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Experimental and numerical study of granular medium-rough wall interface friction
Advanced Powder Technology xxx (2017) xxx–xxx
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Advanced Powder Technology journal homepage: www.elsevier.com/locate/apt
Original Research Paper
Experimental and numerical study of granular medium-rough wall interface friction Khadija El Cheikh a,b,⇑, Chafika Djelal a, Yannick Vanhove a, Patrick Pizette b, Sébastien Rémond b a b
Univ. Artois, EA 4515, Laboratoire de Génie Civil et géo-Environnement (LGCgE), Béthune F-62400, France IMT Lille Douai, Univ. Lille, EA 4515 – LGCgE – Laboratoire de Génie Civil et géoEnvironnement, département Génie Civil & Environnemental, F-59000 Lille, France
a r t i c l e
i n f o
Article history: Received 24 April 2017 Received in revised form 11 July 2017 Accepted 23 October 2017 Available online xxxx Keywords: Granular medium Shear Friction Rough wall DEM
a b s t r a c t Wall roughness plays a crucial role in granular medium - rough wall interface friction. In this study, an experimental device has been designed to study the influence of boundary conditions, more specifically wall roughness, on the behavior of sheared granular medium. The study is based on use of an analog model, and consists of simulating roughness by means of notches and grains in the medium by monodisperse beads and on use of a numerical model based on the discrete element method. The test protocol entails displacing at fixed speed notched rods under confined granular medium. Movement of the beads layer near the rods as well as friction of the beads against the rods are both studied herein. Results indicate that the parameter controlling friction at the granular medium - rough wall interface is primarily the depth of beads embedment in surface asperities. The objective of the associated numerical modeling is to supplement the experimental results. Ó 2017 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
1. Introduction Whether in natural form like agricultural products (e.g. rice, corn), sand or aggregates used in concrete production or in a more elaborate form like bitumen, bricks or pharmaceutical powders, granular media are essential to our environment. The geometric and mechanical characteristics of the grains composing these materials are highly diverse, as are the loads potentially acting upon these media during the phases of fabrication, transportation, storage and/or use. Literature offers valuable information towards an in-depth understanding of the statics and dynamics of granular media, as obtained through both physical experimentation and numerical simulations [1–7]. When studying their flow, granular materials were found to rub against a surface that can be a substrate formed by grain assemblies (avalanche) [8,9] or else a wall (grain flow in a silo) [10–12]. Most research conducted on the rheology of granular media imposed a non-slip condition near the wall. This condition is fulfilled by bonding grains of the same size as mobile grains onto the wall [4]. In this case, the influence of wall roughness on granular medium behavior is not being studied. Nonetheless, an understanding of the phenomena involved at the rough wall contact may ⇑ Corresponding author at: Univ. Artois, EA 4515, Laboratoire de Génie Civil et géo-Environnement (LGCgE), Béthune F-62400, France. E-mail address: [email protected] (K. El Cheikh).
provide information on the bulk-related behavior of the granular medium. A conventional approach to reproduce the phenomena that may occur at the granular medium - rough wall interface is by developing experimental devices in the laboratory. Such experiments may be carried out on model materials, in most cases composed of glass beads. For such a study, the numerical modeling could be a complementary approach to explain physical phenomena from microscopic information that is either difficult or impossible to measure experimentally. To simulate the granular assembly, two numerical approaches are mainly used: a continuous medium [13,14] where the medium is described by finite elements or the use of discrete elements by individually modeling rigid grains of the medium [15,16]. Each of these approaches proves to be pertinent and adapted to a given situation. The continuous medium approach is better adapted to studying global behavior. However, when understanding the phenomena inherent in individual grain movements, the continuity hypothesis is no longer acceptable. This paper focuses on the granular medium-rough wall interface at the scale of grains capable of becoming interlocked in the wall surface asperities, by means of an experimental approach and then contributing additional information through a discrete numerical approach. On the experimental side, a modified plane/plane tribometer [17] was employed and an experimental device was specially designed in the Civil Engineering Department of
https://doi.org/10.1016/j.apt.2017.10.020 0921-8831/Ó 2017 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
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the IUT-Béthune institution (French regional laboratory LGCgE). Without seeking to replicate a granular medium at scale or the typical roughness of a wall, a simple model was developed based on the following premise: simulate the asperities of a wall by introducing ‘‘notches” machined perpendicularly to the shear direction on a rectilinear support (castellated rod), as well as the granular medium by using glass beads of the same dimension. The principle behind this test consists of shearing a granular medium via a horizontal rod displacement. This device enables not only applying a normal pressure on the granular medium and measuring the speed of rough wall displacement, but also assessing the influence of the ratio between bead size and rough wall asperities on friction at the interface. As for the numerical approach, the discrete element method is implemented in order to explain the experimentally observed blocking phenomena. This paper will initially provide a description of the device, along with the methodology adopted to conduct an experimental test and the measurements. Next, a study on test reproducibility will be discussed. A parametric evaluation of the choice of rod displacement speed will be presented in Section 4. The fifth section shares the results obtained with the experimental approach, while Section 6 is devoted to both experimental test modeling and the additional information derived by discrete numerical simulation. The concluding section will review both the work accomplished and primary results measured.
