Microfracturation in rocks: from microtomography images to processes

Eur. Phys. J. Appl. Phys. (2012) 60: 24203 DOI: 10.1051/epjap/2012120093

THE EUROPEAN PHYSICAL JOURNAL APPLIED PHYSICS

Regular Article

Microfracturation in rocks: from microtomography images to processes F. Renard1,2,a 1 2

ISTerre, University Grenoble I and CNRS - BP 53 F-38041 Grenoble, France Physics of Geological Processes, University of Oslo, Norway Received: 11 March 2012 / Received in final form: 30 May 2012 / Accepted: 31 May 2012 c EDP Sciences 2012 Published online: 23 October 2012 –  Abstract. Fracturing of rocks and other geomaterials involves multi-scale processes, from the nucleation of small cracks, their propagation into a complex heterogeneous solid, to their final arrest. In the past 10 years, advances in X-ray tomography imaging techniques, either three dimensional or four dimensional when time-lapse acquisitions are performed, allow detecting fractures at small scale and the growth and coalescence of tiny cracks into well-developed fractures. Some of these fracturing processes involve the coupling between fluids, chemical reactions and fracturing. In the present study I illustrate some of these processes, how they can be imaged using high-resolution X-ray computed tomography; and how conceptual models can make the link between microscopic processes and macroscopic fracturing. This concerns a wide range of applications in geophysics, from fundamental understanding of the rheology of rocks in the Earth’s crust, to salt damage of cultural heritage monuments, hydraulic fracturing of underground reservoirs or emerging technologies of non-conventional hydrocarbon recovery and the underground geological storage of carbon dioxide.

1 Introduction In natural rocks, cracks, fractures and faults are widespread, ranging from small defects in minerals at the microscopic level to the large tectonic faults that shape the continents at the surface of the Earth. These fractures and faults nucleate and propagate in geomaterials, which have the property of being heterogeneous at several scales. Usually, the grain size of a rock represents a natural length scale in a geomaterial, except that rocks may contain particle with a wide range of grain sizes (i.e., power law distribution). The porosity between these grains, the variations of grain composition and therefore of mechanical constants, and the presence of defects at all scales make it challenging to predict how a fracture may propagate in such complex materials. Several experimental techniques, using, for example, acoustic waves recording, elastic wave tomography, neutron imaging can be used to infer the evolution of the solid when strain accumulates and complement stress and strain measurements on the boundaries of the sample. In the present study, I focus on recent advances of imaging in 3D using X-ray computed microtomography. In the past 10 years, the development of high-resolution tomography techniques allows performing direct in-situ imaging of the geometry of heterogeneous materials [1,2]. a

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Moreover, sequential acquisitions are now possible and time-lapse images of 3D materials in which transformations through fluid-rock interactions or deformation occur are also possible [3–6]. Considering geomaterials, these imaging techniques have been applied to several problems: initiation and propagation of shear fractures and strain localization [7–10], formation of magma [11], compaction of mineral aggregates [6], dissolution into fractures [4], process of porosity generation in metamorphic rocks [12], hydraulic fracturing [13], salt damage [14], chemical alteration of rocks [5] or maturation of organic-rich shales [15]. Recent studies of melting process in oceanic rocks and identification of creep process in shear zones are illustrated in Figure 1. The high-resolution geometry obtained when imaging porous media allows also quantifying some macroscopic properties, such as permeability, from the calculation of fluid circulation in a 3D complex porous medium. This was used, for example, to characterize the 3D geometry of porous rocks [16] and estimate the permeability of materials by numerical means [17]. Such approaches are important to evaluate macroscopic properties used for multi-scale modeling of deformation in geomaterials [18] and to quantify which kind of initial damage may control fracture propagation [19]. In the following, the term damage will refer to the localized or diffuse defects that form into rocks in response to internal or external stress variations.

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(a)

(b)

(c)

(d) Fig. 2. (Color online) Various loading conditions for propagation of cracks into rocks. (a) External loading with stress σ. (b) Injection of a fluid and increase of fluid pressure (Pf ) leading to crack propagation. (c) Precipitation of a mineral from a supersaturated solution that exerts a force of crystallization (F) on the surface of the crack. (d) If a defect is filled with a reactive material, phase transformation can change the volume of this material, leading to volume increase and a stress σ exerted on the faces of the defect leading to crack formation and propagation.

