Papers by Jean Schmittbuhl
We present in this paper an experimental study of the invasion activity during unstable drainage ... more We present in this paper an experimental study of the invasion activity during unstable drainage in a 2D random porous medium, when the (wetting) displaced fluid has a high viscosity with respect to that of the (non-wetting) displacing fluid, and for a range of almost two decades in capillary numbers corresponding to the transition between capillary and viscous fingering. We
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999
We study experimentally the propagation of an in-plane fracture into a transparent and heterogene... more We study experimentally the propagation of an in-plane fracture into a transparent and heterogeneous Plexiglas block. A stable crack propagation in mode I is monitored by an imposed displacement. The experimental setup allows a high resolution observation of the crack front in situ. Self-affine properties of the crack front are described over more than three decades using several techniques: variable bandwidth, return probability, Fourier spectrum, and wavelet analysis. The different methods lead to a roughness exponent of 0.63+/-0.03, consistent with a previous work.
Physical Review E, 2002
We have investigated experimentally the competition between viscous, capillary, and gravity force... more We have investigated experimentally the competition between viscous, capillary, and gravity forces during drainage in a two-dimensional synthetic porous medium. The displacement of a mixture of glycerol and water by air at constant withdrawal rate has been studied. The setup can be tilted to tune gravity, and pressure is recorded at the outlet of the model. Viscous forces tend to destabilize the displacement front into narrow fingers against the stabilizing effect of gravity. Subsequently, a viscous instability is observed for sufficiently large withdrawal speeds or sufficiently low gravity components on the model. We predict the scaling of the front width for stable situations and characterize it experimentally through analyses of the invasion front geometry and pressure recordings. The front width under stable displacement and the threshold for the instability are shown, both experimentally and theoretically, to be controlled by a dimensionless number F which is defined as the ratio of the effective fluid pressure drop (i.e., average hydrostatic pressure drop minus viscous pressure drop) at pore scale to the width of the fluctuations in the threshold capillary pressures.
Physical Review E, 2002
The flow paths and instabilities of gravity driven infiltration of a wetting fluid into a porous ... more The flow paths and instabilities of gravity driven infiltration of a wetting fluid into a porous medium are studied. The model experiments and simulations independently represent techniques to study the unsaturated flow in porous media, and they produce a consistent picture of how the paths of fluid transport form and depend on the relative strength of the gravitational force. The experiments, which employ a transparent and quasi-two-dimensional model, reveal that the fluid pathways contain an internal link-blob structure and increase in width with decreasing gravity. The model, which couples the well established invasion percolation model for capillary governed flow with a model that describes the viscous film flow in partially filled pores, corroborates these experimental findings.
We have studied experimentally and numerically the displacement of a highly viscous wetting fluid... more We have studied experimentally and numerically the displacement of a highly viscous wetting fluid by a non-wetting fluid with low viscosity in a random two-dimensional porous medium under stabilizing gravity. In situations where the magnitudes of the viscous-, capillary-and gravity forces are comparable, we observe a transition from a capillary fingering behavior to a viscous fingering behavior, when decreasing apparent gravity. In the former configuration, the vertical extension of the displacement front saturates; in the latter, thin branched fingers develop and rapidly reach breakthrough. From pressure measurements and picture analyzes, we experimentally determine the threshold for the instability, a value that we also predict using percolation theory. Percolation theory further allows us to predict that the vertical extension of the invasion fronts undergoing stable displacement scales as a power law of the generalized Bond number Bo à ¼ Bo À Ca, where Bo and Ca are the Bond and capillary numbers, respectively. Our experimental findings are compared to the results of a numerical modeling that takes local viscous forces into account. Theoretical, experimental and numerical approaches appear to be consistent. #
Physical Aspects of Fracture, 2001
ABSTRACT We study experimentally the propagation of an inter-facial crack through a weak plane of... more ABSTRACT We study experimentally the propagation of an inter-facial crack through a weak plane of a transparent Plexiglas block. The toughness is controlled artificially by a sand blasting procedure and fluctuates locally in space like an uncorrelated random noise. The block is fractured in mode I at low speed (10-7 — 10-4m/s). The crack front is observed optically with a microscope and a high resolution digital camera for pinned fronts or a fast digital camera for local dynamics of fronts. During the propagation, the front is pinned by micro-regions of high toughness and becomes rough. Roughness of the crack front is analyzed in terms of self-affinity. The roughness exponent of trapped fronts is shown to be 0.63 ± 0.05. During propagation, bursts of the front are described as an interface growth process. The dynamical exponent of a Family-Vicsek scaling is measured to: z ≈ 1.15. Velocity fluctuations are measured in the space-time domain.
