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Static and dynamic angles of repose in loose granular materials under reduced gravity

2011; American Geophysical Union; Volume: 116; Issue: E11 Linguagem: Inglês

10.1029/2011je003865

2156-2202

Maarten G. Kleinhans, Henk Markies, S. J. de Vet, A. C. in ‘t Veld, Ferdinand Postema,

Particle Dynamics in Fluid Flows

Journal of Geophysical Research: PlanetsVolume 116, Issue E11 Free Access Static and dynamic angles of repose in loose granular materials under reduced gravity M. G. Kleinhans, M. G. Kleinhans [email protected] Faculty of Geosciences, Utrecht University, Utrecht, NetherlandsSearch for more papers by this authorH. Markies, H. Markies Faculty of Geosciences, Utrecht University, Utrecht, NetherlandsSearch for more papers by this authorS. J. de Vet, S. J. de Vet Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Amsterdam, NetherlandsSearch for more papers by this authorA. C. in 't Veld, A. C. in 't Veld Faculty of Aerospace Engineering, Delft University of Technology, Delft, NetherlandsSearch for more papers by this authorF. N. Postema, F. N. Postema Faculty of Aerospace Engineering, Delft University of Technology, Delft, NetherlandsSearch for more papers by this author M. G. Kleinhans, M. G. Kleinhans [email protected] Faculty of Geosciences, Utrecht University, Utrecht, NetherlandsSearch for more papers by this authorH. Markies, H. Markies Faculty of Geosciences, Utrecht University, Utrecht, NetherlandsSearch for more papers by this authorS. J. de Vet, S. J. de Vet Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Amsterdam, NetherlandsSearch for more papers by this authorA. C. in 't Veld, A. C. in 't Veld Faculty of Aerospace Engineering, Delft University of Technology, Delft, NetherlandsSearch for more papers by this authorF. N. Postema, F. N. Postema Faculty of Aerospace Engineering, Delft University of Technology, Delft, NetherlandsSearch for more papers by this author First published: 17 November 2011 https://doi.org/10.1029/2011JE003865Citations: 119AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract [1] Granular materials avalanche when a static angle of repose is exceeded and freeze at a dynamic angle of repose. Such avalanches occur subaerially on steep hillslopes and wind dunes and subaqueously at the lee side of deltas. Until now it has been assumed that the angles of repose are independent of gravitational acceleration. The objective of this work is to experimentally determine whether the angles of repose depend on gravity. In 33 parabolic flights in a well-controlled research aircraft we recorded avalanching granular materials in rotating drums at effective gravitational accelerations of 0.1, 0.38 and 1.0 times the terrestrial value. The granular materials varied in particle size and rounding and had air or water as interstitial fluid. Materials with angular grains had time-averaged angles of about 40° and with rounded grains about 25° for all effective gravitational accelerations, except the finest glass beads in air, which was explained by static electricity. For all materials, the static angle of repose increases about 5° with reduced gravity, whereas the dynamic angle decreases with about 10°. Consequently, the avalanche size increases with reduced gravity. The experimental results suggest that relatively low slopes of granular material on Mars may have formed by dry flows without a lubricating fluid. On asteroids even lower slopes are expected. The dependence on gravity of angle of repose may require reanalysis of models for many phenomena involving sediment, also at much lower slope angles. Key Points Granular avalanche angles of repose depend on gravity The dynamic angle decreases whilst the static angle increases This implies longer avalanche runout in reduced gravity 1. Introduction Problem Definition and Objective [2] A basic property of noncohesive granular materials is the angle of repose: the maximum slope angle at which the material is at rest [Lowe, 1976]. Above this slope angle, the material starts to flow; below this angle, the material is stable. The angle varies from 25° for smooth spherical particles to 45° for rough angular particles [Carrigy, 1970; Pohlman et al., 2006]. Noncohesive granular materials are found in many contexts, from kitchen to industry and nature (Figure 1). Geomorphologically relevant examples are scree and talus slopes, but even these are, on Earth at least, affected by interstitial fluid or ice. Dry flows may have occurred on Earth, Mars, moons and asteroids [Chuang and Greeley, 2000; Bart, 2007; Dundas et al., 2010], on wind-blown dunes. Entirely submerged flows for which nearly the same angle of repose is observed are found on the lee slope of subaqueous dunes and the subaqueous slopes of deltas [e.g., Kleinhans, 2004, 2010]. Figure 1Open in figure viewerPowerPoint A pile of rounded gravel at the angle of