Renaud Toussaint

• Reis, Paula Kozlowski Pitombeira; Flekkøy, Eirik Grude; Toussaint, Renaud & Måløy, Knut Jørgen (2026). Linear response theory of front back-contraction during a single Haines jump. Journal of Fluid Mechanics. ISSN 0022-1120. 1041. doi: 10.1017/jfm.2026.11960. Fulltekst i vitenarkiv Vis sammendrag

  We study the linear response of a fluid–fluid interface in a porous medium subjected to a localised, transient perturbation. A single pore is driven out of mechanical equilibrium by a small displacement, initiating a back-contraction of the interface. Assuming negligible total flow, the interface relaxes with a time- and space-dependent profile h(x,t), modelled for a flat geometry. This set-up reflects conditions achievable experimentally using a localised heterogeneity in pore-throat sizes. We determine the evolving interface shape during the relaxation process, together with the associated pressure and velocity fields, using both analytical calculations and pore-network simulations.

• Abbasov, Rashad; Fahs, Marwan; Fontaine, Vincent; Baalousha, Husam Musa; Younes, Anis & Toussaint, Renaud (2026). Assessing simplified approaches in modeling rainfall-induced landslides using Richards' equation with Biot poroelasticity. Engineering Geology. ISSN 0013-7952. 360, s. 108481–108481. doi: 10.1016/j.enggeo.2025.108481. Fulltekst i vitenarkiv
• Dodangeh, A.; Toussaint, Renaud; Flekkøy, Eirik Grude & Fahs, M. (2025). Managing seismicity and characterizing reservoirs to enable geothermal energy development while minimizing seismic risk and impacts. doi: 10.3997/2214-4609.202521178. Fulltekst i vitenarkiv
• Sarma, Pritom; Aharonov, Einat; Toussaint, Renaud & Parez, Stanislav (2025). Fault Gouge Failure Induced by Fluid Injection: Hysteresis, Delay and Shear‐Strengthening. Journal of Geophysical Research (JGR): Solid Earth. ISSN 2169-9313. 130(6). doi: 10.1029/2024jb030768. Fulltekst i vitenarkiv Vis sammendrag

  Natural faults often contain a fluid‐saturated, granular fault‐gouge layer, whose failure and sliding processes play a central role in earthquake dynamics. Using a two‐dimensional discrete element model coupled with fluid dynamics, we simulate a fluid‐saturated granular layer, where fluid pressure is incrementally raised. At a critical fluid pressure level, the layer fails and begins to accelerate. When we gradually reduce fluid pressure, a distinct behavior emerges: slip‐rate decreases linearly until the layer halts at a fluid pressure level below that required to initiate failure. During this pressure cycle the system exhibits (a) velocity‐strengthening friction and (b) frictional hysteresis. These behaviors, well established in dry granular media, are shown to extend here to shear of dense fluid‐saturated granular layers. Additionally, we observe a delay between fluid pressure increase and failure, associated with pre‐failure dilative strain and “dilational‐hardening.” During this delay period, small, arrested slip events dilate the layer in preparation for full‐scale failure. Our findings may explain (a) fault motion that continues even after fluid pressure returns to pre‐injection levels, and (b) delayed failure in fluid‐injection experiments, and (c) pre‐failure arrested slip events observed prior to earthquakes.

• Hafermaas, Daniel; Köhler, Saskia; Koehn, Daniel & Toussaint, Renaud (2025). Dynamic System Roughening from Mineral to Tectonic Plate Scale: Similarities Between Stylolites and Mid-Ocean Ridges. Minerals. 15(7), s. 743–743. doi: 10.3390/min15070743. Fulltekst i vitenarkiv Vis sammendrag

  Stylolites are a common mineral dissolution feature in rocks that develop during compression and form distinct tooth structures. On a tectonic plate scale, mid-ocean ridges (MORs) and transform faults are a significant feature of the Earth’s surface that develop due to accretion of new material in an extensional regime. We present a comparison between the two features and argue that transform faults in MOR are similar to the sides of stylolite teeth, with both features representing kinematic faults (KFs). First, we present a numerical model of both stylolite and MOR growth and show that in both cases, KFs nucleate and grow spontaneously. In addition, we use a well-established technique (Family–Vicsek scaling) of describing fractal self-affine interfaces, which has been used for stylolites, to characterize the pattern of MOR systems in both simulations and natural examples. Our results show that stylolites and MOR have self-affine scaling characteristics with similar scaling regimes. They both show a larger roughness exponent at the small scale, a smaller exponent at the intermediate scale, followed by a flattening of the system at the largest scale. For stylolites, the physical forces behind the scaling are the surface energy at the small mineral scale, the elastic energy at the intermediate scale, followed by the system reaching the correlation length where growth stops. For MORs, the physical forces behind the scaling are not yet clear; however, the self-affine scaling shows that transform faults at MORs do not have a preferred spacing, but that the spacing is fractal. Our study offers a new perspective on the study of natural roughening phenomena on various scales, from minerals to tectonic plates, and a new view on the development of MORs.

• Meghraoui, Mustapha; Cakir, Ziyadin; Kariche, Jugurtha; Toussaint, Renaud; Provost, Floriane & Karabacak, Volkan [Vis alle 9 forfattere av denne artikkelen] (2025). The 2023 Mw 7.8 Kahramanmaraş earthquake rupture increases potential failure along the northern Dead Sea Fault. Tectonophysics. ISSN 0040-1951. 910, s. 230799–230799. doi: 10.1016/j.tecto.2025.230799. Fulltekst i vitenarkiv
• Hernandez-Perez, Kevin; Schäfer, Gerhard; Lehmann, François; Piri, Mohammad & Toussaint, Renaud (2025). An innovative experimental device to quantify the water relative permeability and in situ water retention curves of unconsolidated porous media. Comptes rendus Geoscience. ISSN 1631-0713. 357, s. 475–488. doi: 10.5802/crgeos.315. Fulltekst i vitenarkiv Vis sammendrag

  Accurate determination of water relative permeability (krw) is essential for modelling flow in porous media. Traditional methods often rely on bulk averaging and assumed unit hydraulic gradients, which limit spatial resolution and introduce uncertainties. This study presents a novel experimental column setup that integrates a PICO TDR probe for in situ water content measurement and dual pressure transducers for direct pressure gradient monitoring under steady-state flow conditions. Experiments were conducted on two water-wet quartz sands (P100 and P2040), which differed in grain sizes and porosities. A stepwise drainage and imbibition protocol enabled the derivation of both water retention curves and water relative permeability (krw–Sw) curves, using Darcy’s law and matching-point normalization. Initial saturation was achieved through upward imbibition using distilled water, preceded by a nitrogen injection to minimize air entrapment and accurately determine porosity. Each experiment was repeated under identical conditions to verify the reproducibility of the results. Results show minimal hysteresis between drainage and imbibition curves and excellent agreement with the Mualem–van Genuchten predicted krw, using parameters independently derived from the water retention curves. The approach demonstrates high reproducibility and predictive accuracy, providing a strong platform for future studies involving pore-scale simulations, wettability alteration, or hysteresis modelling.

• Khobaib, Khobaib; Reis, Paula Kozlowski Pitombeira; Moura, Marcel; Toussaint, Renaud; Flekkøy, Eirik Grude & Måløy, Knut Jørgen (2025). Gravity stabilized drainage in porous media with controlled disorder. Physical Review Research (PRResearch). 7(2). doi: 10.1103/PhysRevResearch.7.023040. Fulltekst i vitenarkiv Vis sammendrag

  This work presents an experimental, numerical, and theoretical investigation of slow drainage processes in porous media, focusing on systematic variations in pore-scale disorder. We examine a system comprising a monolayer of cylinders in a quasi-two-dimensional (2D) geometry, where the medium's disorder is controlled via a disorder parameter, 𝜀. By systematically altering 𝜀, we randomly shift the positions of the cylinders and analyze the resulting effects on the gravity stabilized invasion front. Our results show that increasing 𝜀 has a significant impact on the stable width of the invasion front, with this width scaling with the disorder parameter according to an exponent 𝛽=0.57, which closely matches the theoretical value predicted by percolation theory for 2D systems. Additionally, we derive a reciprocal relationship between the dimensionless fluctuation number and the disorder parameter 𝜀. Moreover, we find a correlation between the invasion front width and the size of trapped clusters in the system, and we explore how pore disorder affects the air saturation left behind the invasion front. Both our experimental and numerical findings exhibit exponent values that align with theoretical scaling predictions. This study advances the current understanding of multiphase flows in porous media by specifically addressing the influence of pore-scale disorder on the morphology of invasion fronts.

• Reis, Paula Kozlowski Pitombeira; Linga, Gaute; Moura, Marcel; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Vis alle 7 forfattere av denne artikkelen] (2025). Interaction between corner and bulk flows during drainage in granular porous media. Advances in Water Resources. ISSN 0309-1708. 198. doi: 10.1016/j.advwatres.2025.104914. Fulltekst i vitenarkiv
• Hibert, Clément; Noel, Francois; Toe, David; Talib, Miloud; Desrues, Mathilde & Wyser, Emmanuel [Vis alle 11 forfattere av denne artikkelen] (2024). Machine learning prediction of the mass and the velocity of controlled single-block rockfalls from the seismic waves they generate. Earth Surface Dynamics. ISSN 2196-6311. 12(3), s. 641–656. doi: 10.5194/esurf-12-641-2024. Fulltekst i vitenarkiv Vis sammendrag

  Understanding the dynamics of slope instabilities is critical to mitigate the associated hazards, but their direct observation is often difficult due to their remote locations and their spontaneous nature. Seismology allows us to get unique information on these events, including on their dynamics. However, the link between the properties of these events (mass and kinematics) and the seismic signals generated is still poorly understood. We conducted a controlled rockfall experiment in the Riou Bourdoux torrent (southern French Alps) to try to better decipher those links. We deployed a dense seismic network and inferred the dynamics of the block from the reconstruction of the 3D trajectory from terrestrial and airborne high-resolution stereophotogrammetry. We propose a new approach based on machine learning to predict the mass and the velocity of each block. Our results show that we can predict those quantities with average errors of approximately 10 % for the velocity and 25 % for the mass. These accuracies are as good as or better than those obtained by other approaches, but our approach has the advantage in that it does not require the source to be localised, nor does it require a high-resolution velocity model or a strong assumption on the seismic wave attenuation model. Finally, the machine learning approach allows us to explore more widely the correlations between the features of the seismic signal generated by the rockfalls and their physical properties, and it might eventually lead to better constraints on the physical models in the future.

• Arran, M.I.; Mangeney, A.; Rosny, Rosny De & Toussaint, Renaud (2024). Simulated Slidequakes: Insights From DEM Simulations Into the High-Frequency Seismic Signal Generated by Geophysical Granular Flows. Journal of Geophysical Research (JGR): Earth Surface. ISSN 2169-9003. 129(8). doi: 10.1029/2023JF007455. Fulltekst i vitenarkiv Vis sammendrag

  Geophysical granular flows generate seismic signals known as “slidequakes” or “landquakes”, with low-frequency components whose generation by mean forces is widely used to infer hazard-relevant flow properties. Many more such properties could be inferred by understanding the fluctuating forces that generate slidequakes' higher frequency components and, to do so, we conducted discrete-element simulations that examined the fluctuating forces exerted by steady, downslope-periodic granular flows on fixed, rough bases. Unlike our previous laboratory experiments, our simulations precluded basal slip. We show that, in its absence, simulated basal forces' power spectra have high-frequency components more accurately predicted using mean shear rates than using depth-averaged flow velocities, and can have intermediate-frequency components which we relate to chains of prolonged interparticle contacts. We develop a “minimal model”, which uses a flow's collisional properties to even more accurately predict the high-frequency components, and empirically parametrize this model in terms of mean flow properties, for practical application. Finally, we demonstrate that the bulk inertial number determines not only the magnitude ratio of rapidly fluctuating and mean forces on a unit basal area, consistent with previous experimental results, but also the relative magnitudes of the high and intermediate-frequency force components.