Fig. 1. (Color online) Examples of X-ray microtomography studies of deformation processes in rocks. (a) Formation of melt channels along olivine grain triple junctions; melt fractions of 0.02, 0.05, 0.10 and 0.20 are displayed [11]. The resolution was 0.7 microns. (b) Microtomography images of a highly deformed ultramylonite rock sample. Shown in red are pores and the gray colors correspond to different X-ray attenuation of the various minerals. Note the small pores forming parallel sheets (A) and clusters (B) that act as fluid conduits during metamorphic reactions at depth. The volume shown is 1000 × 1000 × 500 voxels, at 1.3 micron resolution [12]. In both studies, images were acquired on beamline 2-BM at the Advanced Photon Source, Argonne National Laboratory.

In this article, I present several recent studies where rocks were imaged during fracture formation. Because of the technological developments in the past 10 years, these imaging techniques have opened new trends to characterize geomaterials: they have allowed identifying several mechanisms of fracture propagation and how fractures may interact with the heterogeneities of the rock matrix. In rocks, different kinds of loading conditions can induce the propagation of an initial crack or defect into a welldeveloped fracture (see Fig. 2). If the load is applied on the

sides of the sample (i.e., external loading), stress concentration at the crack tips will be dissipated by incremental propagation of the crack. A well-known criterion for this propagation, proposed by Griffith [20], is that the elastic strain energy at the crack tip should overcome the energy necessary to create a new surface (Fig. 2a). Other loading conditions involve that stress inside the crack may increase because of: (i) an increase of fluid pressure leading to hydraulic fracturing (Fig. 2b); (ii) the precipitation of minerals into the crack from a supersaturated solution which can induce local stress and crack propagation (Fig. 2c), and (iii) the solid containing a reactive material, due to which phase transformation can lead to volume increase and local stress increase (Fig. 2d). All these four loading conditions may exist in various geomaterials under natural conditions: formation of fractures due to the increase of tectonic loading (Fig. 2a); formation of some veins in lower crust conditions, alteration of cultural heritage buildings due to salt precipitation (Fig. 2b), hydraulic fracturing of reservoir for enhanced oil recovery or the exploitation of high-temperature geothermal reservoirs (Fig. 2c), and phase transformation of minerals under increase of pressure and temperature or the maturation of organic-rich source rocks that tend to expel hydrocarbons by a complex mechanism of maturation of kerogen and fracture formation (Fig. 2c).

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2 High-resolution 4D imaging of geomaterials reconstructed using a back projection, after filtering to remove noise due to the acquisition (spikes and ring artiusing X-ray microtomography Computed microtomography is an imaging technique based on radiography and the adsorption of X-rays. The development of third- and fourth-generation synchrotron sources allows reaching higher and higher resolution in acquiring 3D tomography images. Such synchrotons complement laboratory tomographs and extend their capacities. Their main advantage is that they produce a beam with high flux of photons, low angular aperture, high brightness, linear polarization and a continuous spectrum of wavelengths. The spatial resolution achieved can be varied from ∼0.7 to several microns and the acquisition time in the range of seconds (i.e., ultrafast tomography) to tens of minutes. The synchrotron scientists have also developed experimental devices to modify the thermodynamic conditions of the sample directly on the beamline, allowing to change temperature or pressure while performing successive time-lapse acquisitions. Therefore, processes such as deformation or phase transformation can be followed in-situ. The applications presented below are based on experiments performed on one laboratory tomograph (located at 3S-R (UJF/CNRS/GINP), Grenoble) and two synchrotrons, the beamline ID19 at the European Radiation Synchrotron Facility in Grenoble, France, and the beamline Tomcat at the Swiss Light Synchrotron (Paul Scherrer Institute) close to Z¨ urich, Switzerland. Transmission X-ray tomography delivers a map of the linear attenuation coefficient corresponding to the amount of X-rays adsorbed into a sample. The intensities are recorded by a two-dimensional detector. They are related to the integral attenuation of the various materials encountered inside the sample, along each individual X-ray path. For a specific photon energy and for every sensitive pixel in the detector, the intensity is given by the  Beer-Lambert law I = I0 exp(− ray μ(x)dx) for an inhomogeneous material or I = I0 exp(−μx) for an homogeneous material, where I0 is the intensity of the incoming beam, I is the intensity of the outgoing beam after adsorption in the sample, μ(x) stands for the attenuation coefficient of the inspected material at a given energy along direction x of the ray path. Measuring I and I0 with the imaging device along a great number of paths, it is possible to determine the corresponding integrals of μ(x). It was demonstrated in 1917 by Radon that, using this set of integrals, the 3D μ map of the sample can be reconstructed. Physical interpretation of the attenuation μ is dependent on photon energy and the density ρ of the material. For a given material and a given photon energy μ 4 ρ is constant and μ is proportional to Z where Z is the atomic number of the solid. During acquisition, the sample is sequentially rotated over a total angular range of 180◦ . Projections on an interval [0, π[ are sufficient for reconstruction. Typically equiangular radiographies are acquired (0.1–0.2◦ rotations). This is different from medical scanners where the sample does not move and the X-ray source rotates. Using the obtained set of 2D radiographs, the 3D volume is then