repose, built by Gijsbert F. Kleinhans. [3] The angle of repose is an empirical friction parameter that is essential in models of numerous phenomena involving granular material, most of them actually at slopes much lower than the angle of repose. The angle of repose is therefore relevant for many geomorphological phenomena which is illustrated with the following examples. [4] 1. Subaerial granular avalanche features on Mars have angles that potentially contain information on material properties through the rheological properties [Gerstell et al., 2004; Pirulli and Mangeney, 2008], including the presence of water. Relatively low fan angles formed from gullies have been interpreted to be the lubricating effect of water [Harrison and Grimm, 2003; Heldmann and Mellon, 2004; Dickson et al., 2007; Kreslavsky and Head, 2009]. Mud flows on Mars and Venus may also have larger runout lengths than on Earth [Rickenmann, 1999; Malin, 1992], which remains poorly explained [Lucas and Mangeney, 2007]. [5] 2. The subaqueous angles of static and dynamic repose are similar to the subaerial values, and the difference between static and dynamic angles leads to discrete avalanches at the lee side of dunes, bars and deltas in fluvial and coastal environments [Kleinhans, 2004]. This avalanching, in turn, causes a basic particle size-sorting pattern depending on the angles of repose of the particle mixture [Boutreux et al., 1998; Makse et al., 1998]. Such sorting patterns are ubiquitous in deposits and outcrops and greatly affect the morphodynamics in rivers and deltas [e.g., Kleinhans, 2004, 2005a]. [6] 3. The downstream angle of subaqueous delta slopes on Mars is an important indicator of the magnitude and duration of the flow that created it. Steep angles indicate low (‘bed-load’) sediment transport rates and long duration, whereas gentler slopes indicate higher (‘suspended’) transport rates and shorter formative time periods [Jopling, 1964; Allen, 1970]. Such interpretation has relevance for use of deltas as indicators of paleo-hydrological conditions [Kleinhans, 2010; Kleinhans et al., 2010]. [7] 4. Fluvial and coastal models for beginning of sediment motion, sediment fluidization and sediment transport on horizontal beds and gentle slopes include the angle of repose as a Coulomb friction angle [Bagnold, 1951; Allen and Leeder, 1980; Parker and Andrews, 1985; Wiberg and Smith, 1987; Soulsby and Damgaard, 2005; Vollmer and Kleinhans, 2007]. [8] 5. Impact crater collapse depends on the angle of repose of the material [Melosh and Ivanov, 1999]. [9] Until now it has been assumed in planetary morphology and geology that the angle of repose of a noncohesive granular material is independent of gravity, i.e. has the same angle on other planets as on Earth. Given the importance of this angle it is surprising that the hypothesis of independence of gravity has hardly been tested. The few experiments recorded in literature that did test it have contradicting results varying from opposite effects to no effect at all. However, the lack of data is understandable as the practical difficulties of doing controlled experiments in reduced gravity are significant. As a first attempt to address the question whether the angle of repose is really independent of gravity, we designed experiments for the straightforward case of dense granular flows in discrete avalanches. [10] The objective of this paper is to experimentally determine whether the static and dynamic angles of repose depend on gravity, in order to gain understanding of granular avalanches under gravity lower than on Earth. We will measure the angle of repose systematically for well-rounded and for angular particles, for small and large particles, for particles in air and in water, and for three different relative gravitational accelerations, henceforth g-levels: g = 1 (Earth), g = 0.38 (Mars) and g = 0.1 (practical lower limit), where g = geff/ge with geff = effective gravitational acceleration and ge = gravitational acceleration on Earth (9.81 m/s2). [11] We first discuss the contradicting data reported in literature, then elaborate on possible causes and working hypotheses. After that, we present our methods and results. These are followed by discussion and relevance of results compared to literature, and conclusions. Previous Experiments [12] Angles of repose were determined in three different manners in the past. First, experiments were done with various granular materials to determine the angle of repose as a function of material properties [Carrigy, 1970; Dury et al., 1998; Brucks et al., 2007], and to determine direct relations between the angle of repose, runout length and dynamics [e.g., Rickenmann, 1999; Mangeney et al., 2010]. This has hardly been done for reduced gravity, partly because analyses and modeling studies demonstrated or assumed that it is independent of gravity [e.g., Zhou et al., 2001; Mangeney-Castelnau