characterized experimentally, in terms of amplitude of dispersion, amount of viscoelastic attenuation, and frequency ranges. Biot-Gassmann’s theory was found to apply mainly at seismic frequencies (10–100 Hz). A potential correlation between pore type and possible squirt flow dispersion was investigated. Intragranular microporosity, with either a rimmed or uniform distribution, does not seem to generate any substantial dispersion. On the other hand, cracked intergranular cement and uncemented grain contacts seem to generate substantial squirt flow dispersion, at respectively seismic and sonic log frequencies.

2. Upscaling of Elastic Properties in Carbonates: A Modeling Approach Based on a Multiscale Geophysical Data Set

   C. Bailly ,  J. Fortin ,  M. Adelinet ,  and  Y. Hamon

   Journal of Geophysical Research: Solid Earth, 2019

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   Linking ultrasonic measurements made on samples, with sonic logs and seismic subsurface data, is a key challenge for the understanding of carbonate reservoirs. To deal with this problem, we investigate the elastic properties of dry lacustrine carbonates. At one study site, we perform a seismic refraction survey (100 Hz), as well as “sonic” (54 kHz) and ultrasonic (250 kHz) measurements directly on outcrop and ultrasonic measurements on samples (500 kHz). By comparing the median of each data set, we show that the P wave velocity decreases from laboratory to seismic scale. Nevertheless, the median of the sonic measurements acquired on outcrop surfaces seems to fit with the seismic data, meaning that sonic acquisition may be representative of seismic scale. To explain the variations due to upscaling, we relate the concept of representative elementary volume with the wavelength of each scale of study. Indeed, with upscaling, the wavelength varies from millimetric to pluri-metric. This change of scale allows us to conclude that the behavior of P wave velocity is due to different geological features (matrix porosity, cracks, and fractures) related to the different wavelengths used. Based on effective medium theory, we quantify the pore aspect ratio at sample scale and the crack/fracture density at outcrop and seismic scales using a multiscale representative elementary volume concept. Results show that the matrix porosity that controls the ultrasonic P wave velocities is progressively lost with upscaling, implying that crack and fracture porosity impacts sonic and seismic P wave velocities, a result of paramount importance for seismic interpretation based on deterministic approaches.

3. Combined controls of sedimentology and diagenesis on seismic properties in lacustrine and palustrine carbonates (Upper Miocene, Samos Island, Greece)

   C. Bailly ,  M. Adelinet ,  Y. Hamon ,  and  J. Fortin

   Geophysical Journal International, 2019

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   For the subsurface characterization of carbonates, linking physical properties (e.g. porosity and seismic reflectors) with their geological significance (e.g. sedimentary facies and diage-nesis) is of primary importance. To address this issue, we study the lacustrine and palustrine carbonates on Samos Island through a geological and geophysical characterization of a sed-imentary succession. The microstructures of the samples are described, and the samples’ physical properties are measured (porosity, P-wave velocity and density). The results show that the identification of only the primary (i.e. sedimentary) microstructure is not sufficient for explaining the huge variations in porosity and P-wave velocity. Hence, we highlight two early diagenetic processes that strongly impact the microstructures and control the physical properties: (i) neomorphism occludes porosity and increases the P-wave velocity of mud-and grain-supported microstructures, which implies a mineralogical stabilization of the grains; (ii) conversely, the dissolution process creates porosity and decreases the P-wave velocity of grain-supported microstructures if the mineralogical composition of the grains is not previously stabilized. These two diagenetic processes thus depend on the primary microstructures and mineralogy of the sediments. This work aims to explain the variations in porosity and P-wave velocity for each defined primary microstructure. A 1-D seismogram is then built to highlight seismic reflectors with a metre-scale resolution. These reflectors are associated with several geological contrasts. Hard kicks (positive amplitude reflectors) match well with exposure surfaces related to palaeosols. They correspond to contrasts between non-modified primary microstructures and highly neomorphosed microstructures. Conversely, soft kicks (negative amplitude reflectors) are linked with diagenetic contrasts (e.g. neomorphosed mi-crostructures versus non-modified primary microstructures) and sedimentary contrasts that can be overprinted by diagenesis (e.g. neomorphosed mud-supported microstructures versus dissolved grain-supported microstructures). This study highlights that high-resolution seismic reflectors of lacustrine and palustrine carbonates are strongly related to the spatial contrasts of primary microstructures overprinted by early diagenesis.

4. Fluid Substitution and Shear Weakening in Clay-Bearing Sandstone at Seismic Frequencies

   H. Yin ,  J. Borgomano ,  S. Wang ,  M. Tiennot ,  and  Y. Fortin

   Journal of Geophysical Research: Solid Earth, 2019

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   Abstract Using the forced oscillation method and the ultrasonic transmission method, we measure the elastic moduli of a clay-bearing Thüringen sandstone under dry and water-saturated conditions in a broad frequency band at [0.004–10, 106] Hz for different differential pressures up to 30 MPa. Under water-saturated condition, clear dispersion and attenuation for Young’s modulus, Poisson’s ratio, and Bulk modulus are observed at seismic frequencies, except for shear modulus. The measured dispersion and attenuation are mainly attributed to the drained/undrained transition, which considers the experimentally undrained boundary condition. Gassmann’s predictions are consistent with the measured undrained bulk moduli but not with the shear moduli. Clear shear weakening is observed, and this water-softening effect is stronger at seismic frequencies than at ultrasonic frequencies where stiffening effect related to squirt flow may mask real shear weakening. The reduction in surface free energy due to chemical interaction between pore fluid and rock frame, which is not taken into account by Gassmann’s theory, is the main reason for the departure from Gassmann’s predictions, especially for this rock containing a large number of clay minerals.

5. Cracked, porous rocks and fluids: Moon and earth paradox

   J. Borgomano ,  J. Fortin ,  and  Y. Guéguen

   Minerals, 2019

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   Elastic wave velocities are key parameters in geosciences. In seismology at a large scale, or in seismic exploration at a more local and shallower scale, they were the main source of information for a long time. At the time of the Apollo mission, Anderson explained the unexpected result of very low velocities in Moon surface rocks by an intense cracking resulting from meteoritic impacts. Yet, it was also known that the Q factor was high. This could appear as a paradox. In the shallow layers of the Earth, rocks are porous. These shallow layers are of major importance in the Earth since they contain fluids. This is why velocities are higher and Q values lower in the Earth’s shallow layers than in the Moon’s shallow layers. Cracks have a determining effect on elastic properties because they are very compliant. Fluids also play a key role. Combining poroelasticity and effective elasticity, two independent theories much developed since the time of the Apollo mission, makes it possible to revisit the contrasting results observed in the Moon case and in the Earth case. Experimental results obtained on cracked synthetic glass show that dry cracks result in a strong decrease in velocity. On the other hand, saturated porous limestones exhibit a strong frequency-dependent attenuation when thermally cracked. The presence of fluid is the key factor.

6. Physical and mechanical properties of thermally cracked andesite under pressure

   Z. Li ,  J. Fortin ,  A. Nicolas ,  D. Deldicque ,  and  Y. Guéguen

   Rock Mechanics and Rock Engineering, 2019

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   The effects of thermal crack damage on the physical properties and rupture processes of andesite were investigated under triaxial deformation at room temperature. Thermal cracking was induced by slowly heating and cooling samples. The effects of heat treatment temperatures ranging between 500 °C and 1100 °C on the P-wave velocities and on the microstructure were investigated. Then, the mechanical properties of andesite samples treated at 930 °C were investigated under triaxial stress at room temperature using constant strain rate tests and confining pressures ranging between 0 and 30 MPa. Similar triaxial experiments were conducted on non-heat-treated samples. Our results show that: (1) for heat treatments at temperatures below 500 °C, no significant changes in the physical properties are observed; (2) for heat treatments in the temperature range of 500–1100 °C, crack density increases; and (3) thermal cracking has no influence on the onset of dilatancy but increases the strength of the heat-treated samples. This last result is counterintuitive, but seems to be linked with the presence of a small fraction of clay (3%) in the non-heat-treated andesite. Indeed, for heat treatment above 500 °C, some clay melting is observed and contributes to sealing the longest cracks.

7. Forced oscillation measurements of seismic wave attenuation and stiffness moduli dispersion in glycerine-saturated Berea sandstone

   S. Chapman ,  J. Borgomano ,  H. Yin ,  J. Fortin ,  and  B. Quintal

   Geophysical Prospecting, 2019

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   Fluid pressure diffusion occurring on the microscopic scale is believed to be a significant source of intrinsic attenuation of mechanical waves propagating through fully saturated porous rocks. The so‐called squirt flow arises from compressibility heterogeneities in the microstructure of the rocks. To study squirt flow experimentally at seismic frequencies the forced oscillation method is the most adequate, but such studies are still scarce. Here we present the results of forced hydrostatic and axial oscillation experiments on dry and glycerine‐saturated Berea sandstone, from which we determine the dynamic stiffness moduli and attenuation at micro‐seismic and seismic frequencies (0.004–30 Hz). We observe frequency‐dependent attenuation and the associated moduli dispersion in response to the drained–undrained transition (∼0.1 Hz) and squirt flow (>3 Hz), which are in fairly good agreement with the results of the corresponding analytical solutions. The comparison with very similar experiments performed also on Berea sandstone in addition shows that squirt flow can potentially be a source of wave attenuation across a wide range of frequencies because of its sensitivity to small variations in the rock microstructure, especially in the aspect ratio of micro‐cracks or grain contacts.

2018

1. Anomalous Vp/Vs Ratios at Seismic Frequencies Might Evidence Highly Damaged Rocks in Subduction Zones

   L. Pimienta ,  A. Schubnel ,  M. Violay ,  J. Fortin ,  Y. Guéguen ,  and  H. Lyon-Caen

   Geophysical Research Letters, 2018

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   Abstract Unusually high compressional (P) to shear (S) wave velocity ratios (Vp/Vs) were measured at different subduction zones and interpreted as fluid-pressurized regions. Because no laboratory data reported such high values in isotropic rocks, mineralogical or anisotropic constrains were assumed. However, fluid-saturated rocks’ Vp/Vs is a frequency-dependent property so that standard laboratory measurements cannot be directly upscaled to the field. Using a new methodology, we measured the property in the elastic regime relevant to field measurements for diverse lithologies. We obtained extreme Vp/Vs values, consistent with those reported at seismic frequency in the field. Consistently with a model, it shows that if high fluid pressure is a key factor, anomalous Vp/Vs values could evidence intense degrees of microfracturation in isotropic rocks, whichever its mineralogical content. The permeability of these regions could be larger than 10−16 m2.