• Abbasov, Rashad; Fahs, Marwan; Younes, Anis; Nowamooz, Hossein; Måløy, Knut Jørgen & Toussaint, Renaud (2024). Modeling rainfall-induced landslide using the concept of local factor of safety: Uncertainty propagation and sensitivity analysis. Computers and geotechnics. ISSN 0266-352X. 167. doi: 10.1016/j.compgeo.2024.106102. Fulltekst i vitenarkiv Vis sammendrag

  Rainfall-induced landslides (RILS) are commonly investigated using hydro-mechanical models with the concept of local factor of safety. The inputs of these models are usually prone to uncertainties. An uncertainty analysis is required to investigate how uncertainties propagate through the model and impact the predictions. An appropriate strategy for uncertainty propagation analysis is suggested in this work to deal with nonlinearity and high dimensionality of RILS problems. It proceeds by performing a sensitivity analysis in two steps. A screening technique is first applied to eliminate insignificant parameters. Then, a global sensitivity analysis is performed to rank the parameters by order of importance. The Sobol indices are used as sensitivity metrics. The polynomial chaos expansion is used to compute the Sobol indices. The proposed strategy is first applied to a hypothetical benchmark and then to a more realistic configuration where prior knowledge of parameters and type of soil are considered. The results show that, when prior knowledge of soil is available, the most important parameters are the coefficient of cohesion, friction angle and air entry pressure head, respectively. The results also show that 10% uncertainty on these parameters leads to about 20% uncertainty on the prediction of slope stability.

• Reis, Paula Kozlowski Pitombeira; Linga, Gaute; Moura, Marcel; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Vis alle 7 forfattere av denne artikkelen] (2024). Interaction between corner and bulk flows during drainage in granular porous media. arXiv.org. ISSN 2331-8422. doi: 10.48550/arXiv.2409.05574. Fulltekst i vitenarkiv
• Ben-Zeev, Shahar; Goren, Liran; Toussaint, Renaud & Aharonov, Einat (2023). Drainage explains soil liquefaction beyond the earthquake near-field. Nature Communications. 14(1). doi: 10.1038/s41467-023-41405-4. Fulltekst i vitenarkiv Vis sammendrag

  Abstract Earthquake-induced soil-liquefaction is a devastating phenomenon associated with loss of soil rigidity due to seismic shaking, resulting in catastrophic liquid-like soil deformation. Traditionally, liquefaction is viewed as an effectively undrained process. However, since undrained liquefaction only initiates under high energy density, most earthquake liquefaction events remain unexplained, since they initiate far from the earthquake epicenter, under low energy density. Here we show that liquefaction can occur under drained conditions at remarkably low seismic-energy density, offering a general explanation for earthquake far-field liquefaction. Drained conditions promote interstitial fluid flow across the soil during earthquakes, leading to excess pore pressure gradients and loss of soil strength. Drained liquefaction is triggered rapidly and controlled by a propagating compaction front, whose velocity depends on the seismic-energy injection rate. Our findings highlight the importance of considering soil liquefaction under a spectrum of drainage conditions, with critical implications for liquefaction potential assessments and hazards.

• Flekkøy, Eirik Grude & Toussaint, Renaud (2023). Statistical implications of the n = 1 observation of 1I/'Oumuamua. Monthly Notices of the Royal Astronomical Society: Letters (MNRAS Letters). ISSN 1745-3925. 523(1), s. L9–L14. doi: 10.1093/mnrasl/slad049. Fulltekst i vitenarkiv Vis sammendrag

  ABSTRACT We obtain the exact statistical distribution of expected detection rates that may be obtained from the detection of ‘Oumuamua, which currently belongs to a class of objects that is only observed once in our Solar system. The derivation of the distribution of future detection rates starts from the assumption that the detection is a result of a Poisson process, and uses Bayes theorem along with information theory to get the result. We derive the probability for the next such observation along with the confidence limits of this prediction assuming that observations are done with the forthcoming Vera C. Rubin Observatory. This probability depends on the estimates of detection rates that existed prior to the ‘Oumuamua observation. However, unless the constraints given by these model-based estimates are within an order of magnitude of the actual detection rate, they have a negligible effect on the probability of making a second observation. The results are generalized to the expected future case where more than one observation exists.

• Noel, Francois; Nordang, Synnøve Flugekvam; Jaboyedoff, Michel; Travelletti, Julien; Matasci, Battista & Digout, Michaël [Vis alle 16 forfattere av denne artikkelen] (2023). Highly energetic rockfalls: back analysis of the 2015 event from the Mel de la Niva, Switzerland. Landslides. Journal of the International Consortium on Landslides. ISSN 1612-510X. doi: 10.1007/s10346-023-02054-2. Fulltekst i vitenarkiv Vis sammendrag

  Abstract Process-based rockfall simulation models attempt to better emulate rockfall dynamics to different degrees. As no model is perfect, their development is often accompanied and validated by the valuable collection of rockfall databases covering a range of site geometries, rock masses, velocities, and related energies that the models are designed for. Additionally, such rockfall data can serve as a base for assessing the model’s sensitivity to different parameters, evaluating their predictability and helping calibrate the model’s parameters from back calculation and analyses. As the involved rock volumes/masses increase, the complexity of conducting field-test experiments to build up rockfall databases increases to a point where such experiments become impracticable. To the author’s knowledge, none have reconstructed rockfall data in 3D from real events involving block fragments of approximately 500 metric tons. A back analysis of the 2015 Mel de la Niva rockfall event is performed in this paper, contributing to a novel documentation in terms of kinetic energy values, bounce heights, velocities, and 3D lateral deviations of these rare events involving block fragments of approximately 200 m 3 . Rockfall simulations are then performed on a “per-impact” basis to illustrate how the reconstructed data from the site can be used to validate results from simulation models.

• Bachelet, V.; Mangeney, A.; Toussaint, Renaud; Rosny, Rosny de; Arran, M.I. & Farin, M. [Vis alle 7 forfattere av denne artikkelen] (2023). Acoustic Emissions of Nearly Steady and Uniform Granular Flows: A Proxy for Flow Dynamics and Velocity Fluctuations. Journal of Geophysical Research (JGR): Earth Surface. ISSN 2169-9003. 128(4). doi: 10.1029/2022JF006990. Fulltekst i vitenarkiv Vis sammendrag

  Abstract The seismic waves emitted during granular flows are generated by different sources: high frequencies by interparticle collisions and low frequencies by global motion and large scale deformation. To unravel these different mechanisms, an experimental study has been performed on the seismic waves emitted by dry, dense, quasi‐steady granular flows. The emitted seismic waves were recorded using shock accelerometers and the flow dynamics were captured with a fast camera. The mechanical characteristics of the particle collisions were analyzed, along with the intervals between collisions and the correlations in particles' motion. The high‐frequency seismic waves (1–50 kHz) were found to originate from particle collisions and waves trapped in the flowing layer. The low‐frequency waves (20–60 Hz) were generated by particles' oscillations along their trajectories, that is, from cycles of dilation/compression during coherent shear. The profiles of granular temperature (i.e., the mean squared value of particle velocity fluctuations) and average velocity were measured and related to each other, then used in a simple steady granular flow model, in which the seismic signal consists of the variously attenuated contributions of shear‐induced Hertzian collisions throughout the flow, to predict the rate at which seismic energy was emitted. Agreement with the measured seismic power was reasonable, and scaling laws relating the seismic power, the shear strain rate and the inertial number were derived. In particular, the emitted seismic power was observed to be approximately proportional to the root mean square velocity fluctuation to the power 3.1 ± 0.9, with the latter related to the mean flow velocity.

• Reis, Paula Kozlowski Pitombeira; Moura, Marcel; Linga, Gaute; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Vis alle 7 forfattere av denne artikkelen] (2023). A simplified pore-scale model for slow drainage including film-flow effects. Advances in Water Resources. ISSN 0309-1708. 182. doi: 10.1016/j.advwatres.2023.104580. Fulltekst i vitenarkiv Vis sammendrag

  Liquid-filled corners and capillary bridges can establish networks connecting seemingly isolated clusters during drainage in porous media. Coupled with drainage through the bulk of pores and throats, the flow through these networks constitutes a secondary drainage mechanism that can significantly affect fluid configurations and residual saturations. In order to investigate the prevalence of this drainage mechanism, we propose a quasi-static pore-network model based on modifying the trapped-cluster-identification algorithm in an invasion-percolation model. With the modification, wetting-phase connectivity is provided by direct successions of pores and throats, represented by sites and bonds, as well as by chains of interconnected capillary bridges. The advancement of the fluid interface in the porous matrix is determined by the bonds’ invasion thresholds and local capillary pressure values, calculated taking into consideration gravitational effects. With the proposed model, experimentally verified phenomena related to slow drainage in granular porous media are reproduced, showing good qualitative agreement.

• Alonso-Llanes, L.; Roman, Etien Martinez; Batista-Leyva, A. J; Toussaint, Renaud & Altshuler, E. (2022). Continuous to intermittent flows in growing granular heaps. Physical Review E (PRE). ISSN 2470-0045. 106(1). doi: 10.1103/PhysRevE.106.014904. Fulltekst i vitenarkiv Vis sammendrag

  If a granular material is poured from above on a horizontal surface between two parallel, vertical plates, a sand heap grows in time. For small piles, the grains flow smoothly downhill, but after a critical pile size Xc, the flow becomes intermittent: sudden avalanches slide downhill from the apex to the base, followed by an “uphill front” that slowly climbs up, until a new downhill avalanche interrupts the process. By means of experiments, controlling the distance between the apex of the sandpile and the container feeding it from above, we show that Xc grows linearly with the input flux, but scales as the square root of the feeding height. We explain these facts from a phenomenological model based on the experimental observation that the flowing granular phase forms a “wedge” on top of the static one, differently from the case of stationary heaps. Moreover, we demonstrate that our controlled experiments allow to predict the value of Xc for the common situation in which the feeding height decreases as the pile increases in size.

• Brodin, Joachim Falck; Moura, Marcel; Toussaint, Renaud; Måløy, Knut Jørgen & Rikvold, Per Arne (2022). Visualization by optical fluorescence of two-phase flow in a three-dimensional porous medium. Journal of Physics: Conference Series (JPCS). ISSN 1742-6588. 2241. doi: 10.1088/1742-6596/2241/1/012004. Fulltekst i vitenarkiv Vis sammendrag

  Abstract Slow flow of a single fluid through a porous medium is well understood on a macroscopic level through Darcy’s law, a linear relation between flow rate and a combination of pressure differences, viscosity, and gravitational forces. Two-phase flow is complicated by the interface separating the fluids, but understanding of two-dimensional, two-phase flow has been obtained from experiments using transparent cells. In most three-dimensional media, however, visual observation is difficult. Here, we present preliminary results of experiments on a model medium consisting of randomly packed glass spheres, in which one fluorescent liquid invades another. By refractive index matching and scanning with a sheet-shaped laser beam, we obtain slices of the flow patterns, which we combine into three-dimensional pictures. We observe a compact region of invading fluid, surrounded by finger-like protrusions. The compact region becomes more dominant with increasing invader flow rate. The patterns are theoretically analyzed in terms of the interplay between gravitational, viscous, and capillary forces.