facts). The result is a 3D data set of voxels (i.e., volume elements) coded in a gray scale that represents the linear attenuation coefficient μ in the sample.

3 Examples of imaging fracturing processes in geomaterials 3.1 Hydrofracturing of limestone Hydraulic fractures are produced when a fluid is injected into a rock and its pressure overcomes the tensile strength of the material. To escape, the fluid produces its own space by inducing the formation of fractures, leading to local increase of permeability and flow enhancement [21,22]. Technologies involving hydrofracturing rocks are used for enhanced hydrocarbon recovery, high temperature geothermy or geological storage of carbon dioxide. To study how fractures propagate in a sedimentary rock, a small deformation rig was developed where a rock core sample was submitted to increasing fluid pressure under fracturing [13]. The samples were porous limestones and sandstones, with porosities in the range of 6–18% and contained grains and pores with sizes in the range of 10–300 microns. The core samples were scanned using synchrotron microtomography before and after fracturing (Fig. 3) at a voxel resolution of 4.91 microns. Here, the main purpose was to identify the fracture path and characterize how the initial heterogeneity of the rock (i.e., pores and grain) has controlled fracture. For this, the 3D volumes of the same sample, scanned before fracturing and after fracturing, were rotated to be located in the same reference frame. In the fractured sample volume, the exact coordinates of the fracture paths were selected and the corresponding locations in the non-broken samples could therefore be identified (Fig. 4). The challenge in such study is to compare two different 3D tomography volumes, relocate them in the same reference frame. This was done by selecting some bright grains, several tens of voxels large, and calculating their position in the two scanned volumes. Using this cloud of x-y-z positions, the parameters of a 3D translation and rotation were calculated to move the tomography image of the broken sample into the same reference frame as the initial one. Using this workflow, the fractures can be isolated and their geometry was characterized. The main result is that the fracture path is controlled by the material heterogeneities in the solid: two fractures initiated on the side of the internal hole and then propagated dynamically to its outside, breaking the sample in two parts. During propagation, the fracture tip interfered with mechanical heterogeneities, breaking grain contacts with different strength and connecting the pores between them. As a result, the number of pores crossed by the fracture is much higher than if it propagated randomly into the porous medium. This is observed in Figure 4c, where the topography of the fracture was extracted, showing its

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Fig. 4. (Color online) Tomography images of a fractured limestone core sample [13]. (a) Projection of the surface of the internal hole, showing the porosity (white) and the trace of the two fractures (F1 and F2). (b) 3D tomography representation of the fractured sample. (c) View of the fracture plane (color coding indicates the roughness) that allows characterizing how the fracture propagated by connecting pores (labeled P).

Fig. 3. (Color online) Hydraulic fracturing of a limestone [13]. (a) Sketch of the experimental setup. The sample, 9 mm diameter, has a central hole in which water was injected such that hydraulic fractures formed. Tomography images of a limestone core sample before (b) and after (c) fracturing. (d) Separation of the two broken parts. (e) The unfractured sample (black portion) and the broken sample (white-gray portion) are relocated in the same reference frame to isolate the fracture path).

rough morphology and the pores it crossed during propagation [13]. In such rocks, all grains have similar elastic constants and the heterogeneities have two main origins: the presence of pores and grains of different sizes, and the distribution of strengths of the grain contacts. At scales larger than the grain size, the core samples can be considered as homogeneous solids, with well-defined mechanical constants. At scales below the grain size, the X-ray tomography images have underlined how small variations in grain or pore shape may control out-of-plane fluctuations during fracture propagation. 3.2 Salt damage in porous rocks and the force of crystallization The growth of crystals into a porous medium can lead to the so-called force of crystallization that exerts internal stresses and may alter the mechanical properties of the solid [23,24]. This effect was recognized at the beginning of