600 mm long with a 300 mm stroke length. During rod displacement, the force being exerted on it is measured by a compressive/tensile force sensor placed between the rod and the tribometer auger (Fig. 1). The sensor measurement range covers 2000 N, with an accuracy of ±10 N. The movement of beads in contact with the Plexiglas box walls is filmed with a color camera (at 25 images/s) positioned in front of the box wall. The height and spacing of the rod notches are selected such that the beads are able to interlock or not between two successive notches. Three configurations were examined, whereby greater or lesser roughness with respect to bead size was chosen (Fig. 2.
2. Experimental program
Note that In order to reduce the friction between the plate and the lateral walls of the container, the plate width is made slightly smaller than the width of the container (less 2 mm than the width of the container 800 mm) (Fig. 2a).
2.1. Experimental device The experimental device is composed of a rectangular parallelepiped-shaped box (250 mm high by 300 mm long by 80 mm deep) filled with 10 mm glass beads (Fig. 1). The dimensions of this box are imposed by those of both the tribometer stroke length and its space constraints. The observation of beads movements in the three-dimensional configuration is facilitated by a 10 mm beads dimension. The box has been fitted at its base with an interchangeable brass rod that serves to simulate the asperities of a surface. The upper surface of the granular medium may be left exposed or subjected to normal pressure. A ‘‘T”-shaped steel lid with dimensions slightly less than those of the box, to ensure no friction with the box, may be added to the upper part of the medium while simultaneously authorizing dilatation of the latter. This set-up allows simulating the pressures being exerted by the granular material against a wall (e.g. the case of silos). On this lid, masses may be placed to enable varying the normal pressure. The entire assembly is then positioned on the tribometer [17], a device that makes it possible to move the rod at constant speed and measure the force bearing on the rod. In order to mobilize friction, the rod shifts into a translational motion beneath the granular medium. The rod is
Roughness R1: The beads are unable to completely interlock between two notches, as both the notch height and distance separating two successive notches measure 5 mm. This case represents a roughness of less than the grain size in the medium. Roughness R2: Only one bead is able to completely interlock between two notches. The notch height is 10 mm while the spacing separating two consecutive notches equals 15 mm. This case represents a roughness of the same size as that of the grains in the given medium. Roughness R3: Two beads are able to completely interlock within a hollow space. Notch height is 10 mm, and the spacing between two notches equals 25 mm. This is the case where roughness exceeds the medium grain size.
2.2. Test methodology In its initial configuration, the medium is composed of an assembly of 6450 glass beads 10 mm in diameter with a mass density of q = 2.6 gcm3. A box filling procedure has been devised in order to track the shear profile of the medium during the displacement of the rough rod. For this purpose, the beads are introduced in three columns of two distinct colors (Fig. 3). To prepare the initial configuration of three columns, two plastic plates remaining 100 mm apart are vertically placed in the box (Fig. 3a). Next, 2150 beads are inserted into each column in five layers in order to maintain the vertical plates during filling (Fig. 3b). After introducing the 6450 beads, both plastic plates are carefully removed (Fig. 3c). Then the medium is confined (Fig. 3e) and sheared (Fig. 3f). 2.3. Conducted testing The shear of the granular medium has been studied for various rod roughnesses, imposed rod speeds and levels of confinement
Fig. 1. Experimental device.