Tectonophysics, 2006
To assess the role of the fault thickness on its mechanical behavior, we first present the result... more To assess the role of the fault thickness on its mechanical behavior, we first present the results of an experimental modeling of a thick fault core. Our laboratory setup consists in an annular simple shear apparatus in which we can apply very large shear displacements (50 m) to 100 particle thick granular samples. Thanks to a window in the apparatus, pictures of the microstructures can be continuously taken during shear. We observe from a Correlation Image Velocimetry technique that a significant strain field exists outside of the observable shear band. This strain field, though of small magnitude compared to that existing inside the shear band, is very structured and extends in a region much wider than expected from individual static observations (i.e. wider than the directly observable shear band). Moreover, this strain field controls most of the evolution of the shear strength of the fault. We then propose plausible comparisons of our experimental results to geological observations of fault cores in the region of Aigion (Corinth Gulf, Greece). The studied faults indeed display spectacular indurated fault planes lying on weakly cohesive material. Signatures of cementation, clay mineral distribution and porosity profile of one of the studied fault cores are included and discussed in the light of the experimental results. Our observations suggest that the maximum shear strain during earthquakes might occur not in the center, but on the border of the fault cores. It is presumably localized in a transition zone which exhibits a significant cementation owing to a process of mechanical smearing by fine particles. This zone may also act as a very low permeability layer responsible for a channeling of the fluid flow. Such a scheme of progressive multi sub-localizations, is different from classical descriptions of faults and consistent with a layering of the core consisting of separated zones of high strains or large cataclastic flows.
Pure and Applied Geophysics, 2003
-- A numerical fracture flow simulation based on the lubrication approximation is used to investi... more -- A numerical fracture flow simulation based on the lubrication approximation is used to investigate the influence of roughness on the flow inside a rough fracture, at low Reynolds number. Facing surfaces are described as self-affine topographies with identical roughness magnitude. Resolution of the Reynolds equation is achieved using two distinct numerical schemes, with consistency. Fracture closure is studied assuming perfect plastic contact between facing surfaces. Long-range correlations are shown to exist in the local aperture field due to the fracture geometry and subsequently in the local fluxes inside the fracture. Flow channeling is the result of these correlations in terms of spatial distribution of the flow, and is responsible for either flow-enhancing or flow-inhibiting behavior of the fracture. Matching between the two surfaces at scales larger than a mismatch scale is studied. The mismatch scale is the upper limit scale for the local apertures scale invariance. It appears to control flow channeling and the related dispersion of the possible behaviors over a large statistics of fractures with identical statistical features. Hydraulic anisotropy of a given fracture is investigated: the dependence of the fracture transmittivity on the pressure drop orientation is proved to be sinusoidal, with an amplitude that is controlled by the mismatch scale.
Physical Review Letters, 2001
We address the role of material heterogeneities on the propagation of a slow rupture at laborator... more We address the role of material heterogeneities on the propagation of a slow rupture at laboratory scale. With a high speed camera, we follow an in-plane crack front during its propagation through a transparent heterogeneous Plexiglas block. We obtain two major results. First, the slip along the interface is strongly correlated over scales much larger than the asperity sizes. Second, the dynamics is scale dependent. Locally, mechanical instabilities are triggered during asperity depinning and propagate along the front. The intermittent behavior at the asperity scale is in contrast with the large scale smooth creeping evolution of the average crack position. The dynamics is described on the basis of a Family-Vicsek scaling.