2. Development and Recovery of Stress-Induced Elastic Anisotropy During Cyclic Loading Experiment on Westerly Granite

   F. Passelègue ,  L. Pimienta ,  A. Faulkner ,  J. Fortin ,  and  Y. Guéguen

   Geophysical Research Letters, 2018

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   Abstract In the upper crust, where brittle deformation mechanisms dominate, the development of crack networks subject to anisotropic stress fields generates stress-induced elastic anisotropy. Here a rock specimen of Westerly granite was submitted to differential stress cycles (i.e., loading and unloading) of increasing amplitudes, up to failure and under upper crustal conditions. Combined records of strains, acoustic emissions, and P and S elastic wave anisotropies demonstrate that increasing differential stress promotes crack opening, sliding, and propagation subparallel to the main compressive stress orientation. However, the significant elastic anisotropies observed during loading (≥20%) almost vanish upon stress removal, demonstrating that in the absence of stress, crack-related elastic anisotropy remains limited (≤10%). As a consequence, (i) crack-related elastic anisotropies measured in the crust will likely be a strong function of the level of differential stress, and consequently (ii) continuous monitoring of elastic wave velocity anisotropy along faults could shed light on the mechanism of stress accumulation during interseismic loading.

3. Elastic properties of continental carbonates: From controlling factors to an applicable model for acoustic-velocity predictions

   J-B. Regnet ,  J. Fortin ,  A. Nicolas ,  M. Pellerin ,  and  Y. Guéguen

   Geophysics, 2018

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   We have provided new insights into the controlling factors of elastic properties in continental carbonate rocks and introduced an applicable model for acoustic-velocity predictions in such a medium. Petrophysical properties (porosity, permeability, P- and S-wave velocities) from laboratory measurements have been coupled with thin-section observations and characterizations, and X-ray diffraction (XRD) analyses. A major achievement is the establishment of the link between the mineralogical composition and the P- and S-wave velocity dispersion at a given porosity. This reflects the subtle interplay between physicochemical and biological precipitation of continental carbonates, which can also be associated with a strong influence of detrital mineralogical inputs. The result is a mineralogical commixture, coupled to a wide array of pore types inherited from the strong ability of carbonate rocks to undergo diagenetic alteration. The proposed model takes into account the elastic moduli of the minerals, porosity, and pore shape, and it is based on the effective medium theory. We have considered the case in which the medium contained randomly oriented pores with different aspect ratios. Overall, the fit between the predicted trends and the experimental data is fairly good, especially for calcite and quartz matrix mineralogy. The results are even better when considering mineralogy inferred from XRD data, although in some case, and despite the aspect ratio variation in both simulations, the model fails to accurately predict the P-wave velocities. This probably means that another factor is at stake beside mineralogy. This can be explained by the limitation of the effective medium approach, which oversimplifies the reality and fails to account for the variability of some aspect ratio from one inclusion to another.

4. KG²B, a collaborative benchmarking exercise for estimating the permeability of the Grimsel granodiorite – Part 1: measurements, pressure dependence and pore-fluid effects

   C David ,  J Wassermann ,  F Amann ,  D A Lockner ,  E H Rutter ,  T Vanorio ,  A Amann Hildenbrand ,  J Billiotte ,  T Reuschlé ,  D Lasseux ,  J Fortin ,  R Lenormand ,  A P S Selvadurai ,  P G Meredith ,  J Browning ,  T M Mitchell ,  D Loggia ,  F Nono ,  J Sarout ,  L Esteban ,  C Davy ,  L Louis ,  G Boitnott ,  C Madonna ,  E Jahns ,  M Fleury ,  G Berthe ,  P Delage ,  P Braun ,  D Grégoire ,  L Perrier ,  P Polito ,  Y Jannot ,  A Sommier ,  B Krooss ,  R Fink ,  Q Hu ,  J Klaver ,  and  A Clark

   Geophysical Journal International, 2018

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   Measuring the permeability of tight rocks remains a challenging task. In addition to the traditional sources of errors that affect more permeable formations (e.g. sample selection, non-representative specimens, disturbance introduced during sample acquisition and preparation), tight rocks can be particularly prone to solid–fluid interactions and thus more sensitive to the methods, procedures and techniques used to measure permeability. To address this problem, it is desirable to collect, for a single material, measurements obtained by different methods and pore-fluids. For that purpose a collaborative benchmarking exercise involving 24 laboratories was organized for measuring the permeability of a single low permeability material, the Grimsel granodiorite, at a common effective confining pressure (5 MPa). The objectives of the benchmark were: (i) to compare the results for a given method, (ii) to compare the results between different methods, (iii) to analyze the accuracy of each method, (iv) to study the influence of experimental conditions (especially the nature of pore fluid), (v) to discuss the relevance of indirect methods and models and finally (vi) to suggest good practice for low permeability measurements. In total 39 measurements were collected that allowed us to discuss the influence of (i) pore-fluid, (ii) measurement method, (iii) sample size and (iv) pressure sensitivity. Discarding some outliers from the bulk data set (4 out of 39) an average permeability of 1.11 × 10−18 m² with a standard deviation of 0.57 × 10−18 m² was obtained. The most striking result was the large difference in permeability for gas measurements compared to liquid measurements. Regardless of the method used, gas permeability was higher than liquid permeability by a factor approximately 2 (kgas = 1.28 × 10−18 m² compared to kliquid = 0.65 × 10−18 m²). Possible explanations are that (i) liquid permeability was underestimated due to fluid-rock interactions (ii) gas permeability was overestimated due to insufficient correction for gas slippage and/or (iii) gases and liquids do not probe exactly the same porous networks. The analysis of Knudsen numbers shows that the gas permeability measurements were performed in conditions for which the Klinkenberg correction is sufficient. Smaller samples had a larger scatter of permeability values, suggesting that their volume were below the Representative Elementary Volume. The pressure dependence of permeability was studied by some of the participating teams in the range 1–30 MPa and could be fitted to an exponential law k = ko.exp(–γPeff) with γ = 0.093 MPa−1. Good practice rules for measuring permeability in tight materials are also provided.

5. KG²B, a collaborative benchmarking exercise for estimating the permeability of the Grimsel granodiorite—Part 2: modelling, microstructures and complementary data

   C David ,  J Wassermann ,  F Amann ,  J Klaver ,  C Davy ,  J Sarout ,  L Esteban ,  E H Rutter ,  Q Hu ,  L Louis ,  P Delage ,  D A Lockner ,  A P S Selvadurai ,  T Vanorio ,  A Amann Hildenbrand ,  P G Meredith ,  J Browning ,  T M Mitchell ,  C Madonna ,  J Billiotte ,  T Reuschlé ,  D Lasseux ,  J Fortin ,  R Lenormand ,  D Loggia ,  F Nono ,  G Boitnott ,  E Jahns ,  M Fleury ,  G Berthe ,  P Braun ,  D Grégoire ,  L Perrier ,  P Polito ,  Y Jannot ,  A Sommier ,  B Krooss ,  R Fink ,  and  A Clark

   Geophysical Journal International, 2018

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   Measuring and modelling the permeability of tight rocks remains a challenging task. In addition to the traditional sources of errors that affect more permeable formations (e.g. sample selection, non-representative specimens, disturbance introduced during sample acquisition and preparation), tight rocks can be particularly prone to solid–fluid interactions and thus more sensitive to the methods, procedures and techniques used to measure permeability. To address this problem, it is desirable to collect, for a single material, measurements obtained by different methods and pore fluids. For that purpose, a benchmarking exercise involving 24 laboratories was organized for measuring and modelling the permeability of a single low-permeability material, the Grimsel granodiorite. The objectives of the benchmark were: (i) to compare the results for a given method, (ii) to compare the results between different methods, (iii) to analyse the accuracy of each method, (iv) to study the influence of experimental conditions (especially the nature of pore fluid), (v) to discuss the relevance of indirect methods and models and finally (vi) to suggest good practice for low-permeability measurements. To complement the data set of permeability measurements presented in a companion paper, we focus here on (i) quantitative analysis of microstructures and pore size distribution, (ii) permeability modelling and (iii) complementary measurements of permeability anisotropy and poroelastic parameters. Broad ion beam—scanning electron microscopy, micro-computerized tomography, mercury injection capillary pressure (MICP) and nuclear magnetic resonance (NMR) methods were used to characterize the microstructures and provided the input parameters for permeability modelling. Several models were used: (i) basic statistical models, (ii) 3-D pore network and effective medium models, (iii) percolation model using MICP data and (iv) free-fluid model using NMR data. The models were generally successful in predicting the actual range of measured permeability. Statistical models overestimate the permeability because they do not adequately account for the heterogeneity of the crack network. Pore network and effective medium models provide additional constraints on crack parameters such as aspect ratio, aperture, density and connectivity. MICP and advanced microscopy techniques are very useful tools providing important input data for permeability estimation. Permeability measured—orthogonal to foliation is lower that—parallel to foliation. Combining the experimental and modelling results provide a unique and rich data set.

6. Seismic-refraction field experiments on Galapagos Islands: A quantitative tool for hydrogeology

   M. Adelinet ,  C. Domínguez ,  J. Fortin ,  and  S. Violette

   Journal of Applied Geophysics, 2018

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   Due to their complex structure and the difficulty of collecting data, the hydrogeology of basaltic islands remains misunderstood, and the Galapagos islands are not an exception. Geophysics allows the possibility to describe the subsurface of these islands and to quantify the hydrodynamical properties of its ground layers, which can be useful to build robust hydrogeological models. In this paper, we present seismic refraction data acquired on Santa Cruz and San Cristobal, the two main inhabited islands of Galapagos. We investigated sites with several hydrogeological contexts, located at different altitudes and at different distances to the coast. At each site, a 2D P-wave velocity profile is built, highlighting unsaturated and saturated volcanic layers. At the coastal sites, seawater intrusion is identified and basal aquifer is characterized in terms of variations in compressional sound wave velocities, according to saturation state. At highlands sites, the limits between soils and lava flows are identified. On San Cristobal Island, the 2D velocity profile obtained on a mid-slope site (altitude 150m), indicates the presence of a near surface freshwater aquifer, which is in agreement with previous geophysical studies and the hydrogeological conceptual model developed for this island. The originality of our paper is the use of velocity data to compute field porosity based on poroelasticity theory and the Biot-Gassmann equations. Given that porosity is a key parameter in quantitative hydrogeological models, it is a step forward to a better understanding of shallow fluid flows within a complex structure, such as Galapagos volcanoes.

7. Comportement des roches en température, Chapitre dans le Manuel de mécanique des roches, Tome V, Presse des Mines

   J. Fortin ,  M. Gasc-Barbier ,  and  V. Merrien-Soukatchoff

   2018

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2017

1. Brittle and semibrittle creep of Tavel limestone deformed at room temperature

   A. Nicolas ,  J. Fortin ,  J. B. Regnet ,  B. A. Verberne ,  O. Plümper ,  A. Dimanov ,  C. J. Spiers ,  and  Y. Guéguen

   Journal of Geophysical Research: Solid Earth, 2017

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   Abstract Deformation and failure mode of carbonate rocks depend on the confining pressure. In this study, the mechanical behavior of a limestone with an initial porosity of 14.7% is investigated at constant stress. At confining pressures below 55 MPa, dilatancy associated with microfracturing occurs during constant stress steps, ultimately leading to failure, similar to creep in other brittle media. At confining pressures higher than 55 MPa, depending on applied differential stress, inelastic compaction occurs, accommodated by crystal plasticity and characterized by constant ultrasonic wave velocities, or dilatancy resulting from nucleation and propagation of cracks due to local stress concentrations associated with dislocation pileups, ultimately causing failure. Strain rates during secondary creep preceding dilative brittle failure are sensitive to stress, while rates during compactive creep exhibit an insensitivity to stress indicative of the operation of crystal plasticity, in agreement with elastic wave velocity evolution and microstructural observations.