et al., 2005]. Second, slope angles of dry or submerged dense granular flow deposits were measured in nature, including on other planets and the Moon [e.g., Malin, 1992; Kreslavsky and Head, 2009]. Third, physics-based numerical models were run whereby resulting morphology and dynamics such as velocity and runout length were matched to a real case by calibrating the angle of repose [e.g., Harrison and Grimm, 2003; Pirulli and Mangeney, 2008]. The second and third approach were done for reduced gravity, but, working from natural examples, suffer from underdetermination of the possible causes for different angles due to gravity. Particularly the unknown presence of pore water as lubrication could lead to much lower angles than expected from dry granular flows. Similarly, runout lengths of large landslides on Mars were longer than expected and another hitherto unidentified factor could be involved [Lucas and Mangeney, 2007], potentially the angle of repose. [13] Recent centrifuge experiments with rotating drums suggest a negligible effect of gravity on angle of repose [Brucks et al., 2007]. These were done with glass beads with D = 0.53 mm, where D = particle diameter with 1 < g < 25. A rotating drum partially filled with granular material can represent various avalanching phenomena. In slow rotation, the angle of the material will increase until the static angle of repose is exceeded, and will avalanche until it freezes from the downstream end upwards at the dynamic angle of repose [Carrigy, 1970; Dury et al., 1998; Brucks et al., 2007]. This mode is called discrete avalanching regime. For increasing rotation rate, the avalanching becomes continuous at the dynamic angle of repose, sometimes called rolling flow regime, and the slope starts to deviate from a straight line. At very high rotation rates the slope develops and S-shape with inertial overshoot of particles at the top of the pile, which is called cascading regime. For high enough rotation rates the material is centrifuged to the periphery of the drum and avalanching ceases. In the well-controlled centrifuge experiments of Brucks et al. [2007] the transition from the avalanching to the rolling state was found to be largely independent on the effective gravity for glass beads. The thickness of the continuous flowing layer was also nearly independent of gravitational level, while the flow velocity scaled with . The angle of repose was found to depend nonlinearly on a Froude number Fr = ω2R/geff, where ω = angular frequency of the cylinder and R = radius of the drum. For 10−6 < Fr < 10−3 the angle of repose did not vary more than a few degrees, while this range covers the discrete avalanche regime to the cascading regime. For larger Fr the angle of repose increased rapidly [Brucks et al., 2007]. [14] In contrast, the relatively poorly controlled experiments in parabolic flights by Klein and White [1990] showed that the dynamic angle of repose decreases linearly with increasing for both glass beads of D = 1.35 mm and beach sand of D = 0.4 mm, although nearly a factor of twice less for the latter. The data indicate that the effect of gravity is larger for g < 1 but barely noticeable for g > 1, which could explain why the effect is not obvious in centrifuges. These data were collected with rotating drums at nearly constant ω in parabolic flights with 0.1 < g < 1.9 (see Walton et al. [2007] for reanalysis and discussion). Klein and White [1990] hypothesized that in reduced gravity, inter-particle normal loads decreased which increased particle friction coefficients, so that the angle of repose increased. However, Walton et al. [2007] suggested that some contact force may have increased, particularly as the glass beads with larger contact surface areas showed a stronger trend. ‘Contact force’ can be composed of many components; here static electricity or capillary force by microscopic pockets of water could be significant. [15] In short, a data set at decreased gravity collected in parabolic flights shows a strong trend of increasing angle of repose for decreasing gravity [Klein and White, 1990] whereas data sets for increased gravity collected in a centrifuge shows no effect [Brucks et al., 2007]. For decreasing gravity the relative importance of contact forces could not be excluded. This point is important, because the aim of the experiments in this paper is to assess the effect of reduced gravity on the angle of repose, and to be representative for natural systems with similar to much larger particles, both subaerial and subaqueous. It will be essential to perform the experiments both subaerially and subaqueously because the latter condition excludes significant electrostatic effects and capillary effects, although it adds drag effects. Hypothesis Development [16] The general belief that the angle of repose is independent of gravity is perhaps derived from two classical laws: the Coulomb