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applied to the medium. The roughness thresholds evaluated are R1, R2 and R3, as presented in Section 2.1. The imposed rod displacement speeds are 1, 5 and 10 mm/s. The investigated speed range was determined so as to measure the force being exerted by the rod and then to observe the phenomena taking place at the beads/rod interface. Indeed, for a speed value larger than 10 mm/ s, the shear force recording time is insufficient to compute an average force (short time measurement). Moreover, rapid beads movements interfere with the observation of interface mechanisms. The resultant of beads weight and vertical forces applied by the T-shaped lid and the masses positioned on the granular medium constitutes the normal force applied on the rod. The normal pressure values are chosen according to the masses used to confine the medium. The normal force values are listed in Table 1. 2.4. Measures Tangential force, shear profile, initial packing density, and total number of beads leaving the box have systematically been measured. The tangential force is measured in order to study effects of rod displacement speed, normal pressure applied on the medium, and rod roughness on the friction at the granular mediumrough wall interface. In addition, tangential force, shear profile, initial packing density and number of beads leaving the box all serve as measurements for assessing test reproducibility. During motion, the rod placed at the bottom of the device rubs against both the beads in the medium and the base of the device. The frictional force between the beads and the rod is referred to as the tangential force: it is the force required for the beads to cross both the notches and the other beads remaining interlocked during rod displacement. This force is computed as the difference between the force measured by the sensor and the frictional force between rod and device base. The initial beads arrangement and sequences of images obtained during the test are analyzed using the FIJI/ImageJ image analysis software [18] for the purpose of measuring the initial packing density of the medium and tracking shear profile formation throughout the test. As the rod is moving some beads become locked and then broken between the lateral wall and the notches as shown in Fig. 4b. To enable the beads to exit without being blocked, the end of the front wall is cut open (Fig. 4a). The height of the opening can be
3
adjustable (Fig. 4c). After many tests conducted for different opening height, a height of 12 mm (2 mm more than the bead size) has been chosen in order to ease the exit of the beads and prevent jamming to occur. The number of beads leaving denotes the total number of beads exiting through the box opening once the rod has been displaced a 300 mm distance. 3. Test reproducibility The objective of the test reproducibility is to study the effect of the initial state (initial arrangement of beads) on the measurements. The reproducibility study consists of performing each test three times by keeping the same test conditions (confining pressure, rod roughness and speed, number of beads in the medium) and varying the initial state. For brevity, only the reproducibility of tests conducted for rod R1, with a 175 N normal force and a 5 mm/s rod displacement speed, is presented herein. The results obtained under other conditions are comparable to those discussed and depicted in the following using error bars. 3.1. Packing density Packing density is defined as the volume occupied by the beads divided by total volume (Eq. (1)):
Packing density ¼
Volumebeads Volumetotal
ð1Þ
Total volume is computed as the stacking height multiplied by the box width (300 mm) and depth (80 mm). The stacking height is determined with the FIJI/ImageJ image analysis software [18] by drawing a line whose length can be measured between the stacking base (excluding notch height) and its upper part (Fig. 5). The uncertainty on this height measurement, due to unevenness of the free surface, equals 2 mm. The average packing density and standard deviation of three measurements is 0.597 and 0.003 (0.5%), respectively. Overall, for the various roughness and normal force conditions, the packing density varies between 0.590 and 0.606 (Table 2). The measured packing density values are close to those of a monodisperse stacking laid out without any special arrangement in a large container relative to the bead diameter, which lies on the order of 0.6 with a variability of a few hundredths [19–21]. The low disper-
Fig. 2. Notched rods : R1, R2 and R3.
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Fig. 3. Experimental protocol for preparing and shear a confined granular medium.
Table 1 Normal forces applied to the rod.
Normal force [N] Equivalent pressure [kPa]
Beads weight
Beads weight + T-shaped lid
Beads weight + T-shaped lid + mass of 5 kg
Beads weight + T-shaped lid + mass of 15 kg
85 3.5
125 5
175 7.5
275 11.5
Fig. 4. Diagram depicting the experimental device.
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initial state. While, over the dynamic regime, the average value of the tangential force varies between 27 and 33 N. Unlike its maximum value, the average tangential force value within this dynamic regime does not depend on the initial state of the stacking. For this reason, only the average tangential force value in the dynamic regime will be discussed in the paper. Regarding the number of beads leaving the box for the three reproducibility tests, the results demonstrate that this number varies between 173 and 179. Thus, this number is considered independent of the initial state. Fig. 7 exhibits the shear profiles for the three reproducibility tests. These results indicate that the difference among the three profiles is insignificant. Indeed, in the initial state, the three columns remain vertical, whereas in the final state, the first layer of beads in contact with the rod has been horizontally moved (along the rod displacement direction) by a distance of almost 90 mm. When moving, the first layer drags the upper layers, which then slide on the first one without creating any major disorder in the bulk. The influence of roughness on beads movements near the rod will be discussed in what follows.