2. Elastic Dispersion and Attenuation in Fully Saturated Sandstones: Role of Mineral Content, Porosity, and Pressures

   L. Pimienta ,  Jan . Borgomano ,  J. Fortin ,  and  Y. Guéguen

   Journal of Geophysical Research: Solid Earth, 2017

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   Abstract Because measuring the frequency dependence of elastic properties in the laboratory is a technical challenge, not enough experimental data exist to test the existing theories. We report measurements of three fluid-saturated sandstones over a broad frequency band: Wilkenson, Berea, and Bentheim sandstones. Those sandstones samples, chosen for their variable porosities and mineral content, are saturated by fluids of varying viscosities. The samples elastic response (Young’s modulus and Poisson’s ratio) and hydraulic response (fluid flow out of the sample) are measured as a function of frequency. Large dispersion and attenuation phenomena are observed over the investigated frequency range. For all samples, the variation at lowest frequency relates to a large fluid flow directly measured out of the rock samples. These are the cause (i.e., fluid flow) and consequence (i.e., dispersion/attenuation) of the transition between drained and undrained regimes. Consistently, the characteristic frequency correlates with permeability for each sandstone. Beyond this frequency, a second variation is observed for all samples, but the rocks behave differently. For Berea sandstone, an onset of dispersion/attenuation is expected from both Young’s modulus and Poisson’s ratio at highest frequency. For Bentheim and Wilkenson sandstones, however, only Young’s modulus shows dispersion/attenuation phenomena. For Wilkenson sandstone, the viscoelastic-like dispersion/attenuation response is interpreted as squirt flow. For Bentheim sandstone, the second effect does not fully follow such response, which could be due to a lower accuracy in the measured attenuation or to the occurence of another physical effect in this rock sample.

3. Dispersion and attenuation measurements of the elastic moduli of a dual-porosity limestone

   J. V. M. Borgomano ,  L. Pimienta ,  J. Fortin ,  and  Y. Guéguen

   Journal of Geophysical Research: Solid Earth, 2017

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   Abstract The dispersion and the attenuation of the elastic moduli of a Lavoux limestone have been measured over a large frequency range: 10−3 Hz to 101 Hz and 1 MHz. The studied sample comes from a Dogger outcrop of Paris Basin and has the particularity to have a bimodal porosity distribution, with an equal proportion of intragranular microporosity and intergranular macroporosity. In addition to ultrasonic measurements, two different stress-strain methods have been used in a triaxial cell to derive all the elastic moduli at various differential pressures. The first method consists of hydrostatic stress oscillations (f∈[0.004;0.4] Hz), using the confining pressure pump, from which the bulk modulus was deduced. The second method consists of axial oscillations (f∈[0.01;10] Hz), using a piezoelectric oscillator on top of the sample, from which Young’s modulus and Poisson’s ratio were deduced. With the assumption of an isotropic medium, the bulk modulus (K) and the shear modulus (G) can also be computed from the axial oscillations. The sample was studied under dry, glycerin- and water-saturated conditions, in order to scale frequency by the viscosity of the fluid. Results show a dispersion at around 200 Hz for water-saturated conditions, affecting all the moduli except the shear modulus. This dispersion is related to the drained/undrained transition, and the bulk modulus deduced from the axial and hydrostatic oscillations are consistent with each other and with Biot-Gassmann’s equations. No dispersion has been detected beyond that frequency. This was interpreted as the absence of squirt flow or local diffusion between the microporous oolites and the macropores.

4. Micromechanical constitutive model for low-temperature constant strain rate deformation of limestones in the brittle and semi-brittle regime

   A. Nicolas ,  J. Fortin ,  and  Y. Guéguen

   Geophysical Journal International, 2017

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   Deformation and failure of rocks are important for a better understanding of many crustal geological phenomena such as faulting and compaction. In carbonate rocks among others, low-temperature deformation can either occur with dilatancy or compaction, having implications for porosity changes, failure and petrophysical properties. Hence, a thorough understanding of all the micromechanisms responsible for deformation is of great interest. In this study, a constitutive model for the low-temperature deformation of low-porosity (\<20 per cent) carbonate rocks is derived from the micromechanisms identified in previous studies. The micromechanical model is based on (1) brittle crack propagation, (2) a plasticity law (interpreted in terms of dislocation glide without possibility to climb) for porous media with hardening and (3) crack nucleation due to dislocation pile-ups. The model predicts stress–strain relations and the evolution of damage during deformation. The model adequately predicts brittle behaviour at low confining pressures, which switches to a semi-brittle behaviour characterized by inelastic compaction followed by dilatancy at higher confining pressures. Model predictions are compared to experimental results from previous studies and are found to be in close agreement with experimental results. This suggests that microphysical phenomena responsible for the deformation are sufficiently well captured by the model although twinning, recovery and cataclasis are not considered. The porosity range of applicability and limits of the model are discussed.

5. New method for measuring compressibility and poroelasticity coefficients in porous and permeable rocks

   L. Pimienta ,  J. Fortin ,  and  Y. Guéguen

   Journal of Geophysical Research: Solid Earth, 2017

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   Abstract Over the last decades, a large understanding has been gained on the elastic properties of rocks. Rocks are, however, porous materials, which properties depend on both response of the bulk material and of the pores. Because in that case both the applied external pressure and the fluid pressure play a role, different poroelasticity coefficients exist. While theoretical relations exist, measuring precisely those different coefficients remains an experimental challenge. Accounting for the different experimental complexities, a new methodology is designed that allows attaining accurately a large set of compressibility and poroelasticity coefficients in porous and permeable rocks. This new method relies on the use of forced confining or pore fluid pressure oscillations. In total, seven independent coefficients have been measured using three different boundary conditions. Because the usual theories predict only four independent coefficients, this overdetermined set of data can be checked against existing thermodynamic relations. Measurements have been performed on a Bentheim sandstone under, water- and glycerine-saturated conditions for different values of confining and pore fluid pressure. Consistently with the poroelasticity theory, the effect of the fluid bulk modulus is observed under undrained conditions but not under drained ones. Using thermodynamic relations, (i) the unjacketed, quartz, and skeleton (Zimmerman’s relation) bulk moduli fit, (ii) the drained and undrained properties fit, and (iii) it is directly inferred from the measurements that the pore skeleton compressibility Cϕ is expected to be constant with pressure and to be exceedingly near the bulk skeleton Cs and mineral Cm compressibility coefficients.

2016

1. Brittle and semi-brittle behaviours of a carbonate rock: influence of water and temperature

   A. Nicolas ,  J. Fortin ,  J.B. Regnet ,  A. Dimanov ,  and  Y. Guéguen

   Geophysical Journal International, 2016

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   Inelastic deformation can either occur with dilatancy or compaction, implying differences in porosity changes, failure and petrophysical properties. In this study, the roles of water as a pore fluid, and of temperature, on the deformation and failure of a micritic limestone (white Tavel limestone, porosity 14.7 per cent) were investigated under triaxial stresses. For each sample, a hydrostatic load was applied up to the desired confining pressure (from 0 up to 85 MPa) at either room temperature or at 70 °C. Two pore fluid conditions were investigated at room temperature: dry and water saturated. The samples were deformed up to failure at a constant strain rate of ∼10−5 s−1. The experiments were coupled with ultrasonic wave velocity surveys to monitor crack densities. The linear trend between the axial crack density and the relative volumetric strain beyond the onset of dilatancy suggests that cracks propagate at constant aspect ratio. The decrease of ultrasonic wave velocities beyond the onset of inelastic compaction in the semi-brittle regime indicates the ongoing interplay of shear-enhanced compaction and crack development. Water has a weakening effect on the onset of dilatancy in the brittle regime, but no measurable influence on the peak strength. Temperature lowers the confining pressure at which the brittle–semi-brittle transition is observed but does not change the stress states at the onset of inelastic compaction and at the post-yield onset of dilatancy.

2. Modelling the drained/undrained transition: effect of the measuring method and the boundary conditions

   L. Pimienta ,  J. Borgomano ,  J. Fortin ,  and  Y. Guéguen

   Geophysical Prospecting, 2016

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   The dependence of fluid‐saturated rocks’elastic properties to the measuring frequency is related to fluid‐flow phenomena at different scales. In the frequency range of [10−3,10^6]Hz, for fully saturated rocks, two phenomena have been experimentally documented: (i) the drained/undrained transition (i.e., global flow), and (ii) the relaxed/unrelaxed transition (i.e., local flow). When investigating experimentally those effects or comparing different measurements in rocks, one needs to account for both the boundary conditions involved and the method of measurement used. A one‐dimensional poroelastic model is presented, which aims at calculating the expected poroelastic response during an experiment. The model is used to test different sets of boundary conditions, as well as the role of the measuring setup, i.e., local (strain gauges) or global (linear variable differential transformer) strain measurement. Four properties are predicted and compared with the measurements, i.e., bulk modulus, bulk attenuation, pseudo‐Skempton coefficient, and pore pressure phase shift. For the drained/undrained transition, because fluid pressure may not be homogeneous in the sample, local and global measurements are predicted to differ. Furthermore, the existence of a dead volume at both sample’s ends is shown to be important. Due to the existence of the dead volume, an interplay between sample’s and dead volumes’s storage capacity determines both the magnitudes and the frequency dependence of the dispersion/attenuation measurements. The predicted behaviours are shown to be consistent with the measurements recently reported on very compressible and porous sandstone samples.

3. Frequency, pressure, and strain dependence of nonlinear elasticity in Berea Sandstone

   J. Rivière ,  L. Pimienta ,  M. Scuderi ,  T. Candela ,  P. Shokouhi ,  J. Fortin ,  A. Schubnel ,  C. Marone ,  and  P. Johnson

   Geophysical Research Letters, 2016

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   Abstract Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi-static ( ) and dynamic (few kilohertz) nonlinear elastic response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on strain amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2–3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1f appears frequency independent. This result corroborates previous studies showing that the nonlinear elasticity of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear elasticity. These findings can be used to improve theories relating the macroscopic elastic response to microstructural features.