law and the first law of Amontons. The Coulomb law states that kinetic friction is independent of the sliding velocity. This implies that the angle of repose is the same for granular matter in motion and in rest. Simplistically, we might assume that this is the angle a particle must pivot over underlying particles to move down-slope. The first law of Amontons states that the force of friction is directly proportional to the applied load. A hypothetical pile of spheres is stable despite the increasing load with depth into the pile, because the friction increases with the load. This implies that a reduction of applied load under lower gravity leads to equally lower friction, so that the static angle of repose remains constant. Furthermore, by combination with the Coulomb law it follows that a granular flow the driving gravitational force along the slope, Fz = mgeff sinα, is balanced by friction, which depends on the force normal to the slope, Ff = mgeff cosα, where α = angle of repose. As both scale with the weight of the flow, the dynamic angle of repose for a granular flow is again independent of gravity. [17] However, this oversimplifies the processes. Since Coulomb it has been found that static friction is larger than dynamic friction. For the initiation of a granular flow, the static angle of repose must be exceeded that is larger than the dynamic angle of repose. So the friction effectively depends on flow depth and velocity [e.g., Pouliquen, 1999; Jop et al., 2006], particle roughness [Pohlman et al., 2006], and sorting (also called polydispersity) (see Kleinhans [2004] for review) [Kleinhans, 2005a; Goujon et al., 2007]. [18] The static angle of repose may be related to cohesive forces including Vanderwaals forces, electrostatic forces and capillary forces in case of microscopic fluid pockets between the particles. We will not attempt to unravel the combined forces but aim at excluding those which are due to experimental effects but unlikely to be important in granular materials in nature. We may assume that these forces also act for vanishing gravity and that the arrested granular material attains a packing density independently of gravity as suggested by Brucks et al. [2007]. We therefore hypothesize that the static angle of repose increases with decreasing gravity. [19] The dynamic angle of repose is the product of a granular flow. Mobilization of the material into a moving avalanche necessarily involves dilatation, which reduces the number of contacts and therefore the contact forces. Once a granular flow is moving, the momentum and reduced friction cause it to run out below the static angle of repose to freeze at the dynamic angle of repose [Hungr, 1995; Walton et al., 2007; Mangeney et al., 2010]. This is particularly the case for larger rolling particles [Zhou et al., 2001]. We hypothesize that a moving granular flow is more dilated in lower gravity, so that friction is lower and the dynamic angle of repose decreases with decreasing gravity. 2. Methods and Materials [20] The methodology was to create confined granular avalanches during parabolic flights in a dedicated aircraft and measure the angle as a function of the resultant gravitational acceleration. Under such technically challenging conditions neither contact forces nor dilation can be measured. To exclude the effects of interstitial fluid (water and air), particle size and angularity, various materials and interstitial fluids were used simultaneously in different cylinders. To assess effects of aircraft vibrations we performed the experiment in g = 1 in the aircraft as well as on the ground. Below we describe the aircraft and measurement equipment, the experimental setup and the image analysis procedure to extract the angles from the digital video and the measured accelerations. Aircraft and Flight Data Collection [21] The aircraft is a Cessna Citation 550 II PH-LAB (Figure 2), a research aircraft owned and operated jointly by the National Aerospace Laboratory NLR and Delft University of Technology, Faculty of Aerospace Engineering. The platform is equipped with a partial-gravity flight director designed at Delft University of Technology to maximize the accuracy of the parabolic flights at arbitrary g within operating and safety limits of the aircraft. Figure 2Open in figure viewerPowerPoint The Cessna Citation aircraft of Delft University of Technology and the Dutch National Aerospace Laboratory used for the parabolic flights. [22] An accurate three axis accelerometer and ring laser gyro system recorded all trajectory parameters at 50 Hz, including relative accelerations in flight direction (ax), transversely (ay) and vertically (az) with respect to the aircraft. These accelerations are relative to ge when the aircraft is at rest in horizontal position so that ax = ay = 0. The magnitude of the relative gravitational acceleration geff was calculated as: whereby