• Brodin, Joachim Falck; Rikvold, Per Arne; Moura, Marcel; Toussaint, Renaud & Måløy, Knut Jørgen (2022). Competing Gravitational and Viscous Effects in 3D Two-Phase Flow Investigated With a Table-Top Optical Scanner. Frontiers in Physics. 10. doi: 10.3389/fphy.2022.936915. Fulltekst i vitenarkiv Vis sammendrag

  We present experiments and theory describing the transition from viscosity-stabilized flow to gravitationally unstable fingering for two-phase flow in a cubic box, filled with a synthetic porous medium. Observation is made possible by the use of our newly developed table-top 3D scanner based on optical index matching and laser-induced fluorescence, which is described in detail. In the experiment, a more dense, more viscous fluid injected at a fixed flow rate from a point source at the top of the flow cell displaces a less viscous, less dense fluid. We observe a stable invasion zone near the inlet, which increases in size with increasing flow rates, and presents initially a close to hemispherical shape. At later times, the invasion front transits to an unstable mode and a fingering flow regime. The transition occurs at a predicted critical radius, Rc, corresponding to the zero of the combined viscous and gravitational pressure gradient.

• Vincent-Dospital, Tom Yannick Yves; Moura, Marcel; Toussaint, Renaud & Måløy, Knut Jørgen (2022). Stable and unstable capillary fingering in porous media with a gradient in grain size. Communications Physics. 5(1). doi: 10.1038/s42005-022-01072-1. Fulltekst i vitenarkiv Vis sammendrag

  Multiphase flows in complex porous networks occur in many natural processes and engineering applications. We present an analytical, experimental and numerical investigation of slow drainage in porous media that exhibit a gradient in grain size. We show that the effect of such structural gradient is similar to that of an external force field on the obtained drainage patterns, when it either stabilises or destabilises the invasion front. For instance, gravity can enhance or reverse the drainage pattern in graded porous media. In particular, we show that the width of stable drainage fronts scales both with the spatial gradient of the necessary pressure for pore invasion and with the local distribution of this (disordered) threshold. The scaling exponent results from percolation theory and is − 0.57 for 2D systems. Overall, introducing a dimensionless Fluctuation number, we propose a unifying theory for the up-scaling of dual immiscible fluid flows covering most classical scenarii.

• Koehn, Daniel; Kelka, Ulrich; Toussaint, Renaud; Siegel, Coralie; Mullen, Gary & Boyce, Adrian [Vis alle 7 forfattere av denne artikkelen] (2022). Outcrop scale mixing enhanced by permeability variations: the role of stationary and travelling waves of high saturation indices. Geological Magazine. ISSN 0016-7568. 159(11-12), s. 2279–2292. doi: 10.1017/S001675682200070X. Fulltekst i vitenarkiv Vis sammendrag

  Abstract To study the ore mineralization at the outcrop scale we merge an advection–diffusion simulation with the geochemical software iphreeqc to model the mixing of two realistic fluids. We simulate the infiltration of a metal-rich fluid into a rock that is saturated with pore fluid. We test the feedback effects with a number of scenarios based on an outcrop-scale 5 × 5 m model consisting of two high-permeable vertical faults within a low-permeable host rock that lead into a permeable layer. The hot metal-rich fluid enters the model through the faults from below. We solve the advection–diffusion equation for 12 chemical species and temperature, and use iphreeqc to determine the resulting properties of local fluid domains as well as related saturation indices for minerals. The faults in the model act as pathways for the metal-rich fluid, with the infiltrating fluid displacing the pore fluid. Mixing in the model takes place as a function of advection along permeable faults coupled with diffusion of chemical species at the interface between two fluids, while heat diffusion is fast enough (10 3 times faster) to equilibrate temperature. Simulations show a high saturation index of mixing-derived minerals such as barite at the interface between the two fluids as a result of fluid mixing. Fast fluid pathways (i.e. faults) show travelling waves of high saturation indices of barite, while low-permeability zones such as fault walls and areas below less permeable layers experience stationary waves of high saturation indices. Our results show that, depending on the dominant transport process (advection or diffusion), mineralization will localize next to permeability contrasts in zones where local diffusion dominates.

• Köehn, D.; Köehler, S.; Toussaint, Renaud; Ghani, I. & Stollhofen, H. (2022). Scaling analysis, correlation length and compaction estimates of natural and simulated stylolites. Journal of Structural Geology. ISSN 0191-8141. 161. doi: 10.1016/j.jsg.2022.104670. Fulltekst i vitenarkiv
• Alonso-Llanes, L.; Sánchez-Colina, G.; Batista-Leyva, A.J.; Clément, C.; Altshuler, E. & Toussaint, Renaud (2022). Sink versus tilt penetration into shaken dry granular matter: The role of the foundation. Physical Review E (PRE). ISSN 2470-0045. 105(2). doi: 10.1103/PhysRevE.105.024903. Fulltekst i vitenarkiv Vis sammendrag

  We study the behavior of cylindrical objects as they sink into a dry granular bed fluidized due to lateral oscillations. Somewhat unexpectedly, we have found that, within a large range of lateral shaking powers, cylinders with flat bottoms sink vertically, while those with a “foundation” consisting of a shallow ring attached to their bottom, tilt besides sinking. The latter scenario seems to dominate independently from the nature of the foundation when strong enough lateral vibrations are applied. We are able to explain the observed behavior by quasi-2D numerical simulations, which also demonstrate the influence of the intruder's aspect ratio. The vertical sink dynamics is explained with the help of a Newtonian equation of motion for the intruder. Our findings may shed light on the behavior of buildings and other manmade structures during earthquakes.

• Vincent-Dospital, Tom; Cochard, Alain; Santucci, Stephane; Måløy, Knut Jørgen & Toussaint, Renaud (2021). Thermally activated intermittent dynamics of creeping crack fronts along disordered interfaces. Scientific Reports. 11. doi: 10.1038/s41598-021-98556-x. Fulltekst i vitenarkiv Vis sammendrag

  Abstract We present a subcritical fracture growth model, coupled with the elastic redistribution of the acting mechanical stress along rugous rupture fronts. We show the ability of this model to quantitatively reproduce the intermittent dynamics of cracks propagating along weak disordered interfaces. To this end, we assume that the fracture energy of such interfaces (in the sense of a critical energy release rate) follows a spatially correlated normal distribution. We compare various statistical features from the obtained fracture dynamics to that from cracks propagating in sintered polymethylmethacrylate (PMMA) interfaces. In previous works, it has been demonstrated that such an approach could reproduce the mean advance of fractures and their local front velocity distribution. Here, we go further by showing that the proposed model also quantitatively accounts for the complex self-affine scaling morphology of crack fronts and their temporal evolution, for the spatial and temporal correlations of the local velocity fields and for the avalanches size distribution of the intermittent growth dynamics. We thus provide new evidence that an Arrhenius-like subcritical growth is particularly suitable for the description of creeping cracks.

• Vincent-Dospital, Tom; Toussaint, Renaud & Måløy, Knut Jørgen (2021). Heat Emitting Damage in Skin: A Thermal Pathway for Mechanical Algesia. Frontiers in Neuroscience. ISSN 1662-4548. 15. doi: 10.3389/fnins.2021.780623. Fulltekst i vitenarkiv Vis sammendrag

  Mechanical pain (or mechanical algesia) can both be a vital mechanism warning us for dangers or an undesired medical symptom important to mitigate. Thus, a comprehensive understanding of the different mechanisms responsible for this type of pain is paramount. In this work, we study the tearing of porcine skin in front of an infrared camera, and show that mechanical injuries in biological tissues can generate enough heat to stimulate the neural network. In particular, we report local temperature elevations of up to 24°C around fast cutaneous ruptures, which shall exceed the threshold of the neural nociceptors usually involved in thermal pain. Slower fractures exhibit lower temperature elevations, and we characterise such dependency to the damaging rate. Overall, we bring experimental evidence of a novel—thermal—pathway for direct mechanical algesia. In addition, the implications of this pathway are discussed for mechanical hyperalgesia, in which a role of the cutaneous thermal sensors has priorly been suspected. We also show that thermal dissipation shall actually account for a significant portion of the total skin's fracture energy, making temperature monitoring an efficient way to detect biological damages.

• Arran, Matthew I.; Mangeney, Anne; Rosny, Julien De; Farin, Maxime; Toussaint, Renaud & Roche, Olivier (2021). Laboratory Landquakes: Insights From Experiments Into the High‐Frequency Seismic Signal Generated by Geophysical Granular Flows. Journal of Geophysical Research (JGR): Earth Surface. ISSN 2169-9003. 126(5). doi: 10.1029/2021JF006172. Fulltekst i vitenarkiv Vis sammendrag

  Geophysical granular flows exert basal forces that generate seismic signals, which can be used to better monitor and model these severe natural hazards. A number of empirical relations and existing models link these signals' high-frequency components to a variety of flow properties, many of which are inaccessible by other analyses. However, the range of validity of the empirical relations remains unclear and the models lack validation, owing to the difficulty of adequately controlling and instrumenting field-scale flows. Here, we present laboratory experiments investigating the normal forces exerted on a basal plate by dense and partially dense flows of spherical glass particles. We measured the power spectra of these forces and inferred predictions for these power spectra from the models for debris flows' seismic signals proposed by Kean et al. (2015, https://doi.org/10.1002/2015GL064811), Lai et al. (2018, https://doi.org/10.1029/2018GL077683), and Farin, Tsai, et al. (2019, https://doi.org/10.1002/esp.4677), using Hertz theory to extend Farin, Tsai, et al. (2019)'s models to higher frequencies. Comparison of our observations to these predictions, and to predictions derived from Bachelet (2018) and Bachelet et al. (2021)'s model for granular flows' seismic signals, shows those of Farin, Tsai, et al. (2019)'s “thin-flow” model to be the most accurate, so we examine explanations for this accuracy and discuss its implications for geophysical flows' seismic signals. We also consider the normalization, by the mean force exerted by each flow, of the force's mean squared fluctuations, showing that this ratio varies by 4 orders of magnitude over our experiments, but is determined by the bulk inertial number of the flow.