4. Dispersions and attenuations in a fully saturated sandstone: Experimental evidence for fluid flows at different scales

   L. Pimienta ,  J. Fortin ,  J. Borgomano ,  and  Y. Guéguen

   The Leading Edge, 2016

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   Dispersion and attenuation of elastic waves have been observed in crustal rocks. Existing theories and experimental measurements evidenced the existence of different energy-loss mechanisms. In rocks fully saturated by a Newtonian fluid, one major candidate is fluid flow at different scales, separating three regimes: the drained, undrained, and unrelaxed regimes. Here, two elastic transitions, between these three regimes, are investigated. Both the cause and the consequence of the drained/undrained transition are evidenced. Because the second transition measured occurs at higher frequency, where no global fluid flow occurs, it in turn is associated to the undrained/unrelaxed transition (or squirt flow). For both transitions, the amount of open microcracks seems to be the major contributor to the magnitudes of attenuation.

5. Effect of fluids and frequencies on Poisson’s ratio of sandstone samples

   L. Pimienta ,  J. Fortin ,  and  Y. Guéguen

   Geophysics, 2016

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   Poisson’s ratio ν is an important parameter when interpreting measured geophysical and seismic data. For an isotropic medium, it directly relates to the ratio of P- and S-wave velocities. We have measured ν as a function of pressure and frequency in fluid-saturated sandstones. The method of measuring ν was first tested as a function of pressure and frequency using standard samples. The phase shift φ between radial and axial strains was also measured. For all standard samples, such as the linear viscoelastic Plexiglas, the data indicated that tan(φ) correlated with ν and related to a dissipation on ν. Then, ν and tan(φ) were measured as a function of pressure and frequency for two dry and fluid-saturated Fontainebleau sandstone samples. Under dry conditions, no frequency dependence and very small pressure dependence were observed. Unusual behaviors were observed under fluid-saturated conditions. In particular, ν of one sample indicated a frequency-dependent bell-shaped dispersion under water and glycerin saturation that correlated with peaks in tan(φ). Plotting the measurements as a function of apparent frequency (i.e., normalizing by the fluid viscosity) indicated a good fit between the water- and glycerin-saturated measurements. The bell-shaped dispersion in ν that was observed for one particular sandstone held for all effective pressures. These variations fully correlated with the peaks of tan(φ) observed. Our results can be interpreted using fluid flow and effective medium theories in the case of a porous microcracked rock. Drained/undrained and relaxed/unrelaxed transitions have frequency and magnitude of variations that are consistent with the measurements. The rock sample microcrack density strongly affects this frequency dependence. The inferred VP/VS ratio at low effective pressures also indicates a large frequency-dependent bell-shaped dispersion. The parameter tan(φ) is a clear indicator of the frequency-dependent dissipation of ν and relates to the attenuation of P- and S-waves.

2015

1. Bulk modulus dispersion and attenuation in sandstones

   L. Pimienta ,  J. Fortin ,  and  Y. Guéguen

   Geophysics, 2015

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   We report experimental data on the frequency dependence of bulk elastic modulus in porous sandstones. A new methodology was developed to investigate the dispersion/attenuation phenomena on a rock’s bulk modulus K for varying confining pressures in the range of 1–50 MPa and fluids of varying viscosities (i.e., air, glycerin, and water). This methodology combined (1) ultrasonic (i.e., f∼0.5  MHz) P- and S-wave velocity measurements, leading to the high-frequency (HF) KHF, (2) stress-strain measurements from forced periodic oscillations of confining pressure at low-frequency (LF) ranges (i.e., f∈[4  10-3;4  10-1]  Hz), leading to KLF and QK−1, and (3) pore-pressure measurement to document the induced fluid-flow in the LF range (i.e., f∈[4  10-3;4  10-1]  Hz). The stress-strain method was first checked using three standard samples: glass, gypsum, and Plexiglas samples. Over the frequency and pressure range of the apparatus KLF was stable and accurate and the lowest measurable LF attenuation was QK−1∼0.01. The methodology was applied to investigate Fontainebleau sandstone samples of 7% and 9% porosity. The KLF and QK-1 exhibited correlated variations, which also correlated with an experimental evidence of frequency-dependent fluid-flow out of the sample. Attenuation peaks as high as QK-1∼0.15 and QK-1∼0.25 are measured. The attenuation/dispersion measured under glycerin saturation was compared to Biot-Gassmann predictions. The overall behavior of one sample was consistent with a dispersion/attenuation characteristic of the drained/undrained transition. On the reverse, the other sample exhibited exotic behaviors as the measurements were underestimated by the drained/undrained transition and indicated a direct transition from drained to unrelaxed domain. These different behaviors were consistent with the values of the critical frequencies expected for the drained/undrained (i.e., f1) and relaxed/unrelaxed (i.e., f2) transitions.

2. Brittle creep and subcritical crack propagation in glass submitted to triaxial conditions

   C. Mallet ,  J. Fortin ,  Y. Guéguen ,  and  F. Bouyer

   Journal of Geophysical Research: Solid Earth, 2015

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   An experimental work is presented that aimed at improving our understanding of the mechanical evolution of cracks under brittle creep conditions. Brittle creep may be an important slow deformation process in the Earth’s crust. Synthetic glass samples have been used to observe and document brittle creep due to slow crack-propagation. A crack density of 0.05 was introduced in intact synthetic glass samples by thermal shock. Creep tests were performed at constant confining pressure (15 MPa) for water saturated conditions. Data were obtained by maintaining the differential-stress constant in steps of 24 h duration. A set of sensors allowed us to record strains and acoustic emissions during creep. The effect of temperature on creep was investigated from ambient temperature to 70°C. The activation energy for crack growth was found to be 32 kJ/mol. In secondary creep, a large dilatancy was observed that did not occur in constant strain rate tests. This is correlated to acoustic emission activity associated with crack growth. As a consequence, slow crack growth has been evidenced in glass. Beyond secondary creep, failure in tertiary creep was found to be a progressive process. The data are interpreted through a previously developed micromechanical damage model that describes crack propagation. This model allows one to predict the secondary brittle creep phase and also to give an analytical expression for the time to rupture. Comparison between glass and crystalline rock indicates that the brittle creep behavior is probably controlled by the same process even if stress sensitivity for glass is lower than for rocks.

3. Role of the pore fluid in crack propagation in glass

   C. Mallet ,  J. Fortin ,  Y. Guéguen ,  and  F. Bouyer

   Mechanics of Time-Dependent Materials, 2015

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   We investigate pore fluid effects due to surface energy variation or due to chemical corrosion in cracked glass. Both effects have been documented through experimental tests on cracked borosilicate glass samples. Creep tests have been performed to investigate the slow crack propagation behavior. We compared the dry case (saturated with argon gas), the nonreactive water saturated case (commercial mineralized water), and the distilled and deionized water saturated case (pure water). Chemical corrosion effects have been observed and evidenced from pH and water composition evolution of the pure water. Then, the comparison of the dry case, the mineral water saturated case, and the corrosion case allow to (i) evidence the mechanical effect of the presence of a pore fluid and (ii) show also the chemical effect of a glass dissolution. Both effects enhance subcritical crack propagation.

4. Acoustic and reservoir properties of microporous carbonate rocks: Implication of micrite particle size and morphology

   J. B. Regnet ,  P. Robion ,  C. David ,  J. Fortin ,  B. Brigaud ,  and  B. Yven

   Journal of Geophysical Research: Solid Earth, 2015

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   Abstract This integrated study provides significant insight into parameters controlling the acoustic and reservoir properties of microporous limestones, improving the knowledge of the relationships among petrophysic and microstructural content. Petrophysical properties measured from laboratory and logging tools (porosity, permeability, electrical conductivity, and acoustic properties) have been coupled with thin section and scanning electron microscope observations on the EST205 borehole from the Oxfordian limestone aquifer of the eastern part of the Paris Basin. A major achievement is the establishment of the link between micrite microtexture types (particle morphology and nature of intercrystal contacts) and the physical response, introducing a new effective and interesting rock-typing approach for microporous reservoirs. Fluid-flow properties are enhanced by the progressive augmentation of intercrystalline microporosity and associated pore throat diameter, as the coalescence of micrite particles decreases. Concerning acoustic properties, the slow increase of P wave velocity can be seen as a reflection of crystal size and growing contact cementation leading to a more cohesive and stiffer micrite microtexture. By applying poroelasticity theory on our samples, we show that velocity dispersion can be a very useful tool for data discrimination in carbonates. This dispersion analysis highlights the presence of microcracks in the rocks, and their overall effect on acoustic and transport properties. The presence of microcracks is also confirmed with observations and permeability measurements under high confining pressure. Finally, a possible origin of high porous levels in neritic limestones is a mineralogical transformation of carbonates through freshwater-related diagenesis during subaerial exposure time. Finally, by applying poroelasticity theory on our samples, we show that velocity dispersion can be a very useful tool for data discrimination in carbonates.

5. Experimental study of Young’s modulus dispersion and attenuation in fully saturated sandstones

   L. Pimienta ,  J. Fortin ,  and  Y. Guéguen

   Geophysics, 2015

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   Although seismic wave dispersion and attenuation have been found to occur in sedimentary rocks, it remains challenging to experimentally observe these effects. A new experimental setup has been developed to measure the Young’s modulus and Poisson’s ratio of rocks over a wide range in pressure (Pc∈[0;30]  MPa) and frequency (f∈[5.10−3;102]  Hz). Calibration with standard samples determined the following: (1) no dependence of the apparatus to pressure and frequency and (2) a good fit between published data and the measured and inferred elastic properties. The measured Young’s modulus dispersion and attenuation of Plexiglas were also consistent with the published data. The Young’s modulus and the attenuation of Fontainebleau sandstone samples saturated by water and glycerin were then measured. Although small variations were observed for one sample, the second one exhibited strong pressure- and frequency-dependent variations of Young’s modulus and attenuation. A frequency-dependent fluid flow was simultaneously measured. The characteristic frequency for these variations was highly fluid dependent. Accounting for the in situ fluids’ viscosity using an apparent frequency parameter, we determined the Young’s modulus and attenuation of a fluid-saturated Fontainebleau sandstone over an apparent frequency band of f*∈[10−3;105]  Hz. The measurements under water and glycerin saturation compared favorably, and two frequency-dependent phenomena were observed that were interpreted as the drained/undrained and undrained/unrelaxed transitions. The undrained/unrelaxed transition occurred in a large frequency range, which was attributed to a distribution in aspect ratio of the rock’s microcracks.