Physical Review Letters, 2006
The propagation of an interfacial crack along a heterogeneous weak plane of a transparent Plexigl... more The propagation of an interfacial crack along a heterogeneous weak plane of a transparent Plexiglas block is followed using a high resolution fast camera. We show that the fracture front dynamics is governed by local and irregular avalanches with very large size and velocity fluctuations. We characterize the intermittent dynamics observed, i.e., the local pinnings and depinnings of the crack front by measuring the local waiting time fluctuations along the crack front during its propagation. The deduced local front line velocity distribution exhibits a power law behavior, Pv / v ÿ with 2:55 0:15, for velocities v larger than the average front speed hvi. The burst size distribution is also a power law, PS / S ÿ with 1:7 0:1. Above a characteristic length scale of disorder L d 15 m, the avalanche clusters become anisotropic providing an estimate of the roughness exponent of the crack front line, H 0:66.
Physical Review Letters, 2000
The scaling laws describing the roughness development of crack surfaces are incorporated into the... more The scaling laws describing the roughness development of crack surfaces are incorporated into the Griffith criterion. We show that, in the case of a Family-Vicsek scaling, the energy balance leads to a purely elastic brittle behavior. On the contrary, it appears that an anomalous scaling reflects a R-curve behavior associated to a size effect of the critical resistance to crack growth in agreement with the fracture process of heterogeneous brittle materials exhibiting a microcracking damage.
Physical Review E, 2008
We compare quantitatively two experimental situations concerning injection of a miscible fluid in... more We compare quantitatively two experimental situations concerning injection of a miscible fluid into an initially jammed granular medium saturated with the same fluid, confined in a Hele-Shaw cell. The two experiments are identical, apart from the interstitial and injected fluid, which is in one case air injected into a dry granular packing, and in the other case silicone oil injected into a dense suspension. In spite of the strong differences regarding the nature of the two fluids, strikingly similar dynamical and geometrical features are identified as functions of the control parameters: cell thickness and applied fluid injection pressure. In both cases an initial hydrodynamically driven decompaction process controls the unjamming and prepares the final displacement process characterized by fingerlike patterns empty of grains. The pattern shapes are comparable. In addition, the mobilities of the coupled fluid-grain flow, rescaled by the interstitial fluid viscosity and grain diameter squared, are of the same range and behave comparably. The mobility proves to depend on the initial solid fraction of the medium. Subtle differences are observed in geometrical aspects like the finger width with respect to the control parameters.
Physical Review E, 2008
In a previous paper [Phys. Rev. Lett. 91, 014501 (2003)], the mechanism of "revolving rivers" for... more In a previous paper [Phys. Rev. Lett. 91, 014501 (2003)], the mechanism of "revolving rivers" for sandpile formation is reported: as a steady stream of dry sand is poured onto a horizontal surface, a pile forms which has a river of sand on one side flowing from the apex of the pile to the edge of the base. For small piles the river is steady, or continuous. For larger piles, it becomes intermittent. In this paper we establish experimentally the "dynamical phase diagram" of the continuous and intermittent regimes, and give further details of the piles "topography", improving the previous kinematic model to describe it and shedding further light on the mechanisms of river formation. Based on experiments in Hele-Shaw cells, we also propose that a simple dimensionality reduction argument can explain the transition between the continuous and intermittent dynamics.
Physical Review E, 2008
We investigate experimentally the pattern formation process during injection of air in a noncohes... more We investigate experimentally the pattern formation process during injection of air in a noncohesive granular material confined in a linear Hele-Shaw cell. We characterize the features and dynamics of this pattern formation on the basis of fast image analysis and sensitive pressure measurements. Behaviors are classified using two parameters-injection pressure and plate opening-and four hydrodynamic regimes are defined. For some regions of the parameter space, flows of air and grains are shown to be strongly coupled and instable, and lead to channelization within the granular material with obvious large-scale permeability variations.