Fig. 5. Example of a stacking height measurement using the FIJI software: example for Roughness R1, and a 175 N applied normal force applied on the rod.
sion in initial packing density values indicates that the latter does not seem to be affected by roughness or by the normal force applied on the granular medium.
3.2. Initial state of beads stacking Fig. 6 displays the recording of force applied to rod R1 as a function of its displacement distance for the same test repeated three times. The normal force applied on the rod equals 175 N with a displacement speed of 5 mm/s. For the set of curves shown in Fig. 6, three distinct zones can be identified: A rapid increase in force until reaching a maximum value (first peak). The peak value of the force exerted by the rod is the force required to produce a granular rearrangement by moving the beads from their initial positions (i.e. static friction). A rapid decrease in the force to reach a dynamic regime. Upon moving the rod, each bead needs a sufficient free space in order to initiate its movement. To create this free space, the beads initially lying in a static state (i.e. packing density 0.6) move apart which leads in decrease in the friction between beads and rod, thus causing a drop in the tangential force. A dynamic regime (i.e. characterized by dynamic friction) formed by irregular oscillations. The beads rearrange themselves during rod movement. The oscillations observed within this dynamic regime reflect the bead movements needed to overcome obstacles (whether interlocked beads or notches). Fig. 6 shows that the maximum value of the tangential force varies between 68 and 98 N across the three reproducibility tests. The tangential force mainly depends on the layout of beads in their
4. Parametric study: selection of rod displacement speed The study of the influence of rod displacement speed on tangential force has been conducted on rod R1. The normal force applied on this rod equals 175 N while the studied displacement speed are 1, 5 and 10 mm/s. In the dynamic regime, results reveal that the average tangential force computed over this regime increases slightly with the speed being imposed on the rod. Indeed, the average value of tangential force and their standard deviation lie on the order of 32 (±3.5 N), 33 (±3 N) and 40 N (±10 N) for speeds of 1, 5 and 10 mm/s, respectively. At a 10 mm/s speed, the increase in average tangential force may be explained by a displacement distance not long enough to attain the dynamic regime. Indeed, only for the curve corresponding to a 10 mm/s speed a peak in value (64 N) near that of the first peak (65 N) appears in the dynamic regime. This observation allows stating that for a 10 mm/s displacement speed, a longer rod displacement distance is required. In order to choose between 1 and 5 mm/s, oscillations within the dynamic regime are described by the standard deviation at the various measurement points. These oscillations are more intense at speeds of 1 mm/s (37%) and 10 mm/s (26%) than at 5 mm/s (20%). The 5 mm/s speed has thus been selected for the following experimental study. 5. Results and discussion The influence of roughness is first investigated for a normal force of 85 N. Afterwards, the influence of the normal force on beads/rod interface friction is presented for each rod. 5.1. Influence of rod roughness The variation in tangential force for rods R1, R2 and R3 (85 N normal force and 5 mm/s displacement speed) is measured. The average tangential force values corresponding to R1 (22 ± 1.1 N) and R2 (21 ± 1.3 N) are similar. As well, nearly identical force evo-
Table 2 Initial packing density values measured for various normal forces applied on the granular medium. Normal force [N]
85
125
175
275
R1 R2 R3
0.599 ± 0.008 0.593 ± 0.002 0.593 ± 0.001
0.600 ± 0.004 0.600 ± 0.001 0.598 ± 0.002
0.597 ± 0.003 0.600 ± 0.002 0.598 ± 0.002
0.596 ± 0.001 0.597 ± 0.005 0.602 ± 0.004
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Fig. 6. Recording of force applied on the rod as a function of its displacement distance: Roughness R1, 175 N normal force applied on the rod, and 5 mm/s rod displacement speed.