6. Influence of microporosity distribution on the mechanical behavior of oolithic carbonate rocks

   J.B. Regnet ,  C. David ,  J. Fortin ,  P. Robion ,  Y. Makhloufi ,  and  P.Y. Collin

   Geomechanics for Energy and the Environment, 2015

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   The mechanical behavior of oolithic carbonate rocks was investigated for selected rocks with two different microstructural attributes: uniform (UP) and rimmed (RP) distribution of microporosity within ooids. These oolithic carbonate rocks are from the Oolithe Blanche formation, a deep saline aquifer in the Paris Basin, and a possible target for CO2 sequestration and geothermal production. Samples of similar physical properties (porosity, grain diameter, cement content) but different microporosity textures were deformed under triaxial configuration, in water saturated conditions, at 28 MPa of confining pressure, 5 MPa of pore pressure and at a temperature of 55 °C. During the experiments, acoustic velocities were monitored, and permeability was measured. The results show that the mechanical behavior of these microporous carbonates are strongly controlled by the microporosity distribution within the grains, at the origin of variations in elastic properties, mechanical strength and failure mode. The lower velocities measured in UP samples indicate a larger compliance of the whole structure. The mechanical response indicates that UP samples are characterized by a ductile behavior whereas RP samples display a brittle behavior. Using a conceptual model for the failure envelope of both rocks, our observations can be accounted for if one considers a significant variation of the critical pressure P∗, with UP samples having a lower P∗ than RP samples. The permeability evolution under stress was interpreted using a revised Kozeny–Carman equation, showing that fluid flow is strongly affected by the tortuosity of the pore space, which is controlled by the microporosity distribution within the ooids. This study brings new insight into the parameters controlling the physical and mechanical response of oolithic carbonates, and the possible impact on production of geothermal energy at depth or storativity for CO2 sequestration operations.

2014

1. Radon emanation from brittle fracturing in granites under upper crustal conditions

   A. Nicolas ,  F. Girault ,  A. Schubnel ,  E. Pili ,  F. Passelègue ,  J. Fortin ,  and  D. Deldicque

   Geophysical Research Letters, 2014

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   Abstract Radon-222, a radioactive gas naturally produced in the Earth’s crust, informs us about the migration of fluids and is sometimes considered as a potential earthquake precursor. Here we investigate the effects of mechanical and thermal damage on the radon emanation from various granites representative of the upper crust. Radon concentration measurements performed under triaxial stress and pore fluid pressure show that mechanical damage resulting from cycles of differential stress intensifies radon release up to 170 ± 22% when the sample ruptures. This radon peak is transient and results from the connection of isolated micropores to the permeable network rather than new crack surface creation per se. Heating to 850°C shows that thermal fracturing irreversibly decreases emanation by 59–97% due to the amorphization of biotites hosting radon sources. This study, and the developed protocols, shed light on the relation between radon emanation of crustal rocks, deformation, and pressure-temperature conditions.

2. Investigation of elastic weakening in limestone and sandstone samples from moisture adsorption

   L. Pimienta ,  J. Fortin ,  and  Y. Guéguen

   Geophysical Journal International, 2014

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   Elastic and mechanical weakening from water saturation are widely known to occur in sedimentary rocks, and particularly in carbonate rocks. To improve our understanding of the physics underlying this phenomenon, ultrasonic (f ∼ 0.5 MHz) elastic properties are measured on a large suite of clean limestones and sandstones at very low saturations from relative humidity (RH) variations at ambient conditions. Measurements clearly highlight an elastic weakening (i.e. decrease in elastic wave velocity) from moisture adsorption. P- and S-wave velocities are similarly affected by adsorption, but in a different way for limestones and sandstone samples. While the elastic properties of limestone samples show almost no RH dependence, a large weakening is observed for samples of Fontainebleau sandstone that increases with the samples’ porosity. The main elastic weakening effect is likely to result from adsorption of fluid at grain contacts. It thus affects particularly granular rocks such as sandstones while well-cemented limestones are not affected. The granular model from Murphy et al., accounting for surface energy effects, proves to be appropriate. Applying this model, it is shown that (i) P- and S-wave velocities have the same dependence on surface energy, which is consistent with the measurements and (ii) surface energy values obtained from the ultrasonic data using this model correlate with RH, and are consistent with the expected value for quartz crystals at vapour pressure. Yet, porosity, which relates to degree of cementation in the particular case of Fontainebleau sandstone, appears to be an additional parameter. A modified model is thus derived using the cementation model from Digby, accounting for a bonding radius at grain contact. It proves to apply well to the measured data. The fundamental difference between limestones’ and sandstones’ dependence to RH appears to be related to a microstructural difference. Saturation variations from RH increase depend on specific surface area, which is particularly low in Fontainebleau sandstones and large in microporous limestones. However elastic weakening from RH is more important in sandstones owing to their granular microstructure.

3. Experimental results on the combined effects of frequency and pressure on the dispersion of elastic waves in porous rocks

   J. Fortin ,  L. Pimienta ,  Y. Guéguen ,  A. Schubnel ,  E. C. David ,  and  M. Adelinet

   The Leading Edge, 2014

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   Experimental results are presented on the dispersive nature of elastic waves in porous rocks. These results show the combined effects of frequency, pressure, and fluid viscosity on the bulk modulus in fluid-saturated sandstone and basalt. At low frequency (0.1 Hz), samples behave as though fully drained: The bulk modulus remains unchanged under argon-, glycerin-, and water-saturated conditions. However, the high-frequency (or unrelaxed) bulk modulus, deduced from ultrasonic velocities, is clearly modified by the nature of the fluid. In addition, the bulk dispersion between low and high frequencies is significant at low confining pressure when cracks are open and decreases as cracks are closed. Although cracks represent a small fraction of total porosity, they produce a dispersion caused by squirt-flow processes. A simple quantitative model can be used to predict the frequency effect and explain the experimental results well.

4. Hydrogeology of the Galápagos Archipelago

   S. Violette ,  N. d’Ozouville ,  A. Pryet ,  B. Deffontaines ,  J. Fortin ,  and  M. Adelinet

   The Galápagos: A Natural Laboratory for the Earth Sciences, Geophysical Monograph (AGU), 2014

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   Summary In this paper, we present an original synthesis of recent hydrogeological studies of the Galápagos Islands. We compare and contrast hydrological data from two Galápagos Islands, San Cristóbal and Santa Cruz, for which no baseline data existed prior to the start of the Galápagos Islands Integrated Water Studies project (GIIWS) in 2003. Two complementary datasets are considered in this work, collected using direct methodologies (in situ measurements at watershed-scale experimental sites) and indirect methodologies (satellite imagery interpretation, helicopter-borne geophysics acquisition at regional scale). Using these datasets, we: Present a synthesis of the hydrogeology of San Cristóbal and Santa Cruz; Explain differences in their hydrodynamic functioning; and Explore the implications of these results for water resource management on the Galápagos inhabited islands. We propose that a number of key factors, including geomorphology, near-surface lithology, and age, control the primary hydrological similarities and differences between San Cristóbal and Santa Cruz. Finally, we propose that the distribution and occurrence of groundwater resources on San Cristóbal and Santa Cruz define an evolutionary link between the two classical conceptual hydrogeological models (the Hawaiian model and the Canary Islands model) proposed in the literature for basaltic islands. Indeed, Santa Cruz is similar to the Hawaiian model (valid for young islands under 1 Ma) and San Cristóbal is an advanced stage of the Hawaiian model that is evolving toward the Canary Islands model (valid for old islands over 5 Ma).

5. Evolution of the crack network in glass samples submitted to brittle creep conditions

   C. Mallet ,  J. Fortin ,  Y. Guéguen ,  and  F. Bouyer

   International Journal of Fracture, 2014

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   A crack network is introduced in glass by quenching heated samples. The sharp variation of temperature at the sample boundaries leads to tensile stresses that nucleate cracks. Then, they propagate in the entire sample. Quenching has been performed at 100, 200 and $300\,^∘\hbox C$. Cracks have been imaged with a scanning electron microscope. A transverse isotropic crack network is observed. Crack length and orientation have been measured. Obtained crack density has been compared to that inferred from elastic wave velocity measurements using effective medium theory. Cracked samples have been then submitted to creep tests. Two samples have been recovered, one before its failure and another after. Our observations show that vertical crack propagation takes place during brittle creep and that tertiary creep leads to a localized failure in a shear plane. The damaged and post-mortem microstructural networks have been documented.

2013

1. Elastic envelopes of porous sandstones

   Y. Guéguen ,  and  J. Fortin

   Geophysical Research Letters, 2013

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   In this paper we focus on the case of sandstones for which many experimental data are available. We present a simple 2‒D model derived from granular media mechanics. This model assumes that the granular microstructure is a key point to understand the mechanical behavior. We consider a periodic grain network and focus on the first‒order neighbors of a given grain. These approximations are sufficient to explain the overall mechanical behavior in the Q versus P stress space. In the low pressure range, the controlling micromechanism is assumed to be tensile failure at grain contacts. The “dilatant” envelope is found to be a straight line in the stress space. In the high pressure range, the controlling micromechanism is assumed to be grain fragmentation. The “compactant” envelope is found to be a straight line in the stress space. We observed that this 2‒D model slightly overestimates Q versus P slopes determined experimentally (2.3 instead of 1.5), which can be explained by the approximations made.

2. Physical properties and brittle strength of thermally cracked granite under confinement

   X-Q. Wang ,  A. Schubnel ,  J. Fortin ,  Y. Guéguen ,  and  H-K. Ge

   Journal of Geophysical Research: Solid Earth, 2013

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   Effects of thermal crack damage on the rupture processes of a fine-grained granite were investigated under triaxial stress, under water (wet) and argon gas (dry) saturated conditions, and at room temperature. Thermal cracking was introduced by slowly heating and cooling two samples of La Peyratte granite up to 700°C, which were compared to two intact specimens. For each rock sample, a hydrostatic test was first carried up to 90 MPa effective pressure (5 MPa constant pore pressure). The samples were then deformed to failure at a constant strain rate of 2.10−6s−1, at 30 MPa effective pressure. Our results show that (1) permeability of heat-treated specimens was 4–5 orders of magnitude larger than that of intact specimens at low effective mean pressure; (2) nevertheless, at our experimental conditions (2.10−6 s−1), thermal cracking had no significant influence on the brittle strength; (3) similarly, no obvious water weakening effect was observed; (4) however, with increasing stress, elastic anisotropy appeared at lower differential stress in heat-treated specimens than in intact ones, but close to failure, the magnitude of P wave anisotropy was approximately the same for both types of specimens; (5) acoustic emission hypocenter locations and P wave velocity anisotropy in the basal plane demonstrate that strain localization started right at the onset of dilatancy for heat-treated specimens, later in the intact specimens; and (6) inverting wave velocities for crack density, we show that failure was reached for vertical crack densities of 0.35 for dry specimens and possibly 0.5 for water-saturated specimens.

3. Effective Elastic Properties of Cracked Solids: An Experimental Investigation

   C. Mallet ,  J. Fortin ,  and  Y. Guéguen

   International Journal of Fracture, 2013

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   Non Interaction Approximation (NIA) is currently used to relate effective elastic moduli to crack density. It also allows one to identify the anisotropy of the crack network.