• Koehn, Daniel; Piazolo, Sandra; Beaudoin, Nicolas; Kelka, Ulrich; Spruzeniece, Liene & Putnis, Christine V [Vis alle 7 forfattere av denne artikkelen] (2021). Relative rates of fluid advection, elemental diffusion and replacement govern reaction front patterns. Earth and Planetary Science Letters. ISSN 0012-821X. 565, s. 116950–116950. doi: 10.1016/j.epsl.2021.116950. Fulltekst i vitenarkiv Vis sammendrag

  Replacement reactions during fluid infiltration into porous media, rocks and buildings are known to have important implications for reservoir development, ore formation as well as weathering. Natural observations and experiments have shown that in such systems the shape of reaction fronts can vary significantly ranging from smooth, rough to highly irregular. It remains unclear what process-related knowledge can be derived from these reaction front patterns. In this contribution we show a numerical approach to test the effect of relative rates of advection, diffusion, and reaction on the development of reaction fronts patterns in granular aggregates with permeable grain boundaries. The numerical model takes (i) fluid infiltration along permeable grain boundaries, (ii) reactions and (iii) elemental diffusion into account. We monitor the change in element concentration within the fluid, while reactions occur at a pre-defined rate as a function of the local fluid concentration. In non-dimensional phase space using Péclet and Damköhler numbers, results show that there are no rough fronts without advection (Péclet<70) nor if the reaction is too fast (Damköhler>10−3). As advection becomes more dominant and reaction slower, roughness develops across several grains with a full microstructure mimicking replacement in the most extreme cases. The reaction front patterns show an increase in roughness with increasing Péclet number from Péclet 10 to 100 but then a decrease in roughness towards higher Péclet numbers controlled by the Damköhler number. Our results indicate that reaction rates are crucial for pattern formation and that the shape of reaction fronts is only partly due to the underlying transport mechanism.

• Meghraoui, Mustapha; Toussaint, Renaud & Aksoy, Murat Ersen (2021). The slip deficit on the North Anatolian Fault (Turkey) in the Marmara Sea: insights from paleoseismicity, seismicity and geodetic data. Mediterranean Geoscience Reviews. ISSN 2661-863X. 3(1), s. 45–56. doi: 10.1007/s42990-021-00053-w. Fulltekst i vitenarkiv
• Vincent-Dospital, Tom & Toussaint, Renaud (2021). Thermo-mechanical pain: the signaling role of heat dissipation in biological tissues. New Journal of Physics. 23. doi: 10.1088/1367-2630/abe444. Fulltekst i vitenarkiv Vis sammendrag

  Mechanical algesia is an important process for the preservation of living organisms, allowing potentially life-saving reflexes or decisions when given body parts are stressed. Yet, its various underlying mechanisms remain to be fully unravelled. Here, we quantitatively discuss how the detection of painful mechanical stimuli by the human central nervous system may, partly, rely on thermal measurements. Indeed, most fractures in a body, including microscopic ones, release some heat, which diffuses in the surrounding tissues. Through this physical process, the thermo-sensitive TRP proteins, that translate abnormal temperatures into action potentials, shall be sensitive to damaging mechanical inputs. The implication of these polymodal receptors in mechanical algesia has been regularly reported, and we here provide a physical explanation for the coupling between thermal and mechanical pain. In particular, in the human skin, we show how the neighbouring neurites of a broken collagen fiber can undergo a sudden thermal elevation that ranges from a fraction to tens of degrees. As this theoretical temperature anomaly lies in the sensibility range of the TRPV3 and TRPV1 cation channels, known to trigger action potentials in the neural system, a degree of mechanical pain can hence be generated.

• Vincent-Dospital, Tom; Toussaint, Renaud; Cochard, Alain; Flekkøy, Eirik Grude & Måløy, Knut Jørgen (2021). Thermal dissipation as both the strength and weakness of matter. A material failure prediction by monitoring creep. Soft Matter. ISSN 1744-683X. 17(15), s. 4143–4150. doi: 10.1039/d0sm02089c. Fulltekst i vitenarkiv Vis sammendrag

  In any domain involving some stressed solids, that is, from seismology to general engineering, the strength of matter is a paramount feature to understand. We here discuss the ability of a simple thermally activated sub-critical model, which includes the auto-induced thermal evolution of cracks tips, to predict the catastrophic failure of a vast range of materials. It is in particular shown that the intrinsic surface energy barrier, for breaking the atomic bonds of many solids, can be easily deduced from the slow creeping dynamics of a crack. This intrinsic barrier is however higher than the macroscopic load threshold at which brittle matter brutally fails, possibly as a result of thermal activation and of a thermal weakening mechanism. We propose a novel method to compute this macroscopic energy release rate of rupture, Ga, solely from monitoring slow creep, and we show that this reproduces the experimental values within 50% accuracy over twenty different materials, and over more than four decades of fracture energy.

• Vincent-Dospital, Tom; Steyer, Alain; Renard, Francois & Toussaint, Renaud (2021). Frictional anisotropy of 3D-printed fault surfaces. Frontiers in Earth Science. doi: 10.3389/feart.2021.627823. Fulltekst i vitenarkiv Vis sammendrag

  The surface morphology of faults controls the spatial anisotropy of their frictional properties, and hence their mechanical stability. Such anisotropy is only rarely studied in seismology models of fault slip, although it might be paramount to understand the seismic rupture in particular areas, notably where slip occurs in a direction different from that of the main striations of the fault. To quantify how the anisotropy of fault surfaces affects the friction coefficient during sliding, we sheared synthetic fault planes made of plaster of Paris. These fault planes were produced by 3D-printing real striated fault surfaces whose 3D roughness was measured in the field at spatial scales from millimeters to meters. Here, we show how the 3D-printing technology can help for the study of frictional slip. Results show that fault anisotropy controls the coefficient of static friction, with the friction coefficient along the striations being three to four times smaller than the friction coefficient along the orientation perpendicular to the striations. This is true both at the meter and the millimeter scales. The anisotropy in friction and the average coefficient of static friction are also shown to decrease with the normal stress applied to the faults, as a result of the increased surface wear under increased loading.

• Måløy, Knut Jørgen; Moura, Marcel; Hansen, Alex; Flekkøy, Eirik Grude & Toussaint, Renaud (2021). Burst Dynamics, Upscaling and Dissipation of Slow Drainage in Porous Media. Frontiers in Physics. 9. doi: 10.3389/fphy.2021.796019. Fulltekst i vitenarkiv Vis sammendrag

  We present a theoretical and experimental investigation of drainage in porous media. The study is limited to stabilized fluid fronts at moderate injection rates, but it takes into account capillary, viscous, and gravitational forces. In the theoretical framework presented, the work applied on the system, the energy dissipation, the final saturation and the width of the stabilized fluid front can all be calculated if we know the dimensionless fluctuation number, the wetting properties, the surface tension between the fluids, the fractal dimensions of the invading structure and its boundary, and the exponent describing the divergence of the correlation length in percolation. Furthermore, our theoretical description explains how the Haines jumps’ local activity and dissipation relate to dissipation on larger scales.

• Luu, Jane; Flekkøy, Eirik Grude & Toussaint, Renaud (2020). 'Oumuamua as a Cometary Fractal Aggregate: The Dust Bunny Model. Astrophysical Journal Letters. ISSN 2041-8205. 900(2). doi: 10.3847/2041-8213/abafa7. Fulltekst i vitenarkiv
• Xu, Le; Szymczak, Piotr; Toussaint, Renaud; Flekkøy, Eirik Grude & Måløy, Knut Jørgen (2020). Dissolution phase diagram in radial geometry. Frontiers in Physics. 8. doi: 10.3389/fphy.2020.00369. Fulltekst i vitenarkiv Vis sammendrag

  Fractures play an important role as flow paths in porous media. When an undersaturated reactive fluid is flowing in a fracture, the dissolution process will alter the flow paths locally. Dissolution patterns grow slowly, but they may lead to a dramatic reorganization of the flow. Here, we study dissolution in a radial geometry, which is relevant for a number of practical applications, e.g., the acidization of oil reservoirs. Different dissolution patterns are presented in a phase diagram with the Péclet and Damköhler numbers as parameters. We also analyze quantitatively the density of wormholes and the relation between the aperture roughness and the ramified patterns.

• Moura, Marcel; Måløy, Knut Jørgen; Flekkøy, Eirik Grude & Toussaint, Renaud (2020). Intermittent Dynamics of Slow Drainage Experiments in Porous Media: Characterization Under Different Boundary Conditions. Frontiers in Physics. 7. doi: 10.3389/fphy.2019.00217. Fulltekst i vitenarkiv Vis sammendrag

  The intermittent dynamics of slow drainage flows in a porous medium is studied experimentally. This kind of two-phase flow is characterized by a rich burst activity and our setup allows us to characterize those bursts directly via images of the flow and pressure measurements. Two different boundary conditions were analyzed: controlled withdrawal rate (CWR) and controlled imposed pressure (CIP). We have characterized geometrical and statistical properties of the bursts from images and pressure measurements. We have shown that in spite of leading to similar final invasion patterns, some dynamical features of the invasion differ considerably between the CWR and CIP boundary conditions. In particular, their pressure signatures are very distinct, which then translates into very distinct features on the power spectrum density of the pressure signals. A fully integrable analytical framework is presented which successfully describes the scaling features of the power spectrum for the CIP case.

• Koehn, Daniel; Piazolo, Sandra; Sachau, Till & Toussaint, Renaud (2020). Fracturing and Porosity Channeling in Fluid Overpressure Zones in the Shallow Earth's Crust. Geofluids. ISSN 1468-8115. s. 7621759–7621759. doi: 10.1155/2020/7621759. Fulltekst i vitenarkiv Vis sammendrag

  At the time of energy transition, it is important to be able to predict the effects of fluid overpressures in different geological scenarios as these can lead to the development of hydrofractures and dilating high-porosity zones. In order to develop an understanding of the complexity of the resulting effective stress fields, fracture and failure patterns, and potential fluid drainage, we study the process with a dynamic hydromechanical numerical model. The model simulates the evolution of fluid pressure buildup, fracturing, and the dynamic interaction between solid and fluid. Three different scenarios are explored: fluid pressure buildup in a sedimentary basin, in a vertical zone, and in a horizontal layer that may be partly offset by a fault. Our results show that the geometry of the area where fluid pressure is successively increased has a first-order control on the developing pattern of porosity changes, on fracturing, and on the absolute fluid pressures that sustained without failure. If the fluid overpressure develops in the whole model, the effective differential and mean stress approach zero and the vertical and horizontal effective principal stresses flip in orientation. The resulting fractures develop under high lithostatic fluid overpressure and are aligned semihorizontally, and consequently, a hydraulic breccia forms. If the area of high fluid pressure buildup is confined in a vertical zone, the effective mean stress decreases while the differential stress remains almost constant and failure takes place in extensional and shear modes at a much lower fluid overpressure. A horizontal fluid pressurized layer that is offset shows a complex system of effective stress evolution with the layer fracturing initially at the location of the offset followed by hydraulic breccia development within the layer. All simulations show a phase transition in the porosity where an initially random porosity reduces its symmetry and forms a static porosity wave with an internal dilating zone and the presence of dynamic porosity channels within this zone. Our results show that patterns of fractures, hence fluid release, that form due to high fluid overpressures can only be successfully predicted if the geometry of the geological system is known, including the fluid overpressure source and the position of seals and faults that offset source layers and seals.