transverse accelerations ay were neglected because we have two-dimensional granular flows in narrow cylinders. The ay were twice as small as ax, more than an order of magnitude smaller than az. [23] To maintain the correct velocity for constant geff, the aircraft tilt relative to the g-vector varies during the parabola. The angle ϕ (in °) between aircraft and g is calculated as: [24] A time series of about 7 minutes data during slow descend (between 92.1 and 98.9 minutes time on the acceleration record) was analyzed to study the noise and fluctuations of the three acceleration components and the net geff. Spectral analysis was done by the power spectral density estimate via Welch's method, using window sizes of 400, 2000 and 10000, combined in one plot to show temporal structure at different timescales. Furthermore the spectral power was converted to amplitude expressed in geff and the frequency expressed as period to allow direct interpretation (Figure 3). Figure 3Open in figure viewerPowerPoint Spectral analysis of net g-vector due to aircraft motion. Red wall climber is attributed to electronics noise or engine interference noise. The spectral peak at 20 s is attributed to turbulence and hysteretic aircraft response to pilot feedback. [25] The spectral analysis demonstrated that the ax and ay components had no structure except noise (red wall climber) at 10 Hz and faster (Figure 3). The az and geff also had this red noise but there a clear spectral peak was observed at 0.05 Hz (20 s period). The low-frequency fluctuations are attributed to aircraft movement due to turbulence and hysteretic pilot-aircraft interaction. The high-frequency is explained as noise in the instruments and electronics and perhaps interference between the two jet engines. The effect of the high-frequency noise on the experimental results will be assessed by comparing the results of the 1 g flight experiments to control experiments on the ground. [26] To remove the noise, the 50 Hz acceleration time series was median filtered with a window size of 1 s before calculating equations (1) and (2). A binary signal was recorded and shown as a signal LED on the experimental setup when the required g-level was obtained within a tolerance of ±0.01. For each parabola equations (1) and (2) were applied to the period of accepted g-levels. Averages and [10,90] percentiles of g-levels and ϕ (Figure 4) were used to select acceptable parabolas for further analysis. Figure 4Open in figure viewerPowerPoint Mean, 10% and 90% percentiles of (top) g-levels and of (bottom) aircraft angle relative to the acceleration vector in each parabola. Rejected data have open symbols. Experimental Setup and Granular Materials [27] The basic idea is to fill half of a cylinder with a transparent sidewall with granular material and then rotate it continuously at a constant angular velocity in the discrete avalanching regime. To cover the parameter space of particle diameter, roughness and interstitial fluid a fixed array of nine cylinders was used. [28] The rotating cylinder system was here preferred over a sand pile or funnel for a theoretical and a practical reason. A continuous flow in a pouring setup would not allow measurement of the static angle of repose, whereas a granular material in a slowly rotating cylinder exhibits both static and dynamic phases. The angular velocity was chosen at 0.14 RPM to optimize the number of avalanches per parabola but remain in the linear avalanche slope regime rather than in the cascading S-shaped regime [Brucks et al., 2007]. Furthermore, the cylinder can remain closed so that there is no risk of spilling light granular material and water in the experimental aircraft. Moreover, it can continuously be rotated without having to empty and reload the measurement volume, so that no valuable time is lost during the mission. [29] Nine cylinders were built of PVC with a perspex front, with a diameter of 0.210 m and a height of 0.060 m. The height was a compromise: the angle of repose is affected by wall friction for large ratios of particle diameter and cylinder height [Dury et al., 1998; Zhou et al., 2001], but the avalanches should remain two-dimensional with the entire front moving at similar velocity rather than forming a tongue-shaped avalanche flanked by immobile particles [Kleinhans, 2005a]. The cylinders were mounted on the frame (Figure 5) and driven at the same rate by a pulse width controlled three-phase brushless electromotor. Figure 5Open in figure viewerPowerPoint The experimental setup. Cylinders are 0.21 m in diameter. Cameras are located to the left. [30] The cylinders were filled with granular materials (Table 1), where the top row, with the lighter air-filled cylinders, refers to the top of the frame. Both sand and glass beads have a specific density of 2.65 (water has 1, air has about 0.001) and a porosity of about 30–40%. The materials were chosen to range