the twentieth century when experiments of crystal growth under stress were performed by [25] and [26]. Later, [27] and [28] proposed a thermodynamic interpretation of the force exerted by a crystal growing from a supersaturated solution, which was then reanalyzed [24,29]. This force of crystallization is interpreted as the cause of mineral replacement in crustal rocks [30], rock and concrete weathering [31,32], or salt damage of cultural heritage monuments [33]. It can be understood when considering the thermodynamic equilibrium of a non-hydrostatically stressed solid in contact with its solution [29]. In the absence of stress, the chemical potential Δμ necessary for a crystal to grow is given by Δμ = kB T ln(Ω), where kB is the Boltzmann constant, T is the temperature and Ω is the supersaturation of the fluid, defined as the ratio between the ion activity product in solution and the solubility product of the solid. When stress is applied to the solid surface, this reduces the chemical potential to Δμ = kB T ln(Ω) − σn V0 , where σn is the normal stress applied to the solid and V0 is the molecular volume of the mineral. This reduction of chemical potential can lead to the build-up of a chemical potential gradient at the origin of the force of crystallization. As the growing crystal applies a force, mechanical work can be performed by displacing the confining wall in the direction perpendicular to the direction of load. Note that a thin liquid film, stabilized by a disjoining pressure, must be present between the wall and the growing crystal. Depending on the force exerted by the crystal and its growth rate, a crack may propagate or not [34]. To image the microfractures produced by growing crystals into a porous rock, experiments were conducted where

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Fig. 5. (Color online) Salt damage into rocks [14]. Left: Experimental setup for salt crystallization into porous limestone and sandstone rocks. A core sample was left in contact with glass capillaries in which a saturated solution of NaCl rose by capillary forces. A dead weight imposed a normal load to the system. An evaporation front formed into the sample, leading to salt precipitation and sample damage through the formation of cracks. Right: Tomography images of the sample showing the evaporation fronts (salt appears in light gray levels), and the formation of fractures due to the force of crystallization.

limestone and sandstone core samples were left in contact with an aqueous solution saturated with sodium chloride (Fig. 5). Each core sample was located above thin glass tubes with a well-defined length that allowed to control the height of the capillary rise of the fluid into the core sample. A modest normal load in the range of 25–250 kPa was imposed on the sample. The setup was designed such that an evaporation front formed into the sample, leading to localized salt precipitation [14]. There, a high local supersaturation could be achieved because, as the brine evaporated, salt crystals precipitated into the pores and exerted a force on their walls. The result was the formation of a network of fractures that could be imaged using X-ray microtomography (Fig. 5, right side). These fractures nucleated exactly where salt crystals precipitated, and microscopic observations (Fig. 6) showed the formation of salt crystals in the pores. These crystals surrounded the grains of the rock, leading to the quasi-static propagation of fractures. The evaporation front, with a parabolic shape, was the location of a first fracture. Then, secondary fractures radiated from the first one (Fig. 6a). The force exerted by the growing salt crystals was therefore large enough to overcome the tensile strength of the rock and the imposed normal load by breaking grain contacts or even the grains themselves (Fig. 6b–e). Because the normal load was small, it did not control the orientation of the microfractures, which developed primarily at

Fig. 6. (Color online) Microscopy images of salt damage into sedimentary rocks [14]. (a) Salt precipitation in a limestone core sample leads to the formation of fractures. The curve underlines the salt precipitation front and the main fracture produced by the force of crystallization. (b)–(e) Scanning electron microscopy images of salt crystals into a sandstone. The salt crystals (labeled S) have precipitated into the pores and exerted a force on the grain boundaries, leading to the disaggregation of the solid matrix and fracture propagation.

the evaporation front. In this experiment, the microtomography imaging technique allowed visualizing the fractures into the sample. A 3D geometrical model of microfracture formation into a porous rock during salt damage could therefore be proposed [14].