• Vincent-Dospital, Tom; Toussaint, Renaud; Santucci, Stephane; Vanel, Loïc; Bonamy, Daniel & Hattali, Lamine [Vis alle 9 forfattere av denne artikkelen] (2020). How heat controls fracture: the thermodynamics of creeping and avalanching cracks. Soft Matter. ISSN 1744-683X. 16(41), s. 9590–9602. doi: 10.1039/D0SM01062F. Fulltekst i vitenarkiv Vis sammendrag

  While of paramount importance in material science, the dynamics of cracks still lacks a complete physical explanation. The transition from their slow creep behavior to a fast propagation regime is a notable key, as it leads to full material failure if the size of a fast avalanche reaches that of the system. We here show that a simple thermodynamics approach can actually account for such complex crack dynamics, and in particular for the non-monotonic force-velocity curves commonly observed in mechanical tests on various materials. We consider a thermally activated failure process that is coupled with the production and the diffusion of heat at the fracture tip. In this framework, the rise in temperature only affects the sub-critical crack dynamics and not the mechanical properties of the material. We show that this description can quantitatively reproduce the rupture of two different polymeric materials (namely, the mode I opening of polymethylmethacrylate (PMMA) plates, and the peeling of pressure sensitive adhesive (PSA) tapes), from the very slow to the very fast fracturing regimes, over seven to nine decades of crack propagation velocities. In particular, the fastest regime is obtained with an increase of temperature of thousands of kelvins, on the molecular scale around the crack tip. Although surprising, such an extreme temperature is actually consistent with different experimental observations that accompany the fast propagation of cracks, namely, fractoluminescence (i.e., the emission of visible light during rupture) and a complex morphology of post-mortem fracture surfaces, which could be due to the sublimation of bubbles.

• Vincent-Dospital, Tom; Toussaint, Renaud; Cochard, Alain; Måløy, Knut Jørgen & Flekkøy, Eirik Grude (2020). Thermal weakening of cracks and brittle-ductile transition of matter: A phase model. PHYSICAL REVIEW MATERIALS. 4(2). doi: 10.1103/PhysRevMaterials.4.023604. Fulltekst i vitenarkiv Vis sammendrag

  We present a model for the thermally activated propagation of cracks in elastic matrices. The propagation is considered as a subcritical phenomenon, the kinetics of which is described by an Arrhenius law. In this law, we take the thermal evolution of the crack front into account, assuming that a portion of the released mechanical energy is transformed into heat in a zone surrounding the tip. We show that such a model leads to a two-phase crack propagation: the first phase at low velocity in which the temperature elevation is of little effect and the propagation is mainly governed by the mechanical load and by the toughness of the medium, and the second phase in which the crack is thermally weakened and propagates at greater velocity. We illustrate, with numerical simulations of mode I cracks propagating in thin disordered media, how such a dual behavior can explain the usual stick-slip in brittle fracturing. In addition, we predict the existence of a limiting ambient temperature above which the weakened phase ceases to exist and we propose this critical phenomenon as a novel explanation for the brittle-ductile transition of solids.

• Ayaz, Atta-Ul-Monem; Toussaint, Renaud; Schäfer, Gerhard & Måløy, Knut Jørgen (2020). Gravitational and Finite-Size Effects On Pressure Saturation Curves During Drainage. Water Resources Research. ISSN 0043-1397. 56(10). doi: 10.1029/2019WR026279. Fulltekst i vitenarkiv Vis sammendrag

  We experimentally and numerically study the influence of gravity and finite-size effects on the pressure-saturation relationship in a given porous medium during slow drainage. The effect of gravity is systematically varied by tilting the system relative to the horizontal configuration. The use of a quasi two-dimensional porous media allows for direct spatial monitoring of the saturation. Exploiting the fractal nature of the invasion structure, we obtain a relationship between the final saturation and the Bond number SFnw = Bo0.097 using percolation theory. Moreover, the saturation, pressure, and Bond number are functionally related, allowing for pressure-saturation curves to collapse onto a single master curve, parameterized by the representative elementary volume size and by the Bond and capillary numbers. This allows to upscale the pressure-saturation curves measured in a laboratory to large representative elementary volumes used in reservoir simulations. The large-scale behavior of these curves follows a simple relationship, depending on Bond and capillary numbers, and on the flow direction. The size distribution of trapped defending fluid clusters is also shown to contain information on past fluid flow and can be used as a marker of past flow speed and direction.

• Ben-Zeev, Shahar; Aharonov, Einat; Toussaint, Renaud; Parez, Stanislav & Goren, Liran (2020). Compaction front and pore fluid pressurization in horizontally shaken drained granular layers. Physical Review Fluids. 5:054301(5), s. 1–24. doi: 10.1103/PhysRevFluids.5.054301. Fulltekst i vitenarkiv Vis sammendrag

  In many natural granular systems, the interstitial pores are filled with a fluid. Deformation of this two-phase system is complex, is highly coupled, and depends on the initial and boundary conditions. Here we study granular compaction and fluid flow in a saturated, horizontally shaken, unconfined granular layer, where the fluid is free to flow in and out of the layer through the free upper surface during shaking (i.e., drained boundary condition). The geometry, boundary conditions, and parameters are chosen to resemble a shallow soil layer, subjected to horizontal cyclic acceleration simulating that of an earthquake. We develop a theory and conduct coupled discrete element and fluid numerical simulations. Theoretical and simulation results show that under drained conditions and above a critical acceleration, the grain layer compacts at a rate governed by the fluid flow parameters of permeability and viscosity and is independent of the shaking parameters of frequency and acceleration. A compaction front develops, swiping upward through the system. Above the front, compaction occurs and the fluid becomes pressurized. Pressure gradients drive fluid seepage upward and out of the compacting layer while supporting the granular skeleton. The rate of compaction and the interstitial fluid pressure gradient coevolve until fluid seepage forces balance solid contact forces and grain contacts disappear. As an outcome, the imposed shear waves are not transmitted and the region is liquefied. Below the compaction front (i.e., after its passage), the grains are well compacted, and shaking is transmitted upward. We conclude that the drained condition for the interstitial pore fluid is a critical ingredient for the formation of an upward-moving compaction front, which separates a granular region that exhibits a liquidlike rheology from a solidlike region.

• Turquet, Antoine Leo; Toussaint, Renaud; Eriksen, Fredrik Kvalheim; Daniel, Guillaume; Lengline, Oliver & Flekkøy, Eirik Grude [Vis alle 7 forfattere av denne artikkelen] (2019). Source localization of microseismic emissions during pneumatic fracturing. Geophysical Research Letters. ISSN 0094-8276. 46(7), s. 3726–3733. doi: 10.1029/2019GL082198. Fulltekst i vitenarkiv Vis sammendrag

  Localization of signals is a widely applied technique used in different areas of science telecommunication, medicine, or seismology. In this work, we study microseismic emissions due to stick‐slip events during pneumatic fracture in a transparent setup at laboratory scale and apply a localization method “Estimated Source Energy Homogeneity.” The seismic location results are compared with the image correlation results for displacement maps corresponding to the event times. We have observed (using optics and acoustics) that the movement starts inside the porous medium and progresses toward the channel tips, eventually causing channels to grow further. This finding could be of interest in understanding fluid‐induced earthquake nucleation processes. Similar to in‐site applications of pneumatic or fluid‐related fracturing, it shows that the area influenced extends beyond the fracture tips. This also shows why even after the end of pumping, we may get earthquakes, such as in the Basel case (Haring et al., 2008, https://doi.org/10.1016/j.geothermics.2008.06.002).

• Moura, Marcel; Flekkøy, Eirik Grude; Måløy, Knut Jørgen; Schäfer, Gerhard & Toussaint, Renaud (2019). Connectivity enhancement due to film flow in porous media. Physical Review Fluids. 4(9). doi: 10.1103/PhysRevFluids.4.094102. Fulltekst i vitenarkiv Vis sammendrag

  We study the effects of connectivity enhancement due to film flow phenomena on the drainage of an artificial porous medium and the relative influence of gravity for such effects. The medium is initially fully saturated with a liquid (wetting phase), which is displaced by air (nonwetting phase). Our setup allows us to directly visualize the dynamics of the flow and, in particular, to pinpoint which pore invasion events are due to film flow phenomena. We have observed the formation of an active zone behind the liquid-air interface, inside which film flow drainage events are more likely to occur. Understanding the basic mechanisms of film flow in artificial porous media is of relevance for the analysis of real three-dimensional porous systems, in which gravity cannot be neglected and film flow is bound to be present.

• Flekkøy, Eirik Grude; Luu, Jane & Toussaint, Renaud (2019). The interstellar object ’Oumuamua as a fractal dust aggregate. Astrophysical Journal Letters. ISSN 2041-8205. 885(2), s. 1–6. doi: 10.3847/2041-8213/ab4f78. Fulltekst i vitenarkiv Vis sammendrag

  The first known interstellar object 'Oumuamua exhibited a nongravitational acceleration that appeared inconsistent with cometary outgassing, leaving radiation pressure as the most likely force. Barring the alien lightsail hypothesis, an ultra-low density due to a fractal structure might also explain the acceleration of 'Oumuamua by radiation pressure. In this Letter we report a decrease in 'Oumuamua's rotation period based on ground-based observations, and show that this spin-down can be explained by the YORP effect if 'Oumuamua is indeed a fractal body with the ultra-low density of 10−2 kg m−3. We also investigate the mechanical consequences of 'Oumuamua as a fractal body subjected to rotational and tidal forces, and show that a fractal structure can survive these mechanical forces.

• Aleksans, Janis; Koehn, Daniel; Toussaint, Renaud & Daniel, Guillaume (2019). Simulating Hydraulic Fracturing: Failure in soft versus hard rocks. Pure and Applied Geophysics (PAGEOPH). ISSN 0033-4553. 177, s. 2771–2789. doi: 10.1007/s00024-019-02376-0. Fulltekst i vitenarkiv Vis sammendrag

  In this contribution we discuss the dynamic development of hydraulic fractures, their evolution and the resulting seismicity during fluid injection in a coupled numerical model. The model describes coupling between a solid that can fracture dynamically and a compressible fluid that can push back at the rock and open fractures. With a series of numerical simulations we show how the fracture pattern and seismicity change depending on changes in depth, injection rate, Young’s Modulus and breaking strength. Our simulations indicate that the Young’s Modulus has the largest influence on the fracture dynamics and the related seismicity. Simulations of rocks with a Young’s modulus smaller than 10 GPa show dominant mode I failure and a growth of fracture aperture with a decrease in Young’s modulus. Simulations of rocks with a Young’s modulus higher than 10 GPa show fractures with a constant aperture and fracture growth that is mainly governed by a growth in crack length and an increasing amount of mode II failure. These results are very important for the prediction of fracture dynamics and seismicity during fluid injection, especially since we see a transition from one failure regime to another at around 10 GPa, a Young’s modulus that lies in the middle of possible values for natural shale rocks.

• Farin, Maxime; Mangeney, Anne; Rosny, Julien De; Toussaint, Renaud & Trinh, Phuong‐Thu (2019). Relations between the characteristics of granular column collapses and resultant high‐frequency seismic signals. Journal of Geophysical Research (JGR): Earth Surface. ISSN 2169-9003. 124(12), s. 2987–3021. doi: 10.1029/2019JF005258. Fulltekst i vitenarkiv Vis sammendrag

  Deducing relations between the dynamic characteristics of landslides and rockfalls and the resultant high‐frequency (>1 Hz) seismic signal is challenging. To investigate relations that can be tested in the field, we conducted laboratory experiments of 3‐D granular column collapse on a rough inclined thin plate, for a large set of column masses, aspect ratios, particle diameters, and slope angles. The dynamics of the granular flows were recorded using a high‐speed camera, and the generated seismic signal was measured using piezoelectric accelerometers. Empirical scaling laws are established between the characteristics of the granular flows and deposits and that of the generated seismic signals. The radiated seismic energy scales with particle diameter as d 3, column mass as M and aspect ratio as a 1.1. The increase of the radiated seismic energy as slope angle increases correlates with a similar increase in particle agitation. Based on our experimental results, we revisit scaling laws reported in the field and discuss their possible physical origin. The discrepancy between field and experimental observations can be explained by the complex influence of the substrate on seismic signal and the difference of flow initiation in both cases. However, our empirical scaling laws allow us to determine which flow parameters could be inferred from a given seismic characteristic in the field. In particular, by assuming the flow average speed is known, we show that we can retrieve parameters d , M , and a within a factor of two from the seismic signal.