from small to large size ranging from Stokes to inertial settling regimes in water [Dietrich, 1982], from rounded glass beads (ballotini) to angular fluvial sand, and with air and water as interstitial fluid. The cylindrical wall was coated with the same granular material for each cylinder. The cylinders were prepared at 70% humidity of the air so we cannot exclude the possibility of formation of microscopic water pockets in the dry cases. Table 1. Granular Material and Interstitial Fluid for the Rotating Cylindersa Cylinder Column 1 Cylinder Column 2 Cylinder Column 3 Cylinder row 1 2.4 mm gravel in air 0.21 mm sand in air 0.2 mm glass beads in air St = 530, 1033, 1675 St = 13, 26, 42 St = 11, 21, 34 Cylinder row 2 2 mm glass beads in air 0.6 mm sand in air 0.6 mm sand in water St = 327, 637, 1033 St = 66, 129, 209 St = 0.9, 1.8, 3.0 Cylinder row 3 2.4 mm gravel in water 2 mm glass beads in water 0.6 mm glass beads in water St = 7.5, 14.6, 23.7 St = 4.6, 9.0, 14.6 St = 0.8, 1.5, 2.4 a Order same as in Figure 5. Stokes numbers are calculated for 0.1, 0.38 and 1 g. For comparison, the transition from viscous to inertial regime in water takes place at about St = 3–4 and the transition from viscous to free-fall regime in air takes place at St = 10 [Courrech du Pont et al., 2003]. [31] The rationale for performing experiments in both water and air is not merely that loose granular materials avalanche in both environments, but also that the subaqueous experiments have negligible electrostatic force effects and can also not be affected by surface tension of microscopic water pockets in the dry cases. However, fluid friction is present in the subaqueous systems, and it varies with particle diameter squared depending on the Stokes number, which describes the relative effects of grain inertia and fluid viscous effects [Allen, 1965, 1972; Dietrich, 1982; Courrech du Pont et al., 2003]. [32] The materials were selected based on the phase diagram by Courrech du Pont et al. [2003, Figure 3]. This diagram defines three regimes: the viscous limit regime, inertial limit regime and free-fall regime. This is based on two variables: r, which is the material density ρs relative to fluid density ρw: r = (ρs/ρw)1/2, and the Stokes number St, here calculated as the ratio of the characteristic time to reach the viscous limit velocity, and the characteristic time of free falling over a distance equal to the particle diameter: where η = fluid viscosity and sinθ = angle of repose. [33] Stokes numbers were calculated for 0.1, 0.38 and 1 g (Table 1) assuming a fluid viscosity of 1.0 × 10−3 Ns/m2 and air viscosity of 1.8 × 10−5 Ns/m2 at room temperature, and an angle of repose of 25° for glass beads and 40° for angular particles. For translation to Martian conditions the air viscosity of a carbon dioxide atmosphere at the freezing point for water is about 75% of the value for standard air at room temperature. For comparison, the transition from viscous to inertial regime in water takes place at about St = 3–4, the transition from viscous to free-fall regime in air takes place at St = 10 and the transition from inertial to free-fall regime for St > 10 takes place at r = 4 [Courrech du Pont et al., 2003]. As a result, in air all materials are always in the free-fall regime but approach the viscous regime for the 0.2 mm material, all materials of 0.6 mm in water are in the viscous regime but approach the inertial regime for the highest gravity, and all materials of 2 mm and larger in water are always in the inertial regime but approach the viscous regime transition in lower gravity. Courrech du Pont et al. [2003] found that the difference between static and dynamic angle of repose only depended on Stokes number for St < 10, where it decreased with decreasing St. The selected materials allow the isolation of the effect of gravity on the angles of repose independently of the dependence on Stokes number. [34] Furthermore, preliminary laboratory experiments indicated that interstitial fluid dynamics were very important for the static angle of repose in very fine granular materials, including the 0.2 mm glass beads and sand in water. A granular material transitioning from static to mobile will have to dilate, which means that fluid has to enter the interstices. For fine materials this takes significant time so that the material oversteepens up to 90° [Van den Berg et al., 2002]. The dynamic angle is unaffected given enough time for the flow to occur. As the duration of such avalanches far exceeds the duration of reduced gravity in a parabolic flight, we did not include subaqueous fine sediments. Image Analysis [35] Two High Definition (HD) consumer video cameras (Canon HF10E) recorded the avalanching process. The cameras were mounted on a small frame on the opposite side of the cabin. The high-frequency measurement of angles of the aeroplane relative to the ‘gravity’ force vec