3.3 Fracturing during chemical decomposition of shales Shales are low-permeability sedimentary rocks that contain organic matter trapped into the rock matrix during deposition. With burial, the organic matter may mature toward kerogen heavy molecules and then to hydrocarbons. This transformation leads to the formation of source rocks, from which hydrocarbons are transferred to reservoir porous rocks; the whole process is called primary migration [35]. During this process of migration, the produced hydrocarbon must percolate in the source rock that has a very low permeability. Moreover, kerogen transformation into hydrocarbon can lead to volume increase that creates internal stress into the rocks, at the origin of crack formation [36–38]. To study this process, core samples from the immature Green River Shales formation (USA) were heated and

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Fig. 7. (Color online) Microscopic images of the shale material [15]. (a, b) Optical views of the fine-grained shale rock that contains patches of kerogen organic matter, noted k. (c) Scanning electron microscopy image of the shale rock, with kerogen patches indicated (k). (d) Tomography view of the sample, showing homogeneous fine grain microstructure.

tomography scans were acquired at step stages of increasing temperature. Here, the temperature increase induced an artificial maturation of the organic matter contained into the shale and the production of gases that escaped from the low-permeability matrix [15,39]. The Green River shales are fine-grained (Fig. 7) cohesive rocks that contain organic matter distributed in the form of elongated patches of immature organic material (Figs. 7b and 7c). The rock is more or less homogeneous, except that these organic patches are distributed along well-defined planes that correspond to sedimentation layers. The organic matter starts decomposing at 350 ◦ C, producing gases. One shale sample was scanned at a pixel resolution of 4.91 microns during temperature increase from room temperature to 400 ◦ C. The rate of temperature increase was continuous, equal to 1 ◦ C per minute and each scan lasted for 15 min. Under these conditions, the shale sample could be scanned several tens of times between the two end-member temperatures of the experiment. This temperature increase was possible because an oven was installed directly on the microtomography stage on beamline ID19 at ESRF. Upon heating, the shale sample showed a transition from unbroken to broken at around 370 ◦ C (Figs. 8a–8c). Several cracks, with the same orientation as the kerogen patches, have broken the sample into individual pieces. Interestingly, the formation of fractures was not instantaneous. Small cracks first initiated along planes that presumably corresponded to the decomposition of kerogen

Fig. 8. (Color online) Microtomography views of the shale sample during heating and formation of cracks [15]. (a) Sample heated to 400 ◦ C and set of fractures. (b) 2D vertical slice in the sample showing the fractures (arrows). (c) Zoom on two fractures. (d)–(f) The same fracture plane visualized at three increasing temperatures (T1 , T2 , T3 ) and showing how a full fracture developed by merging several smaller cracks that nucleated in the same plane. (g) Surface area of the same fracture that increased abruptly with temperature.

patches. This led to local gas overpressure that overcame the tensile strength of the shale. Then, these small cracks expanded laterally, until merging together into fractures that broke the whole sample (Figs. 8d–8f). The whole fracturing process occurred by the quasi-static merging of smaller cracks as kerogen decomposed. The fracture surface area increased abruptly (Fig. 8, like for percolation processes [15]). In this experiment, the difficulty was to obtain time-lapse images of an ongoing fracturing process and control the time scale of kerogen decomposition such that it could fit the 15 min duration of each scan.

4 Effect of disorder on crack propagation In the three examples of rock fracturing presented here, the resulting phenomenology is that the fracturing process

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is correlated to an increase of fluid escape. As the permeability of the rocks was not large enough, fluid pressure had built up, overcoming locally the resistance of the rock. In the three examples, the loading conditions and the rate at which the fractures propagated vary. Several time scales are involved. The nucleation time scale corresponds to the increase in stress intensity with time at a nucleation site before a crack starts propagating. Then, the time scale of fracture front propagation is the velocity of a single fracture. Finally, another time scale is the time at which several fractures start interacting and merge together. For hydrofracturing, the fracture nucleates at a point of stress concentration and propagates dynamically in the experiment. The relevant time scale here is the velocity of the crack tip. In Nature, however, when water is injected underground to fracture a reservoir and increase its permeability, the fracture tip advances at a rate that is controlled by the injection rate of the fluid. For the two other examples, salt damage and chemical decomposition in shales, the rate of fracture generation is controlled by the rate of chemical reaction: salt precipitation or kerogen decomposition. However, the question arises on the control parameters of fracture expansion: in a quasi-static manner or dynamically? And what is the effect of material heterogeneity on fracture propagation? To answer these two questions, two main kinds of fracture models may be used: continuous models (analytical and numerical) or discrete models (statistical and numerical). These two approaches are complementary and described shortly in the following. Disorder has important effect on material strength as (i) fractures may nucleate from a weak point, (ii) the propagation front of a single fracture may be sensitive to local disorder and (iii) several fractures may interact and merge (see Chapter 7 in [40] for the role of microstructure in fracture propagation). On the one hand, fundamental understanding of fracture processes comes from statistical physics [41] and the development of lattice simulations and discrete models. One of the most famous of these models is the random fuse network [42], in which a fracture propagates into a solid material by the successive failure of weakest bonds. Such an approach provides new concepts on how frozen properties of the solid (i.e., disorder) control fracture propagation. On the other hand, continuum fracture mechanics describes the propagation of cracks in terms of macroscopic field equations, based on the theory of linear elasticity and the proposition that the stability of a crack is given by a simple energy criterion provided by Griffith in 1920 [20]. Fuse networks can be used to study the microscopic dynamics of damage, where the several microcracks will nucleate, propagate, connect and finally span the entire system into a well-developed fracture. In such a model, depinning scenario is also proposed where the crack tip is pinned by heterogeneities during its propagation, leading to the deformation of the crack front and the development of a roughness corresponding to out-of-plane fluctuations of the crack position (see Fig. 4). The localization of damage corresponds to a transition when local microfailures