• Xu, Le; Szymczak, Piotr; Toussaint, Renaud; Flekkøy, Eirik Grude & Måløy, Knut Jørgen (2019). Experimental Observation of Dissolution Finger Growth in Radial Geometry. Frontiers in Physics. 7(JULY), s. 1–10. doi: 10.3389/fphy.2019.00096. Fulltekst i vitenarkiv Vis sammendrag

  Reaction-infiltration instability refers to the morphological instability of a reactive fluid front flowing in a soluble porous medium. This process is important for many naturally occurring phenomena, such as the weathering and diagenesis of rocks, dissolution in salt deposits and melt extraction from the mantle. This paper is focused on experiments on dissolution finger growth in radial geometries in an analog fracture. In the experiments, pure water dissolves a plaster sample forming one of the fracture walls in a Hele-Shaw cell with controlled injection rate and aperture. The flow is directed inwards to the center, and we observe the reaction-infiltration instability developing along the relatively long perimeter of the plaster. Our experimental results show a number of features consistent with the theoretical and numerical predictions on the finger growth dynamics such as screening and selection between the fingers. Statistical properties of the dissolved part evolution with time are also investigated.

• Clement, C; Toussaint, Renaud; Stojanova, M. & Aharonov, E. (2018). Sinking during earthquakes: Critical acceleration criteria control drained soil liquefaction. Physical Review E (PRE). ISSN 2470-0045. 97(2). doi: 10.1103/PhysRevE.97.022905. Fulltekst i vitenarkiv Vis sammendrag

  This article focuses on liquefaction of saturated granular soils, triggered by earthquakes. Liquefaction is defined here as the transition from a rigid state, in which the granular soil layer supports structures placed on its surface, to a fluidlike state, in which structures placed initially on the surface sink to their isostatic depth within the granular layer. We suggest a simple theoretical model for soil liquefaction and show that buoyancy caused by the presence of water inside a granular medium has a dramatic influence on the stability of an intruder resting at the surface of the medium. We confirm this hypothesis by comparison with laboratory experiments and discrete-element numerical simulations. The external excitation representing ground motion during earthquakes is simulated via horizontal sinusoidal oscillations of controlled frequency and amplitude. In the experiments, we use particles only slightly denser than water, which as predicted theoretically increases the effect of liquefaction and allows clear depth-ofsinking measurements. In the simulations, a micromechanical model simulates grains using molecular dynamics with friction between neighbors. The effect of the fluid is captured by taking into account buoyancy effects on the grains when they are immersed. We show that the motion of an intruder inside a granular medium is mainly dependent on the peak acceleration of the ground motion and establish a phase diagram for the conditions under which liquefaction happens, depending on the soil bulk density, friction properties, presence of water, and peak acceleration of the imposed large-scale soil vibrations. We establish that in liquefaction conditions, most cases relax toward an equilibrium position following an exponential in time. We also show that the equilibrium position itself, for most liquefaction regimes, corresponds to the isostatic equilibrium of the intruder inside a medium of effective density. The characteristic time to relaxation is shown to be essentially a function of the peak ground velocity.

• Eriksen, Jon Alm; Toussaint, Renaud; Måløy, Knut Jørgen; Flekkøy, Eirik Grude; Galland, Olivier & Sandnes, Bjørnar (2018). Pattern formation of frictional fingers in a gravitational potential. Physical Review Fluids. 3(1). doi: 10.1103/PhysRevFluids.3.013801. Fulltekst i vitenarkiv Vis sammendrag

  Aligned finger structures, with a characteristic width, emerge during the slow drainage of a liquid-granular mixture in a tilted Hele-Shaw cell. A transition from vertical to horizontal alignment of the finger structures is observed as the tilting angle and the granular density are varied. An analytical model is presented, demonstrating that the alignment properties are the result of the competition between fluctuating granular stresses and the hydrostatic pressure. The dynamics is reproduced in simulations. We also show how the system explains patterns observed in nature, created during the early stages of a dike formation.

• Eriksen, Fredrik Kvalheim; Toussaint, Renaud; Turquet, Antoine Léo; Måløy, Knut Jørgen & Flekkøy, Eirik Grude (2018). Pressure evolution and deformation of confined granular media during pneumatic fracturing. Physical Review E (PRE). ISSN 2470-0045. 97(1), s. 1–19. doi: 10.1103/PhysRevE.97.012908. Fulltekst i vitenarkiv Vis sammendrag

  By means of digital image correlation, we experimentally characterize the deformation of a dry granular medium confined inside a Hele-Shaw cell due to air injection at a constant overpressure high enough to deform it (from 50 to 250 kPa). Air injection at these overpressures leads to the formation of so-called pneumatic fractures, i.e., channels empty of beads, and we discuss the typical deformations of the medium surrounding these structures. In addition we simulate the diffusion of the fluid overpressure into the medium, comparing it with the Laplacian solution over time and relating pressure gradients with corresponding granular displacements. In the compacting medium we show that the diffusing pressure field becomes similar to the Laplace solution on the order of a characteristic time given by the properties of the pore fluid, the granular medium, and the system size. However, before the diffusing pressure approaches the Laplace solution on the system scale, we find that it resembles the Laplacian field near the channels, with the highest pressure gradients on the most advanced channel tips and a screened pressure gradient behind them. We show that the granular displacements more or less always move in the direction against the local pressure gradients, and when comparing granular velocities with pressure gradients in the zone ahead of channels, we observe a Bingham type of rheology for the granular paste (the mix of air and beads), with an effective viscosity μB and displacement thresholds ∇ Pc evolving during mobilization and compaction of the medium. Such a rheology, with disorder in the displacement thresholds, could be responsible for placing the pattern growth at moderate injection pressures in a universality class like the dielectric breakdown model with η = 2, where fractal dimensions are found between 1.5 and 1.6 for the patterns.

• Turquet, Antoine Léo; Toussaint, Renaud; Eriksen, Fredrik Kvalheim; Daniel, Guillaume; Koehn, Daniel & Flekkøy, Eirik Grude (2018). Microseismic Emissions During Pneumatic Fracturing: A Numerical Model to Explain the Experiments. Journal of Geophysical Research (JGR): Solid Earth. ISSN 2169-9313. 123(8), s. 6922–6939. doi: 10.1029/2017JB014613. Fulltekst i vitenarkiv Vis sammendrag

  Modeling of fluid injection processes into a deformable porous medium is a challenging area of physics that has a wide range of applications like the food, construction, and petroleum industries. In this research, we investigate pneumatic fracturing of a porous medium experimentally and numerically in a Hele‐Shaw cell. In the experiments, we inject air into the porous medium (initially random loose packed) to create compaction, channeling, and fracturing while monitoring the cell with accelerometers and a high‐speed camera. Furthermore, we develop a numerical model in two steps: (1) a poroelastoplasticity‐based model to explain dynamic fluid pressure variations and (2) a solid stress model based on Janssen's theory. The contributions of the different pressure sources air in channels and solid stress in the experiments, and the simulations are compared with respect to amplitude and frequency. Afterward, the variations of the normal stress exerting on the plates are convolved with a Lamb Wave green function to generate acoustic emissions numerically. The physics behind the evolution of the experimentally recorded power spectrum of the out‐of‐plane plate vibrations are explained using numerical models. The frequency bands (in the simulated power spectra) are influenced by the size of the opened channels and the Hele‐Shaw cell and are in the same range with the experimentally measured peaks of the acoustic emissions.

• Cochard, Alain; Lengliné, Olivier; Måløy, Knut Jørgen & Toussaint, Renaud (2018). Thermally activated crack fronts propagating in pinning disorder: simultaneous brittle/creep behaviour depending on scale. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. ISSN 1364-503X. 377(2136), s. 1–23. doi: 10.1098/rsta.2017.0399. Fulltekst i vitenarkiv
• Farin, Maxime; Mangeney, Anne; Rosny, Julien De; Toussaint, Renaud & Trinh, PT (2018). Link between the dynamics of granular flows and the generated seismic signal: insights from laboratory experiments. Journal of Geophysical Research (JGR): Earth Surface. ISSN 2169-9003. 123(6), s. 1407–1429. doi: 10.1029/2017JF004296. Fulltekst i vitenarkiv Vis sammendrag

  Granular column collapse experiments have been conducted on a flat rough surface tilted at various angles with synchronous measurements of the flow dynamics and the emitted seismic signal. Our results show that the ratio of radiated seismic energy to potential energy lost by the granular flows decreases slightly from 0.033% to 0.017% with increasing slope angle on a poly(methyl methacrylate) (acrylic) plate. This is about 90 times lower than for the impact of a single particle of the same diameter. The experimental granular flows generated signals with frequencies lower than 20 kHz, with a mean value around 5 kHz, which are shown to be similar to the frequencies emitted by a single‐particle impact. The rise phase and maxima of the amplitude and frequencies of the seismic signals generated by our experimental granular flows are mostly controlled by flow motion in the direction normal to the slope, while their decay phase depends on downslope particle speeds. The granular flow regime changes from dense to more agitated flows above a critical slope angle that is about half the friction angle of the granular material. This change is reflected in (1) the shape of the temporal variation of the seismic amplitude and frequencies, with a decay phase lasting much longer and (2) the shape of the cumulative radiated seismic energy, which changes above the same critical slope angle. Implications of these results for the interpretation of seismic emissions from experimental and natural granular flows are discussed.

• Xu, Le; Marks, Benjy; Toussaint, Renaud; Flekkøy, Eirik Grude & Måløy, Knut Jørgen (2018). Dispersion in fractures with ramified dissolution patterns. Frontiers in Physics. 6. doi: 10.3389/fphy.2018.00029. Fulltekst i vitenarkiv Vis sammendrag

  The injection of a reactive fluid into an open fracture may modify the fracture surface locally and create a ramified structure around the injection point. This structure will have a significant impact on the dispersion of the injected fluid due to increased permeability, which will introduce large velocity fluctuations into the fluid. Here, we have injected a fluorescent tracer fluid into a transparent artificial fracture with such a ramified structure. The transparency of the model makes it possible to follow the detailed dispersion of the tracer concentration. The experiments have been compared to two dimensional (2D) computer simulations which include both convective motion and molecular diffusion. A comparison was also performed between the dispersion from an initially ramified dissolution structure and the dispersion from an initially circular region. A significant difference was seen both at small and large length scales. At large length scales, the persistence of the anisotropy of the concentration distribution far from the ramified structure is discussed with reference to some theoretical considerations and comparison with simulations.