4. Deformation modes in an Icelandic basalt: From brittle failure to localized deformation bands

   M. Adelinet ,  J. Fortin ,  A. Schubnel ,  and  Y. Guéguen

   Journal of Volcanology and Geothermal Research, 2013

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   According to the stress state, deformation mode observed in rocks may be very different. Even in the brittle part of the crust a differential stress can induce shear failure but also localized compacting deformation, such as compaction bands in porous sedimentary rocks. The mode of deformation controls many hydrodynamic factors, such as permeability and porosity. We investigate in this paper two different modes of deformation in an Icelandic basalt by using laboratory seismological tools (elastic waves and acoustic emissions) and microstructural observations. First of all, we show that at low effective confining pressure (Peff=5MPa) an axial loading induces a shear failure in the basalt with an angle of about 30° with respect to the main stress direction. On the contrary, at high effective confining pressure (Peff≥75MPa and more) an increase of the axial stress induces a localization of the deformation in the form of subhorizontal bands again with respect to the main stress direction. In this second regime, focal mechanisms of the acoustic emissions reveal an important number of compression events suggesting pore collapse mechanisms. Microstructural observations confirm this assumption. Similar compaction structures are usually obtained for porous sedimentary rocks (20–25%). However, the investigated basalt has an initial total porosity of only about 10% so that compaction structures were not expected. The pore size and the ratio of pore to grain size are likely to be key factors for the particular observed mechanical behavior.

5. Laboratory measurements of low- and high-frequency elastic moduli in Fontainebleau sandstone

   Emmanuel D. ,  J. Fortin ,  A. Schubnel ,  Y. Guéguen ,  and  R. Zimmerman

   Geophysics, 2013

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   The presence of pores and cracks in rocks causes the fluid-saturated wave velocities in rocks to be dependent on frequency. New measurements of the bulk modulus at low frequencies (0.02–0.1 Hz) were obtained in the laboratory using oscillation tests carried out on two hydrostatically stressed Fontainebleau sandstone samples, in conjunction with ultrasonic velocities and static measurements, under a range of differential pressures (10–95 MPa), and with three different pore fluids (argon, glycerin, and water). For the 13% and 4% porosity samples, under glycerin- and water-saturated conditions, the low-frequency bulk modulus at 0.02 Hz matched well the low-frequency and ultrasonic dry bulk modulus. The glycerin- and water-saturated samples were much more compliant at low frequencies than at high frequencies. The measured bulk moduli of the tested rocks at low frequencies (0.02–0.1 Hz) were much lower than the values predicted by the Gassmann equation. The frequency dispersion of the P and S velocities was much higher at low differential pressures than at high pressures, due to the presence of open cracks at low differential pressures.

2012

1. High Vp/Vs ratio: Saturated cracks or anisotropy effects?

   X.-Q. Wang ,  A. Schubnel ,  J. Fortin ,  E. C. David ,  Y. Guéguen ,  and  H.-K. Ge

   Geophysical Research Letters, 2012

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   We measured Vp/Vs ratios of thermally cracked Westerly granite, thermally cracked Carrara marble and 4% porosity Fontainebleau sandstone, for an effective mean pressure ranging from 2 to 95 MPa. Samples were fluid-saturated alternatively with argon gas and water (5 MPa constant pore pressure). The experimental results show that at ultrasonic frequencies, Vp/Vs ratio of water saturated specimen never exceeded 2.15, even at effective mean pressure as low as 2 MPa, or for a lithology for which the Poisson’s ratio of minerals is as high as 0.3 (calcite). In order to check these results against theoretical models: we examine first a randomly oriented cracked medium (with dispersion but without anisotropy); and second a medium with horizontally aligned cracks (with anisotropy but without dispersion). The numerical results show that experimental data agree well with the first model: at high frequency, Vp/Vs ratios range from 1.6 to 1.8 in the dry case and from 1.6 to 2.2 in the saturated case. The second model predicts both Vp/Sv and Vp/Sh to vary from 1.2 to 3.5, depending on the raypath angle relative to the crack fabric. In addition, perpendicular to the crack fabric, a high Vp/Vs ratio is predicted in the absence of shear wave splitting. From these results, we argue the possibility that high Vp/Vs ratio (>2.2) as recently imaged by seismic tomography in subduction zones, may come from zones presenting important crack anisotropy. The cumulative effects of crack anisotropy and high pore fluid pressure are required to get Vp/Vs ratios above 2.2.

2. Mechanical behavior and localized failure modes in a porous basalt from the Azores

   S. Loaiza ,  J. Fortin ,  A. Schubnel ,  Y. Gueguen ,  S. Vinciguerra ,  and  M. Moreira

   Geophysical Research Letters, 2012

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   Basaltic rocks are the main component of the oceanic upper crust, thus of potential interest for water and geothermal resources, storage of CO2and volcanic edifice stability. In this work, we investigated experimentally the mechanical behavior and the failure modes of a porous basalt, with an initial connected porosity of 18%. Results were acquired under triaxial compression experiments at confining pressure in the range of 25–200 MPa on water saturated samples. In addition, a purely hydrostatic test was also performed to reach the pore collapse critical pressure P*. During hydrostatic loading, our results show that the permeability is highly pressure dependent, which suggests that the permeability is mainly controlled by pre-existing cracks. When the sample is deformed at pressure higher than the pore collapse pressure P*, some very small dilatancy develops due to microcracking, and an increase in permeability is observed. Under triaxial loading, two modes of deformation can be highlighted. At low confining pressure (Pc < 50 MPa), the samples are brittle and shear localization occurs. For confining pressure > 50 MPa, the stress-strain curves are characterized by strain hardening and volumetric compaction. Stress drops are also observed, suggesting that compaction may be localized. The presence of compaction bands is confirmed by our microstructure analysis. In addition, the mechanical data allows us to plot the full yield surface for this porous basalt, which follows an elliptic cap as previously observed in high porosity sandstones and limestones.

3. Elastic anisotropy of core samples from the Taiwan Chelungpu Fault Drilling Project (TCDP): direct 3-D measurements and weak anisotropy approximations

   L. Louis ,  C. David ,  P. Spacek ,  T-f. Wong ,  J. Fortin ,  and  S. Song

   Geophysical Journal International, 2012

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   The study of seismic anisotropy has become a powerful tool to decipher rock physics attributes in reservoirs or in complex tectonic settings. We compare direct 3-D measurements of P-wave velocity in 132 different directions on spherical rock samples to the prediction of the approximate model proposed by Louis et al. based on a tensorial approach. The data set includes measurements on dry spheres under confining pressure ranging from 5 to 200 MPa for three sandstones retrieved at a depth of 850, 1365 and 1394 metres in TCDP hole A (Taiwan Chelungpu Fault Drilling Project). As long as the P-wave velocity anisotropy is weak, we show that the predictions of the approximate model are in good agreement with the measurements. As the tensorial method is designed to work with cylindrical samples cored in three orthogonal directions, a significant gain both in the number of measurements involved and in sample preparation is achieved compared to measurements on spheres. We analysed the pressure dependence of the velocity field and show that as the confining pressure is raised the velocity increases, the anisotropy decreases but remains significant even at high pressure, and the shape of the ellipsoid representing the velocity (or elastic) fabric evolves from elongated to planar. These observations can be accounted for by considering the existence of both isotropic and anisotropic crack distributions and their evolution with applied pressure.

2011

1. Influence of thermal and mechanical cracks on permeability and elastic wave velocities in a basalt from Mt. Etna volcano subjected to elevated pressure

   J. Fortin ,  S. Stanchits ,  S. Vinciguerra ,  and  Y. Guéguen

   Tectonophysics, 2011

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   We report simultaneous laboratory measurements of seismic velocities and fluid permeability on lava flow basalt from Etna (Italy). Results were obtained for dry and saturated samples deformed under triaxial compression. During each test, the effective pressure was first increased up to 190MPa to investigate the effect of pre-existing crack closure on seismic properties. Then, the effective pressure was unloaded down to 20MPa, a pressure which mirrors the stress field acting under a lava pile of approximately 1.5–2km thick, and deviatoric stress was increased until failure of the specimens. Using an effective medium model, the measured elastic wave velocities were inverted in terms of two crack densities: ρi the crack density of the pre-existing thermal cracks and ρv the crack density of the stress-induced cracks. In addition a link was established between elastic properties (elastic wave velocities Vp and Vs) and permeability using a statistical permeability model. Our results show that the velocities increase with increasing hydrostatic pressure up to 190MPa, due to the closure of the pre-existing thermal cracks. This is interpreted by a decrease of the crack density ρi from  1 to 0.2. The effect of pre-existing cracks closure is also highlighted by the permeability evolution which decreases of more than two orders of magnitude. Under deviatoric loading, the velocities signature is interpreted, in the first stage of the loading, by the closure of the pre-existing thermal cracks. However, with increasing deviatoric loading newly-formed vertical cracks nucleate and propagate. This is clearly seen from the velocity signature and its interpretation in term of crack density, from the location of the acoustic emission sources, and from microstructural observations. This competition between pre-existing cracks closure and propagation of vertical cracks is also seen from the permeability evolution, and our study shows that mechanically-induced cracks has lesser influence on permeability change than pre-existing thermal cracks.

2. Permeability and elastic properties of cracked glass under pressure

   A. Ougier-Simonin ,  Y. Guéguen ,  J. Fortin ,  A. Schubnel ,  and  F. Bouyer

   Journal of Geophysical Research: Solid Earth, 2011

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   Fluid flow in rocks is allowed through networks of cracks and fractures at all scales. In fact, cracks are of high importance in various applications ranging from rock elastic and transport properties to nuclear waste disposal. The present work aims at investigating thermomechanical cracking effects on elastic wave velocities, mechanical strength, and permeability of cracked glass under pressure. We performed the experiments on a triaxial cell at room temperature which allows for independent controls of the confining pressure, the axial stress, and pore pressure. We produced cracks in original borosilicate glass samples with a reproducible method (thermal treatment with a thermal shock of 300°C). The evolution of the elastic and transport properties have been monitored using elastic wave velocity sensors, strain gage, and flow measurements. The results obtained evidence for (1) a crack family with identified average aspect ratio and crack aperture, (2) a very small permeability which decreases as a power (exponential) function of pressure, and depends on (3) the crack aperture cube. We also show that permeability behavior of a cracked elastic brittle solid is reversible and independent of the fluid nature. Two independent methods (permeability and elastic wave velocity measurements) give these consistent results. This study provides data on the mechanical and transport properties of an almost ideal elastic brittle solid in which a crack population has been introduced. Comparisons with similar data on rocks allow for drawing interesting conclusions. Over the timescale of our experiments, our results do not provide any data on stress corrosion, which should be considered in further study.

3. How cracks modify permeability and introduce velocity dispersion: Examples of glass and basalt

   Y. Guéguen ,  M. Adelinet ,  A. Ougier-Simonin ,  J. Fortin ,  and  A. Schubnel

   The Leading Edge, 2011

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   The porosity of igneous rocks is usually very small, although for some basalts it can be nonnegligible due to gas exsolution. In the case of glass, it is vanishingly small. Why is it of any interest to look at this kind of material from the point of view of rock physics? Two series of reasons indeed motivate such investigations.