Physical Review E, 2004
We present in this paper an experimental study of the invasion activity during unstable drainage ... more We present in this paper an experimental study of the invasion activity during unstable drainage in a 2D random porous medium, when the (wetting) displaced fluid has a high viscosity with respect to that of the (non-wetting) displacing fluid, and for a range of almost two decades in capillary numbers corresponding to the transition between capillary and viscous fingering. We show that the invasion process takes place in an active zone within a characteristic screening length λ from the tip of the most advanced finger. The invasion probability density is found to only depend on the distance z to the latter tip, and to be independent of the value for the capillary number Ca. The mass density along the flow direction is related analytically to the invasion probability density, and the scaling with respect to the capillary number is consistent with a power law. Other quantities characteristic of the displacement process, such as the speed of the most advanced finger tip or the characteristic finger width, are also consistent with power laws of the capillary number. The link between the growth probability and the pressure field is studied analytically and an expression for the pressure in the defending fluid along the cluster is derived. The measured pressure are then compared with the corresponding simulated pressure field using this expression for the boundary condition on the cluster.
Journal of Geophysical Research, 2001
Journal of Geophysical Research, 2002
1] Localization of deformation during fracture mechanical tests leads to the development of shear... more 1] Localization of deformation during fracture mechanical tests leads to the development of shear bands. We performed triaxial tests using Sidobre granite at four different confining pressures (from 20 to 80 MPa). We compared two sets of tests: one set was stopped immediately after the formation of the shear band; a second one included additional shear deformation. From the analysis of thin sections of these laboratory samples, we characterize the typical microstructures in the shear band (mode I and II cracks, Riedel cracks, cataclastic flow). Statistical properties of rupture surface roughness and gouge grain size reveals scaling invariance. Using a mechanical profiler, the fracture roughness is measured along parallel profiles and shown to be correctly described over up to 3 orders of magnitude by self-affine geometry with a roughness exponent close to z = 0.80. This property is very similar to tensile crack even if local processes are different. The influence of the slip is observed. Fracture surfaces are rougher along the slip direction (z = 0.74) than perpendicular to it (z* = 0.80). The confining pressure is shown to have a weak effect on the fracture roughness. It smoothes the surface: slight increase of the roughness exponent. Gouge particles extracted from the shear band present a power law distribution with an exponent ranging from 1.44 to 1.91. This exponent appears to increase with the shearing displacement and the confining pressure. When a significant shear of the band is combined with a high confining pressure (i.e., impeded dilation of the band), the hallmark of fragmentation is observed for the particle distribution and related to a smoothing of the band boundary.
International Journal of Fracture, 2000
Recently the R-curve behavior observed on quasi-brittle materials was proposed to be related to t... more Recently the R-curve behavior observed on quasi-brittle materials was proposed to be related to the roughness development of fracture surfaces. However, many experiments have shown that the R-curve behavior is not a material property but depends on the specimen shape. It is also expected that the roughening of fracture surfaces is influenced by the specimen geometry and so R-curve behaviors related to this roughening. From mode I fracture tests on wood specimens of three different shapes, R-curves are estimated and the morphology of the crack surfaces are analysed. We show that the scaling exponents of the anomalous scaling law used to describe accurately the roughness development of crack surfaces, are not influenced by the specimen geometry and appear as material dependent parameters. Nevertheless, the fracture surfaces exhibit a roughness growth region that reduces with the average stiffness of the specimens. Accordingly, the maximum roughness magnitude of fracture surfaces is a function of the initial stiffness: the higher the stiffness, the smaller the maximum magnitude of the roughness. We show that the analytical R-curves deduced from the roughnening of fracture surfaces provide good fits of the experimental macroscopic R-curves. However, if the scaling exponents obtained from the R-curve fits are close to those measured from the microscopic roughness analysis, the description of the experimental R-curves requires a magnification of the real area of the main crack. This magnification can be explained by the weakness of the assumption of an energy only dissipated by a single crack and not by a process zone. Finally, we argue that an approach where the energy is dissipated by a set of microcracks that follow the same anomalous scaling, could fully explain the experimental R-curves.
Geophysical Research Letters, 2000
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Papers by Jean Schmittbuhl