• Bachelet, Vincent; Mangeney, Anne; Rosny, Julien De; Toussaint, Renaud & Farin, Maxime (2018). Elastic wave generated by granular impact on rough and erodible surfaces. Journal of Applied Physics. ISSN 0021-8979. 123(4), s. 1–9. doi: 10.1063/1.5012979. Fulltekst i vitenarkiv Vis sammendrag

  The elastic waves generated by impactors hitting rough and erodible surfaces are studied. For this purpose, beads of variable materials, diameters, and velocities are dropped on (i) a smooth PMMA plate, (ii) stuck glass beads on the PMMA plate to create roughness, and (iii) the rough plate covered with layers of free particles to investigate erodible beds. The Hertz model validity to describe impacts on a smooth surface is confirmed. For rough and erodible surfaces, an empirical scaling law that relates the elastic energy to the radius Rb and normal velocity Vz of the impactor is deduced from experimental data. In addition, the radiated elastic energy is found to decrease exponentially with respect to the bed thickness. Lastly, we show that the variability of the elastic energy among shocks increases from some percents to 70% between smooth and erodible surfaces. This work is a first step to better quantify seismic emissions of rock impacts in natural environment, in particular on unconsolidated soils.

• Kariche, Jugurtha; Meghraoui, Mustapha; Timoulali, Youssef; Cetin, Esra & Toussaint, Renaud (2018). The Al Hoceima earthquake sequence of 1994, 2004 and 2016: Stress transfer and poroelasticity in the Rif and Alboran Sea region. Geophysical Journal International. ISSN 0956-540X. 212(1), s. 42–53. doi: 10.1093/gji/ggx385. Fulltekst i vitenarkiv Vis sammendrag

  The 2016 January 25 earthquake (Mw 6.3) follows in sequence from the1994 May 26 earthquake (Mw 6.0) and the 2004 February 24 earthquake (Mw 6.4) in the Rif Mountains and Alboran Sea. The earlier two seismic events which were destructive took place on inland conjugate faults, and the third event occurred on an offshore fault. These earthquake sequences occurred within a period of 22 yr at ∼25 km distance and 11–16-km depth. The three events have similar strike-slip focal mechanism solutions with NNE-SSW trending left-lateral faulting for the 1994 and 2016 events and NW-SE trending right-lateral faulting for the 2004 event. This shallow seismic sequence offers the possibility (i) to model the change in Coulomb Failure Function (ΔCFF with low μ΄ including the pore pressure change) and understand fault-rupture interaction, and (ii) to analyse the effect of pore fluid on the rupture mechanism, and infer the clock-time advance. The variation of static stress change has a direct impact on the main shock, aftershocks and related positive lobes of the 2004 earthquake rupture with a stress change increase of 0.7–1.1 bar. Similarly, the 2004 main shock and aftershocks indicate loading zones with a stress change (>0.25 bar) that includes the 2016 earthquake rupture. The tectonic loading of 19–24 nanostrain yr−1 obtained from the seismicity catalogue of Morocco is comparable to the 5.0 × 1017 N·m yr−1 seismic strain release in the Rif Mountains. The seismic sequence is apparently controlled by the poroelastic properties of the seismogenic layer that depend on the undrained and drained fluid conditions. The short interseismic period between main shocks and higher rate of aftershocks with relatively large magnitudes (4 < Mw < 5.5) implies the pore-fluid physical effect in undrained and drained conditions. The stress-rate ranges between 461 and 582 Pa yr−1 with a ΔCFF of 0.2–1.1 bar. The computed clock-time advance reaches 239 ± 22 yr in agreement with the ∼10 yr delay between main shocks. The calculated static stress change of 0.9–1.3 bar, under pore-fluid stimulus added with well-constrained geodetic and seismic strain rates are critical for any seismic hazard assessment.

• Santucci, Stephane; Tallakstad, Ken Tore; Angheluta, Luiza; Laurson, Lasse; Toussaint, Renaud & Måløy, Knut Jørgen (2018). Avalanches and extreme value statistics in interfacial crackling dynamics. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. ISSN 1364-503X. 377(2136), s. 1–15. doi: 10.1098/rsta.2017.0394. Fulltekst i vitenarkiv
• Toussaint, Renaud; Aharonov, Einat; Koehn, Daniel; Gratier, Jean-Pierre; Ebner, Martin & Baud, Patrick [Vis alle 8 forfattere av denne artikkelen] (2018). Stylolites: A review. Journal of Structural Geology. ISSN 0191-8141. 114, s. 163–195. doi: 10.1016/j.jsg.2018.05.003. Fulltekst i vitenarkiv Vis sammendrag

  Stylolites are ubiquitous geo-patterns observed in rocks in the upper crust, from geological reservoirs in sedimentary rocks to deformation zones, in folds, faults, and shear zones. These rough surfaces play a major role in the dissolution of rocks around stressed contacts, the transport of dissolved material and the precipitation in surrounding pores. Consequently, they play an active role in the evolution of rock microstructures and rheological properties in the Earth's crust. They are observed individually or in networks, in proximity to fractures and joints, and in numerous geological settings. This review article deals with their geometrical and compositional characteristics and the factors leading to their genesis. The main questions this review focuses on are the following: How do they form? How can they be used to measure strain and formation stress? How do they control fluid flow in the upper crust? Geometrically, stylolites have fractal roughness, with fractal geometrical properties exhibiting typically three scaling regimes: a self-affine scaling with Hurst exponent 1.1 ± 0.1 at small scale (up to tens or hundreds of microns), another one with Hurst exponent around 0.5 to 0.6 at intermediate scale (up to millimeters or centimeters), and in the case of sedimentary stylolites, a flat scaling at large scale. More complicated anisotropic scaling (scaling laws depending of the direction of the profile considered) is found in the case of tectonic stylolites. We report models based on first principles from physical chemistry and statistical physics, including a mechanical component for the free-energy associated with stress concentrations, and a precise tracking of the influence of grain-scale heterogeneities and disorder on the resulting (micro)structures. Experimental efforts to reproduce stylolites in the laboratory are also reviewed. We show that although micrometer-size stylolite teeth are obtained in laboratory experiments, teeth deforming numerous grains have not yet been obtained experimentally, which is understandable given the very long formation time of such geometries. Finally, the applications of stylolites as strain and stress markers, to determine paleostress magnitude are reviewed. We show that the scalings in stylolite heights and the crossover scale between these scalings can be used to determine the stress magnitude (its scalar value) perpendicular to the stylolite surface during the stylolite formation, and that the stress anisotropy in the stylolite plane can be determined for the case of tectonic stylolites. We also show that the crossover between medium (millimetric) scales and large (pluricentimetric) scales, in the case of sedimentary stylolites, provides a good marker for the total amount of dissolution, which is still valid even when the largest teeth start to dissolve – which leads to the loss of information, since the total deformation is not anymore recorded in a single marker structure. We discuss the impact of the stylolites on the evolution of the transport properties of the hosting rock, and show that they promote a permeability increase parallel to the stylolites, whereas their effect on the permeability transverse to the stylolite can be negligible, or may reduce the permeability, depending on the development of the stylolite.

• Moura, Marcel; Måløy, Knut Jørgen; Flekkøy, Eirik Grude & Toussaint, Renaud (2017). Verification of a Dynamic Scaling for the Pair Correlation Function during the Slow Drainage of a Porous Medium. Physical Review Letters. ISSN 0031-9007. 119(15). doi: 10.1103/PhysRevLett.119.154503. Fulltekst i vitenarkiv Vis sammendrag

  In this Letter we give experimental grounding for the remarkable observation made by Furuberg et al. [Phys. Rev. Lett. 61, 2117 (1988)] of an unusual dynamic scaling for the pair correlation function N(r,t)during the slow drainage of a porous medium. Those authors use an invasion percolation algorithm to show numerically that the probability of invasion of a pore at a distance r away and after a time t from the invasion of another pore scales as N(r,t)∝ r − 1 f ( r D / t ) , where D is the fractal dimension of the invading cluster and the function f(u)∝ u 1.4 , for u≪ 1 and f(u)∝ u − 0.6 , for u≫ 1 . Our experimental setup allows us to have full access to the spatiotemporal evolution of the invasion, which is used to directly verify this scaling. Additionally, we connect two important theoretical contributions from the literature to explain the functional dependency of N(r,t) and the scaling exponent for the short-time regime ( t ≪ r D ). A new theoretical argument is developed to explain the long-time regime exponent ( t ≫ r D ).

• Eriksen, Fredrik Kvalheim; Toussaint, Renaud; Turquet, Antoine Léo; Måløy, Knut Jørgen & Flekkøy, Eirik Grude (2017). Pneumatic fractures in confined granular media. Physical Review E (PRE). ISSN 2470-0045. 95(6). doi: 10.1103/PhysRevE.95.062901. Fulltekst i vitenarkiv Vis sammendrag

  We perform experiments where air is injected at a constant overpressure Pin , ranging from 5 to 250 kPa, into a dry granular medium confined within a horizontal linear Hele-Shaw cell. The setup allows us to explore compacted configurations by preventing decompaction at the outer boundary, i.e., the cell outlet has a semipermeable filter such that beads are stopped while air can pass. We study the emerging patterns and dynamic growth of channels in the granular media due to fluid flow, by analyzing images captured with a high speed camera (1000 images/s). We identify four qualitatively different flow regimes, depending on the imposed overpressure, ranging from no channel formation for Pin below 10 kPa, to large thick channels formed by erosion and fingers merging for high Pin around 200 kPa. The flow regimes where channels form are characterized by typical finger thickness, final depth into the medium, and growth dynamics. The shape of the finger tips during growth is studied by looking at the finger width w as function of distance d from the tip. The tip profile is found to follow w(d)∝ d β , where β = 0.68 is a typical value for all experiments, also over time. This indicates a singularity in the curvature d2d/dw2∼ κ ∼ d 1 − 2 β , but not of the slope dw/dd∼ d β − 1 , i.e., more rounded tips rather than pointy cusps, as they would be for the case β > 1 . For increasing Pin , the channels generally grow faster and deeper into the medium. We show that the channel length along the flow direction has a linear growth with time initially, followed by a power-law decay of growth velocity with time as the channel approaches its final length. A closer look reveals that the initial growth velocity v0 is found to scale with injection pressure as v0∝ P 3 2 in , while at a critical time tc there is a cross-over to the behavior v(t)∝ t − α , where α is close to 2.5 for all experiments. Finally, we explore the fractal dimension of the fully developed patterns. For example, for patterns resulting from intermediate Pin around 100–150 kPa, we find that the box-counting dimensions lie within the range DB∈ [ 1.53 , 1.62 ] , similar to viscous fingering fractals in porous media.