4. X-ray imaging of water motion during capillary imbibition: A study on how compaction bands impact fluid flow in Bentheim sandstone

   A. Pons ,  C. David ,  J. Fortin ,  S. Stanchits ,  B. Menéndez ,  and  J. M. Mengus

   Journal of Geophysical Research: Solid Earth, 2011

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   To investigate the effect of compaction bands (CB) on fluid flow, capillary imbibition experiments were performed on Bentheim sandstone specimens (initial porosity ∼22.7%) using an industrial X-ray scanner. We used a three-step procedure combining (1) X-ray imaging of capillary rise in intact Bentheim sandstone, (2) formation of compaction band under triaxial tests, at 185 MPa effective pressure, with acoustic emissions (AE) recording for localization of the induced damage, and (3) again X-ray imaging of capillary rise in the damaged specimens after the unloading. The experiments were performed on intact cylindrical specimens, 5 cm in diameter and 10.5 cm in length, cored in different orientations (parallel or perpendicular to the bedding). Analysis of the images obtained at different stages of the capillary imbibition shows that the presence of CB slows down the imbibition and disturbs the geometry of water flow. In addition, we show that the CB geometry derived from X-ray density maps analysis is well correlated with the AE location obtained during triaxial test. The analysis of the water front kinetics was conducted using a simple theoretical model, which allowed us to confirm that compaction bands act as a barrier for fluid flow, not fully impermeable though. We estimate a contrast of permeability of a factor of ∼3 between the host rock and the compaction bands. This estimation of the permeability inside the compaction band is consistent with estimations done in similar sandstones from field studies but differs by 1 order of magnitude from estimations from previous laboratory measurements.

5. Deriving microstructure and fluid state within the Icelandic crust from the inversion of tomography data

   M. Adelinet ,  C. Dorbath ,  M. Le Ravalec ,  J. Fortin ,  and  Y. Guéguen

   Geophysical Research Letters, 2011

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   The inversion of seismic data to infer rock microstructural properties and fluid flow patterns in the crust is a challenging issue. In this paper, we develop an effective medium model for estimating velocities in porous media including both pores and cracks and use it to derive the distribution of crack density beneath the Reykjanes Peninsula from accurate tomography data. Outside the active hydrothermal areas, crack density is shown to decrease with depth. There are two main reasons for this: the closure of cracks because of the increasing overburden and the secondary filling of cracks because of hydrothermal flows. However, crack density may locally increase with depth beneath the southwestern part of the Kleifarvatn lake. This is consistent with the presence of a deep reservoir with supercritical fluids under pressure, which may activate hydrofracturing processes. We recognize that capturing the link between seismic data and the physical properties of crust is very difficult. This study shows that a combination of mechanical concepts and effective medium theory contributes to improve our understanding of the phenomena occurring within the Icelandic crust.

6. Cracks in glass under triaxial conditions

   A. Ougier-Simonin ,  J. Fortin ,  Y. Guéguen ,  A. Schubnel ,  and  F. Bouyer

   International Journal of Engineering Science, 2011

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   This experimental work documents the mechanical evolution of synthetic glass (SON68) under compressive triaxial stresses (hydrostatic and deviatoric conditions). The experimental setup enabled to monitor and vary independently confining pressure (range: [0,50]MPa) and axial stress (up to 680MPa) at room temperature. An optimized set of sensors allowed us to perform measurements during the experiments of: (i) axial and radial deformation, (ii) P- and S-elastic wave velocities, and (iii) acoustic emissions. In addition, in some samples, initial crack densities up to a value of 0.24 were introduced by thermal cracking. We compare the original synthetic glass data set to results obtained in the same experimental conditions on thermally cracked glass and on a basaltic rock with similar petrophysical properties (porosity, chemistry). Stress–strain data depict original linear elastic glass properties even up to an axial stress of 680MPa (under 15MPa confining pressure). A strong strength decrease (370MPa at 15MPa confining pressure) is observed for thermally cracked samples. Elastic wave velocity data highlight that cracks are mostly closed at a confining pressure of ∼30MPa. The basaltic rock seems to correspond to an intermediate state between an original and a thermally treated glass. In all samples, damage was accompanied by dynamic crack propagation, producing large magnitude acoustic emissions. Thanks to a continuous recorder, we could locate a number of acoustic emissions in order to image the microcracking pattern evolution prior to failure.

7. Dispersion of elastic moduli in a porous-cracked rock: Theoretical predictions for squirt-flow

   M. Adelinet ,  J. Fortin ,  and  Y. Guéguen

   Tectonophysics, 2011

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   Crustal rocks contain variable amount of both cracks and equant pores depending on tectonic and thermal stresses but also on their geological origin. Crack damage and porosity change result in effects on elastic waves velocities. When rocks are fluid saturated, dispersion of the P- and S-waves should be taken into account. This paper deals with frequency dispersion of elastic moduli in a fluid saturated porous and cracked rock with the assumption that squirt-flow is the dominant process. We develop a theoretical approach to calculate both high (HF) and low (LF) frequency bulk and shear moduli. The HF moduli are derived from a new effective medium model, called CPEM, with an isotropic distribution of pores or cracks with idealized geometry, respectively spheres and ellipsoids. LF moduli are obtained by taking HF dry moduli from the CPEM and substituting into Gassmann’s equations. In the case of a porosity only supported by equant pores, the calculated dispersion in elastic moduli is equal to zero. In the case of a crack porosity, no bulk dispersion is predicted but a shear dispersion appears. Finally in the general case of a mixed porosity (pores and cracks), dispersion in bulk and in shear is predicted. Our results show that the maximum dispersion is predicted for a mixture of pores and spheroidal cracks with a very small aspect ratio (≤10−3). Our theoretical predictions are compared to experimental data obtained during hydrostatic experiment performed on a basaltic rock and a good agreement is observed. We also used our theoretical model to predict elastic waves velocities and Vp/Vs ratio dispersion. We show that the P-waves dispersion can reach almost 20% and the Vp/Vs dispersion a maximum value of 9% for a crack porosity of about 1%. Since laboratory data are ultrasonic measurements and field data are obtained at much lower frequencies, these results are useful for geophysicists to interpret seismic data in terms of fluid and rock interactions.

2010

1. Frequency and fluid effects on elastic properties of basalt: Experimental investigations

   M. Adelinet ,  J. Fortin ,  Y. Guéguen ,  A. Schubnel ,  and  L. Geoffroy

   Geophysical Research Letters, 2010

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   In order to investigate the effects of fluid and frequency on the elastic properties, we performed hydrostatic experiments on an Icelandic basalt specimen under both dry and saturated conditions. This basalt is characterized by a bimodal porosity, i.e., cracks and equant pores. The elastic properties -bulk moduli in our case- were investigated under high pressure through two experimental methods: (1) a classical one using ultrasonic P- and S-waves velocities (frequency 106 Hz), (2) and a new one, using oscillation tests (frequency 10−2 Hz). In dry condition, experimental data show no significant difference between high (HF) and low (LF) frequency bulk moduli. However, in saturated conditions, two effects are highlighted: a physico-chemical effect emphasized by a difference between drained and dry moduli, and a squirt-flow effect evidenced by a difference between HF and LF undrained moduli.

2009

1. Acoustic emissions monitoring during inelastic deformation of porous sandstone: comparison of three modes of deformation

   J. Fortin ,  S. Stanchits ,  and  Y. Dresen

   Pure and Applied Geophysics, 2009

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   In some reservoirs, large deformations can occur during oil or gas production because of the effective stress change. For very porous rocks, these production operations can be sufficient to cause inelastic deformation and irreversible damage. Rock formations can undergo deformation by different mechanisms, including dilatancy or pore collapse. In the laboratory, it has been shown that the inelastic deformation and failure mode of porous rocks are pressure sensitive. Indeed, when subjected to an overall compressive loading, a porous rock may fail by shear localization, compaction localization, or by cataclastic compaction. Acoustic emission (AE) records provide important information to understand the failure mode of rocks: the spatial evolution of damage as well as the source mechanisms can be followed using this technique. In this paper, we present three different laboratory axisymmetric compression experiments, performed on Bleurswiller sandstone, which enable us to compare the acoustic emission signature of these three modes of deformation. Our data show that compaction localization and cataclastic compaction are characterized by similar acoustic signatures (in terms of AE sources characteristics and evolution of AE number), in comparison to the acoustic signature from shear localization. This implies similar micromechanisms involved during compaction bands formation and cataclastic compaction.

2. Cracks in porous rocks : Tiny defects, strong effects

   Y. Guéguen ,  J. Sarout ,  J. Fortin ,  and  A. Schubnel

   The Leading Edge, 2009

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   Understanding the physics and mechanics of porous sedimentary rocks is a stimulating challenge. Indeed, these rocks are of great economical interest for two main reasons: they are the places for hydrocarbon resources and for underground storage. Yet the complexity of these natural composites would suggest low expectations for research projects aiming at a fundamental understanding of their behavior. However progress has been observed, not limited to the study of pure quartz sandstones such as Fontainebleau sandstones. Many experiments and models have been developed that deal with more typical, complex sandstones. Even shales, that are certainly the most complex sedimentary rocks, have also been well documented. But why is it of interest to understand better the fundamental physics and mechanics of sedimentary rocks? And how has progress been made possible, given those difficulties?

3. Initiation and propagation of compaction bands in dry and wet Bentheim sandstone

   S. Stanchits ,  J. Fortin ,  Y. Gueguen ,  and  G. Dresen

   Pure and Applied Geophysics, 2009

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   We investigated initiation and propagation of compaction bands (CB) in six wet and four dry Bentheim sandstone samples deformed in axial compression tests with strain rates ranging from 3.2 × 10−8 s−1 to 3.2 × 10−4 s−1. Circumferential notches with 0.8-mm width and 5-mm depth served to initiate CB at mid-sample length. Wet samples were saturated with distilled water and deformed at 195 MPa confining pressure and 10 MPa pore pressure. Dry samples were deformed at 185 MPa confining pressure. Twelve P-wave sensors, eight S-wave sensors and two pairs of orthogonally oriented strain-gages were glued to the sample surface to monitor acoustic emission (AE), velocities and local strain during the loading process. Nucleation of compaction bands is indicated by AE clusters close to the notch tips. With progressive loading, AE activity increased and AE hypocenters indicated propagation of a single CB normal to the sample axis. CB propagation from the sample periphery towards the centre was monitored. Microstructural analysis of deformed samples shows excellent agreement between location of AE clusters and CBs. In both dry and wet samples the lateral propagation of CBs was about 100 times faster than axial shortening rates. At the slowest displacement rate, AE activity during band propagation was reduced and CB nucleation in wet samples occurred at 20% lower stresses. This may indicate an increasing contribution of stress corrosion processes to the formation of the compaction bands. In dry and wet samples inelastic compaction energy per area ranged between 16 and 80 kJ m−2. This is in good agreement with previous estimates from laboratory and field studies.