become correlated, leading, for example, to the development of fractures in the shale heating experiments (Fig. 8). A rupture propagates if stress prevails over the resistance of the solid at the surface of the fracture. The stress field at the tip of a loaded crack may be characterized by the stress intensity factor K that describes local stress concentration [40]. For the opening mode (Mode I) the stress intensity factor at the crack tip is c (r) dr, where r is the distance given by KI = √2πc 0 √rσc2r−r 2 from the center of the crack and c is the crack length. If K is greater than a critical value Kc , the crack then propagates and its rate is given by the energy release rate G, which is a function of the applied stress, crack length and crack geometry. When G = G0 , the elastic energy released during incremental crack growth exactly matches the incremental surface energy of the material under the prevailing environmental conditions, and the crack is in thermodynamic equilibrium. If G is larger than G0 , but smaller than the critical energy release rate, Gc , subcritical crack growth will take place. The absolute value of G0 is highly dependent on the environmental conditions, but it is typically of the order of 20–90% of Gc . For an energy release rate greater than Gc , the crack propagates dynamically. The crack front may deform because heterogeneities in the rock give rise to local fluctuations of toughness K or surface energy G. The influence of disorder on fracture propagation may have several origins, such as variations of elastic properties or fluctuations of the crack surface energy release. When the disorder is dilute, there is no interaction between the heterogeneities and fracture onset occurs at the weakest spot. However, as the damage in the solid increases, the large number of interactions leads to the formalism of damage mechanics [19,43] which describes the progressive loss of integrity of a solid due to the propagation and coalescence of microcracks, pores and other defects. As the cracks grow slowly and continuously, the sample is considered at each time step in a quasi-equilibrium stage. The dynamics of individual cracks can be disregarded and the damage can be treated by homogenization at a macro scale. This is valid as long as the interactions between individual cracks remain moderate. For example, in the case of the shale heating or salt damage experiments (Figs. 6 and 8b), microcracks are initiated by chemical reactions in the solid, creating a diffuse damage. Then these cracks start growing, interacting with each other (Figs. 6d–6f), and merging until the complete failure of the samples. The out-of plane fluctuations (i.e., roughness) of the produced fractures in the hydraulic fracture experiments (Fig. 4c) are also due to the presence of local disorder during rupture propagation.

5 Conclusion Simulation of fracture in heterogeneous materials is complicated by the presence of disorder, whose presence naturally leads to statistical distribution of failure stresses

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and accumulated damage. On the one hand, standard continuum constitutive equations are based on mean-field or coarse grained approaches and hence may have difficulties to deal with the effects of fluctuations. On the other hand, discrete or network models reproduce some statistical properties of fracture propagation but fail to predict the exact fracture path in a complex material. Regardless of whether one can solve numerically and in a continuous manner damage generation and fracture propagation into a complex medium, the dynamics of rupture will be perturbed by the presence of heterogeneities at all scales. The advantage of high-resolution microtomography imaging techniques is that such disorder can be characterized precisely, and not only in a statistical manner, providing data to more completely understand how fracture have nucleated, propagated and arrested in complex geomaterials. This study was funded by the ANR Project JCJC-0011-01. The author would like to thank Dominique Bernard (ICMCB, Bordeaux), Elodie Boller (ESRF, Grenoble), Pascal Charrier and Jacques Desrues (University of Grenoble), Maya Kobchenko (University of Olso), Marco Stampanoni (SLS, Paul Scherrer Institute) and Catherine Noiriel (University of Toulouse) for enlightening discussions. Wenlu Zhu and Florian Fusseis are warmly thanked for providing the images displayed in Figure 1.

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