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• Toussaint, Renaud; Sandnes, Bjørnar; Koehn, Daniel; Szymczak, Piotr & Aharonov, Einat (2017). Flow and Transformations in Porous Media. Frontiers Media SA. ISBN 9782889450770. 202 s. Fulltekst i vitenarkiv

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• Reis, Paula Kozlowski Pitombeira; Flekkøy, Eirik Grude; Toussaint, Renaud & Måløy, Knut Jørgen (2026). Linear Response Theory of Front-Back Contraction During a Single Haines Jump. Fulltekst i vitenarkiv
• Moura, Marcel; Brodin, Joachim Falck; Reis, Paula Kozlowski Pitombeira; Pierce, Kevin; Jankov, Mihailo & Rikvold, Per Arne [Vis alle 11 forfattere av denne artikkelen] (2026). From Thin Films to Stable Fronts: Tabletop Experimental Approaches to 2D and 3D Porous Media Flows. doi: https:/www.youtube.com/live/bSQ-sHK6FTU?si=W9_rbJ5BkyRPHP0m. Fulltekst i vitenarkiv
• Moura, Marcel; Reis, Paula Kozlowski Pitombeira; Rikvold, Per Arne; Linga, Gaute; Flekkøy, Eirik Grude & Schäfer, Gerhard [Vis alle 8 forfattere av denne artikkelen] (2026). Thin Film Flow: Fluid Transport via Thin Liquid Films in Slow Porous Media Flows. Fulltekst i vitenarkiv
• Moura, Marcel; Reis, Paula Kozlowski Pitombeira; Rikvold, Per Arne; Linga, Gaute; Flekkøy, Eirik Grude & Schäfer, Gerhard [Vis alle 8 forfattere av denne artikkelen] (2025). Thin Film Flow: Fluid Transport via Thin Liquid Films in Slow Porous Media Flows. Fulltekst i vitenarkiv
• Reis, Paula Kozlowski Pitombeira; Moura, Marcel; Linga, Gaute; Toussaint, Renaud; Rikvold, Per Arne & Flekkøy, Eirik Grude [Vis alle 7 forfattere av denne artikkelen] (2025). Modeling Gas-Liquid Drainage in Porous Media with Network Models. Fulltekst i vitenarkiv
• Reis, Paula Kozlowski Pitombeira; Linga, Gaute; Moura, Marcel; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Vis alle 7 forfattere av denne artikkelen] (2024). Investigation of liquid connectivity and drainage in granular porous media. Fulltekst i vitenarkiv
• Reis, Paula Kozlowski Pitombeira; Linga, Gaute; Moura, Marcel; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Vis alle 7 forfattere av denne artikkelen] (2024). Investigation of liquid connectivity and drainage in granular porous media. Fulltekst i vitenarkiv
• Reis, Paula Kozlowski Pitombeira; Vincent-Dospital, Tom Yannick Yves; Toussaint, Renaud & Måløy, Knut Jørgen (2024). Modeling drainage in porous media with stratified gradient in pore sizes. Fulltekst i vitenarkiv
• Reis, Paula Kozlowski Pitombeira; Linga, Gaute; Moura, Marcel; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Vis alle 7 forfattere av denne artikkelen] (2024). Network modeling of corner and bulk flows during drainage in granular porous media. Fulltekst i vitenarkiv
• Moura, Marcel; Reis, Paula Kozlowski Pitombeira; Schäfer, Gerhard; Toussaint, Renaud; Flekkøy, Eirik Grude & Rikvold, Per Arne [Vis alle 7 forfattere av denne artikkelen] (2023). Thin film flow: fluid transport via thin liquid films in slow porous media flows. Fulltekst i vitenarkiv
• Brodin, Joachim Falck; Rikvold, Per Arne; Moura, Marcel; Pierce, James Kevin; Toussaint, Renaud & Måløy, Knut Jørgen (2023). Experimental investigation of two phase flow with a table top optical scanner: the competition between viscous and gravitational effects under different boundary conditions. Fulltekst i vitenarkiv
• Reis, Paula Kozlowski Pitombeira; Moura, Marcel; Linga, Gaute; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Vis alle 7 forfattere av denne artikkelen] (2023). Numerical analysis of drainage in porous media using network models. Fulltekst i vitenarkiv
• Moura, Marcel; Brodin, Joachim Falck; Måløy, Knut Jørgen; Rikvold, Per Arne; Flekkøy, Eirik Grude & Jankov, Mihailo [Vis alle 8 forfattere av denne artikkelen] (2022). Thin film flow: fluid transport and pollution spreading in porous media. Fulltekst i vitenarkiv
• Moura, Marcel; Reis, Paula Kozlowski Pitombeira; Eriksen, Fredrik Kvalheim; Turquet, Antoine Léo; Flekkøy, Eirik Grude & Toussaint, Renaud [Vis alle 8 forfattere av denne artikkelen] (2022). Complexity: “More is Different” also in porous media flows. Fulltekst i vitenarkiv
• Kyriakopoulos, C; Barth, N.C.; Koelemeijer, Paula; Winterbourne, Jeffrey & Toussaint, Renaud (2021). 3D Printing in Geology and Geophysics: A New World of Opportunities in Research, Outreach, and Education. Frontiers in Earth Science. doi: 10.3389/feart.2021.734291. Fulltekst i vitenarkiv
• Moura, Marcel; Eriksen, Fredrik Kvalheim; Turquet, Antoine Leo; Flekkøy, Eirik Grude; Toussaint, Renaud & Jankov, Mihailo [Vis alle 7 forfattere av denne artikkelen] (2021). Complexity: “More is Different” also in porous media flows. Fulltekst i vitenarkiv
• Moura, Marcel; Måløy, Knut Jørgen; Flekkøy, Eirik Grude & Toussaint, Renaud (2021). Coffee is for drinking, tea is for porous media science: intermittent burst dynamics in slow drainage experiments in porous media. Fulltekst i vitenarkiv
• Måløy, Knut Jørgen; Brodin, Joachim Falck; Rikvold, Per Arne; Moura, Marcel; Toussaint, Renaud & Schaefer, Gerhard [Vis alle 7 forfattere av denne artikkelen] (2020). Drainage in porous media under influence of a gravitational field. Fulltekst i vitenarkiv
• Moura, Marcel; Måløy, Knut Jørgen; Flekkøy, Eirik Grude; Schäfer, Gerhard & Toussaint, Renaud (2020). Thin film flow: fluid transport via thin liquid films in slow porous media flows. Fulltekst i vitenarkiv
• Brodin, Joachim Falck; Måløy, Knut Jørgen; Moura, Marcel; Toussaint, Renaud & Rikvold, Per Arne (2020). An experimental study of the interplay between viscous, capillary and gravitational forces in two-phase flow in a three-dimensional porous medium. Fulltekst i vitenarkiv Vis sammendrag

  We study the interplay between viscous, capillary and gravitational forces in two-phase flow in a threedimensional porous medium, with the use of an optical scanner based on index-matched medium and fluorescent fluids. A more viscous, denser, fluid is injected into a less viscous, less dense fluid in a 3D porous medium, comprised of randomly packed glass beads of uniform size. We tune the injection rate over 10 experiments. Experience from the 2D scenario suggests that with a slow injection rate capillary and gravitational forces will dominate, and we should observe an unstable displacement and fingering. Conversely, with a high injection rate, viscous forces will dominate, leading to a more stable displacement and a narrower invasion front. How do the 2D findings hold up in the 3D scenario? We confirm the qualitative findings from the 2D experiments and establish a clear regime change, from unstable to stable displacement. We seek to derive a dimensionless number to quantify the relevant balance of forces and consider this number in relation to the invasion pattern. We characterize the invasion by Minkowski-functionals and fractal dimensions and seek relations between the found geometries and the derived dimensionless numbers.

• Turquet, Antoine Leo; Toussaint, Renaud; Eriksen, Fredrik Kvalheim; Flekkøy, Eirik Grude & Måløy, Knut Jørgen (2020). Reverse Engineering Earthquakes using Lab-scale Replicas: Application to Mw5. 5 2017 Pohang Earthquake. Fulltekst i vitenarkiv
• Måløy, Knut Jørgen; Eriksen, Jon Alm; Flekkøy, Eirik Grude; Toussaint, Renaud; Galland, Olivier & Sandnes, Bjørnar (2019). Pattern formation of frictional fingers in a gravitational potential. Fulltekst i vitenarkiv
• Måløy, Knut Jørgen; Eriksen, Jon Alm; Flekkøy, Eirik Grude; Toussaint, Renaud; Galland, Olivier & Sandnes, Bjørnar (2019). Pattern formation of frictional fingers in a gravitational field. Fulltekst i vitenarkiv
• Moura, Marcel; Måløy, Knut Jørgen; Flekkøy, Eirik Grude; Schäfer, Gerhard & Toussaint, Renaud (2019). Unconventional transport mechanisms in porous media: connectivity enhancement due to thin film flow. Fulltekst i vitenarkiv
• Moura, Marcel; Måløy, Knut Jørgen; Flekkøy, Eirik Grude; Schäfer, Gerhard & Toussaint, Renaud (2019). Unconventional transport mechanisms in porous media: connectivity enhancement due to thin film flow. Fulltekst i vitenarkiv
• Noël, François; Wyser, Emmanuel; Jaboyedoff, Michel; Hibert, Clément; Talib, Miloud & Malet, Jean-Philippe [Vis alle 15 forfattere av denne artikkelen] (2019). Real-size rockfall experiment: Applying observed impact dynamics to 3D rockfall simulations on highly detailed terrain models. Fulltekst i vitenarkiv
• Kariche, Jugurtha; Meghraoui, Mustapha & Toussaint, Renaud (2019). Stress transfer and poroelasticity associated to the 2019 Ridgecrest (California) earthquake sequences. Fulltekst i vitenarkiv
• Arran, Matthew; Mangeney, Anne; Rosny, Julien De; Farin, Maxime & Toussaint, Renaud (2019). High-frequency Seismic Signals from Landslides: Insight from Laboratory Flows and DEM Simulations. Fulltekst i vitenarkiv
• Koelemeijer, Paula; Winterbourne, Jeffrey; Toussaint, Renaud & Zaroli, Christophe (2019). 3D printing the world: developing geophysical teaching materials and outreach packages. Fulltekst i vitenarkiv
• Hibert, Clément; Talib, Miloud; Noël, François; Gracchi, Teresa; Bourrier, Franck & Brenguier, Ombeline [Vis alle 12 forfattere av denne artikkelen] (2019). Analysis of the dynamics of supervised single-block rockfalls from intra-block accelerometers, seismology and remote sensing. Fulltekst i vitenarkiv
• Vincent-Dospital, Tom; Toussaint, Renaud; Cochard, Alain; Måløy, Knut Jørgen; Flekkøy, Eirik Grude & Santucci, Stephane [Vis alle 7 forfattere av denne artikkelen] (2019). Hot cracks or cool cracks? A model for the brittle-ductile transition of solids. Fulltekst i vitenarkiv
• Moura, Marcel; Måløy, Knut Jørgen & Toussaint, Renaud (2018). Intermittent burst dynamics during slow drainage flows. Fulltekst i vitenarkiv
• Moura, Marcel; Måløy, Knut Jørgen; Flekkøy, Eirik Grude & Toussaint, Renaud (2018). Burst dynamics slow drainage in porous media. Fulltekst i vitenarkiv
• Moura, Marcel; Måløy, Knut Jørgen; Flekkøy, Eirik Grude & Toussaint, Renaud (2018). Burst dynamics in porous media drainage flows. Fulltekst i vitenarkiv
• Moura, Marcel; Dumazer, Guillaume; Eriksen, Fredrik Kvalheim; Måløy, Knut Jørgen; Flekkøy, Eirik Grude & Toussaint, Renaud (2018). Marangoni induced fracturing in two-dimensional frictional flows. Fulltekst i vitenarkiv
• Moura, Marcel; Måløy, Knut Jørgen; Flekkøy, Eirik Grude & Toussaint, Renaud (2018). Direct experimental measurement of the pair correlation function during the slow drainage of a porous medium. Fulltekst i vitenarkiv
• Xu, Le; Marks, Benjy; Toussaint, Renaud; Flekkøy, Eirik Grude & Måløy, Knut Jørgen (2018). Dissolution Patterns and Dispersion in Fractures. Fulltekst i vitenarkiv
• Moura, Marcel; Måløy, Knut Jørgen & Toussaint, Renaud (2017). Intermittent burst dynamics during slow drainage flows. Fulltekst i vitenarkiv

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