2008

1. The relationship between hydrodynamic properties and weathering of soils derived from volcanic rocks, Galapagos Islands (Ecuador)

   M Adelinet ,  J Fortin ,  N d’Ozouville ,  and  S Violette

   Environmental geology, 2008

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   The aim of this interdisciplinary study is to examine a component of the hydrological cycle in Galapagos by characterizing soil properties. Nine soil profiles were sampled on two islands. Their physical and hydrodynamic properties were analyzed, along with their mineralogical composition. Two groups of soils were identified, with major differences between them. The first group consists of soils located in the highlands (>350 m a.s.l.), characterized by low hydraulic conductivity (<10−5 m s−1) and low porosity (<25%). These soils are thick (several meters) and homogeneous without coarse components. Their clay fraction is considerable and dominated by gibbsite. The second group includes soils located in the low parts of the islands (<300 m a.s.l.). These soils are characterized by high hydraulic conductivity (>10−3 m s−1) and high porosity (>35%). The structure of these soils is heterogeneous and includes coarse materials. The physical properties of the soils are in good agreement with the variations of the rainfall according to the elevation, which appears as the main factor controlling the soil development. The clayey alteration products constrain soils physical and hydrodynamic properties by reducing the porosity and consequently the permeability and also by increasing water retention.

2007

1. Effects of pore collapse and grain crushing on ultrasonic velocities and Vp/Vs

   J. Fortin ,  Y. Guéguen ,  and  A. Schubnel

   Journal of Geophysical Research: Solid Earth, 2007

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   Compressional, shear wave velocities and their ratio, Vp/Vs, were measured along with porosity variations during wet and dry hydrostatic compaction of Bleurswiller sandstone, a 25% porosity Vosgian sandstone. At first, increase in hydrostatic pressure was accompanied by a simultaneous increase of both Vp and Vs as expected. At a critical effective confining pressure P*, a large mechanical decrease of porosity was observed that was due to pore collapse and grain crushing. Theoretically, two different processes are affecting the elastic wave velocities in counteracting ways during cataclastic compaction: cracking and porosity decrease. Our experimental results show that cracking is the dominant effect, so that grain crushing and porosity reduction were accompanied by a large decrease in velocities. The ratio Vp/Vs was also observed to change during our experiments: In the wet specimen, Vp/Vs value increased from 1.72 to 1.84, while in the dry specimen, it increased from 1.59 below P* to 1.67 beyond P*, respectively. To quantitatively interpret these results, an isotropic effective medium model (EM) was used that considered the sandstone as a mixture of spheroidal pores and penny-shaped cracks. In particular, the increase in Vp/Vs, in the wet case, is well reproduced and shows the important role played by the mechanical coupling of fluid with low aspect ratio cracks (<10−2). In the dry case, however, our experimental results highlight an increase of Vp/Vs ratio during cataclastic compaction, in apparent contradiction with the predictions of the EM model. Indeed, increases in Vp/Vs ratio, and hence in Poisson’s ratio, are, in general, attributed to fluid saturation. A closer look to the microstructure may provide a possible interpretation: Beyond P*, grains are no longer cemented. Using Digby’s granular model as an alternative model, we were able to reach a quantitative agreement with the experimental results. The possible implication is that in both dry and wet conditions, cataclastic compaction due to grain crushing induces an increase in Vp/Vs ratio.

2. Fluid-induced rupture experiment on Fontainebleau sandstone: Premonitory activity, rupture propagation, and aftershocks

   A. Schubnel ,  B. D. Thompson ,  J. Fortin ,  Y. Guéguen ,  and  R. P. Young

   Geophysical Research Letters, 2007

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   A 14% porosity Fontainebleau sandstone sample (diameter = 40 mm, length = 88 mm) was loaded tri-axially, under 100 MPa confining pressure and 240 MPa differential stress. In drained conditions and under constant load, pore pressure (water) was raised until failure was triggered. During the experiment, elastic wave velocities and permeability were monitored while more than 3000 Acoustic Emissions (AE) were located prior and after failure. AE locations show that macroscopic fracture propagated from a large nucleation patch at speeds comprised between 0.1 and 4 m/s. Number of AE hits per second followed Omori’s law, with exponents of 0.92 and 1.18 pre- and post-failure respectively. No quiescence was observed post failure, except where rupture initially nucleated from. Fast depressurization of the pore space induced secondary aftershocks located within the fracture plane, possibly indicating a heterogeneous fault geometry after rupture, of lower permeability, that compacted during the release of pore pressure.

2006

1. Acoustic emission and velocities associated with the formation of compaction bands in sandstone

   J. Fortin ,  S. Stanchits ,  G. Dresen ,  and  Y. Guéguen

   Journal of Geophysical Research: Solid Earth, 2006

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   A series of laboratory experiments has been conducted in which three-dimensional (3-D) locations of acoustic emissions (AE) were recorded and used to analyze the development of compaction bands in Bleurswiller sandstone, which has a porosity of 25%. Results were obtained for saturated samples deformed under triaxial compression at three different confining pressures (60, 80, and 100 MPa), a pore pressure of 10 MPa, and room temperature. We recorded acoustic emissions, compressional and shear wave velocities, and porosity reduction under hydrostatic condition and under triaxial loading conditions at a constant axial strain rate. Our results show that seismic velocities and their amplitude increased during hydrostatic pressure build up and during initial axial loading. During shear-enhanced compaction, axial and radial velocities decreased progressively, indicating an increase of stress-induced damage in the rock. In experiments performed at confining pressures of 80 and 100 MPa during triaxial loading, acoustic emissions were localized in clusters. During progressive loading, AE clusters grow horizontally, perpendicular to the maximum principal stress direction, indicating formation of compaction bands throughout the specimens. Microstructural analysis of deformed specimens confirmed a spatial correspondence of AE clusters and compaction bands. For the experiment performed at a confining pressure of 60 MPa, AE locations and microstructural observations show symmetric compaction bands inclined to the cylinder axis of the specimen, in agreement with predictions from recent theoretical models.

2. Transient creep, aseismic damage and slow failure in Carrara marble deformed across the brittle-ductile transition

   A. Schubnel ,  E. Walker ,  B. D. Thompson ,  J. Fortin ,  Y. Guéguen ,  and  R. P. Young

   Geophysical Research Letters, 2006

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   Two triaxial compression experiments were performed on Carrara marble at high confining pressure, in creep conditions across the brittle-ductile transition. During cataclastic deformation, elastic wave velocity decrease demonstrated damage accumulation (microcracks). Keeping differential stress constant and reducing normal stress induced transient creep events (i.e., fast accelerations in strain) due to the sudden increase of microcrack growth. Tertiary creep and brittle failure followed as damage came close to criticality. Coalescence and rupture propagation were slow (60–200 seconds with ∼150 MPa stress drops and millimetric slips) and radiated little energy in the experimental frequency range (0.1–1 MHz). Microstructural analysis pointed out strong interactions between intra-crystalline plastic deformation (twinning and dislocation glide) and brittle deformation (microcracking) at the macroscopic level. Our observations highlight the dependence of acoustic efficiency on the material’s rheology, at least in the ultrasonic frequency range, and the role played by pore fluid diffusion as an incubation process for delayed failure triggering.

2005

1. Elastic wave velocities and permeability evolution during compaction of Bleurswiller sandstone

   J. Fortin ,  A. Schubnel ,  and  Y. Guéguen

   International Journal of Rock Mechanics and Mining Sciences, 2005

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   Field observations and laboratory experiments have recently documented the formation of compaction bands in porous sandstones [Mollema and Antonellini, Tectonophysics 1996;267:209–28; Olsson and Holcomb, Geophys Res Lett 2000;27:3537–40; Bésuelle, J Geophys Res 2001;106:13435–42; Klein et al., Phys Chem Earth 2001;26:21–5]. It has been observed experimentally [Wong et al., J Geophys Res 2001;28:2521–4; Baud et al., J Geophys Res 2003, submitted; Fortin et al., 2003, Abstract EGS-AGU Nice] that under axisymmetric compression, compaction bands develop sub-perpendicular to the main compressive stress which is predicted theoretically in the framework of strain localization theory [Bésuelle, J Geophys Res 2001;106:13435–42; Issen and Rudnicki, J Geophys Res 2000;105:21529–36]. Volumetric strain, fluid transport and elastic properties are intimately coupled to one another, for they all depend on a few intrinsic parameters such as the porosity, the crack density, and the matrix and fluid elastic properties. On the one hand, Scott et al. [Rock Mech Min Sci Geomech 1993;30:763–9] showed that elastic wave velocities were clearly affected during the deformation of porous sandstones. On the other hand, Zhu and Wong [J Geophys Res 1997;102:3027–41] showed that the relation between the evolution of permeability and volumetric strain during compaction of sandstones was not straightforward. In this study, we present for the first time the simultaneous evolution of volumetric strain, elastic wave velocities and permeability for a set of deformation experiments of Bleurswiller sandstone. We show that, although very coherent to one another, those three sets are not systematically correlated. Indeed, inelastic compaction, whether it is distributed or localized, is accompanied by a drastic decrease of elastic wave velocities due to grain crushing, a decrease of permeability and porosity due to pore collapse. Using simple statistical physics concepts based on the study of Kachanov [Adv Appl Mech 1993;30:259–445] and Guéguen and Dienes [Math Geol 1989;21:1–13], we try to understand and address the issue of coupling/decoupling between volumetric strain (mainly sensitive to equant porosity variations), elastic properties (mainly sensitive to crack density) and permeability (theoretically sensitive to both) during the formation of compaction bands. Finally, we show that the mineral composition of a sandstone is a key parameter controlling the effective pressure at which the onset of pore collapse P* takes place.

2. Damage and recovery of calcite rocks deformed in the cataclastic regime

   A. Schubnel ,  J. Fortin ,  L. Burlini ,  and  Y. Gueguen

   Geological Society, London, Special Publications, 2005

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   Compressional and shear wave velocities have been measured during the experimental deformation of Carrara marble and Solnhofen limestone in the cataclastic regime, both in dry and wet conditions at room temperature. Measurements were performed under hydrostatic conditions (up to 260 MPa confining pressure and 10 MPa pore pressure) during triaxial loading (at the constant strain rate of 10−5s−1) as well as during differential stress relaxation. During a full cycle, our results show that the seismic velocities first increase as effective mean stress increases. However, when the stress onset of cataclastic deformation was reached, elastic velocities showed rapid decrease due to stress-induced damage in the rock. During stress relaxation tests we observed an increase of elastic velocities with time, which suggested a fast ‘recovery’ of the microstructure. A substantial and rapid drop in the velocities occurred when reloading, suggesting that the previous ‘recovery’ was only transient. Subsequent relaxation tests showed other marked increases in velocities. These experimental results suggests that during the deformation of low-porosity calcite-rich rocks, dilatant (crack opening and frictional sliding) and compaction micro-mechanism (pore closure) compete. Evolutions of elastic properties (mainly sensitive to crack density) and macroscopic volumetric strain (more sensitive to porosity) are therefore not systematically correlated and depend on the strain rate, the solid stress conditions and the pore pressure.

3. Mécanique des roches en géologie: des processus microscopiques au comportement macroscopique

   Yves Guéguen ,  and  Jérôme Fortin

   “Microstructure et Propriétés des Matériaux”, presse ENPC, 2005