Fig. 7. Shear profiles for the reproducibility tests: Roughness R1, 175 N normal force applied on the rod, and 5 mm/s rod displacement speed.
lution described by oscillations standard deviation for the two rods R1 (4.4%) and R2 (3.8%) are observed. However, the average tangential force value rises for R3 (27 ± 2.9 N) and higher oscillations (7%) with comparison to R1 and R2 are detected. The influence of rod roughness on tangential force has been explained by observing the mechanisms at the vicinity of the beads/rod interface. To simplify the schematic representation of these phenomena, the motion of an individual bead observed through the Plexiglas wall during rod displacement has been studied for each rod. Bead rotation has been highlighted by means of a white bead marked with red1 lines and initially placed near the rod (Fig. 8). Note that the marked bead allows only to describe its rotation by observation under different test conditions but the rotation speed variation can not plotted. For rod R1, in the initial state, each bead in contact with rod notches is positioned inside a hollow space 1 mm deep (Fig. 9a). When a speed is imposed on the rod, the bead systematically crosses both the hollow spaces and notches. The number of hollow spaces and notches crossed by the bead depends on its initial position on the rod. For rod R1, a 250 mm displacement distance corresponds to 25 hollow spaces and 25 notches. During rod displacement, regardless of its initial position, the bead can either move (sliding motion) at the same speed as the rod (Fig. 9b), undergo rotation (Fig. 9c) or cross the notch ridge by simultaneously sliding and rotating motions (Fig. 9d). The examples shown in Figs. 9–12 correspond to beads placed in their initial state near the intermediate column. For rod R2, bead dimension equals the depth of hollow spaces (10 mm). In the initial state, the first beads layer (black beads in
1 For interpretation of color in Fig. 8, the reader is referred to the web version of this article.
Fig. 8. White bead marked in order to observe its rotation.
Fig. 10) lie completely inside the hollow spaces between notches. The (white) beads of the next layer above may adopt a position: in a 1 mm deep hollow space (Fig. 10a), on the notches (Fig. 10b), or on a bead interlocked between two notches (Fig. 10c). As the rod is being displaced, 3 cases may happen. The white bead (in the beads layer lying directly above) may: The nearly identical force evolution for the two rods R1 and R2 may be explained by the fact that the phenomena observed solely on rod R2 and not on R1 are: rod sliding beneath the bead, and bead rotation on the notch. These motions do not generate additional force in comparison of that of R1. In the case of rod R3, an additional mechanism is observed, in comparison with R2, it is the possibility that beads embed within a 2 mm deep hollow space to then extend beyond the bead interlocked in the hollow space of the rod (Fig. 12). Note that this depth may be greater in the medium further from the Plexiglas wall but it cannot be observed.
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Fig. 9. Mechanisms observed on rod R1.
Fig. 10. R2 - Initial configuration.
-
Be immobile, while the rod slides underneath the bead:
-
Rotate on the notches:
-
Become partially interlocked in the rod hollow space and extend beyond the bead interlocked in this space:
Fig. 11. Mechanisms observed on rod R2.
To disengage from a 2 mm deep hollow space, the given bead must push the bead already interlocked inside the rod hollow space. In this case, the white bead applies a force on the notch
ridge and/or the black interlocked bead. The notch then applies the same magnitude of force on the bead (known by reaction force). If the magnitude of the reaction force exceeds the bead’s
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Fig. 12. Mechanism observed on rod R3.
rupture limit, then the bead breaks, which is reflected by a peak within the dynamic regime equals to that of the static value. The tangential force value corresponding to this peak is thus removed from the average tangential force computation. In the case of roughness R3, higher oscillations with comparison with R1 and R2 in tangential force overtime reveal that the phenomena occurring in this case are more complex (crossing of a 2 mm deep hollow space) than those encountered for rods R1 and R2. Broken beads were only observed in the case of rod R3. It is impossible however to observe whether these broken beads indicate blockage at the box exit or obstacles on the rod surface. The various mechanisms observed regarding R1, R2 and R3 show that crossing more challenging obstacles (crossing of a 2 mm deep hollow space) requires a greater force than that needed to overcome multiple obstacles of lesser severity (case of rods R1 and R2). These results are in agreement with our previous study conducted on a discrete modeling of symmetrical shear of a monodisperse granular medium under periodic conditions [23]. In fact, it was demonstrated that for a given normal pressure and imposed displacement speed, the tangential force at the granular medium-rough surface interface depends on the depth of grain interlocking into the surface asperities. This study also found that for an interlocking depth of less than 0.25d (where d is the diameter of grains in the medium), the tangential force increases with interlocking depth. Yet these various observations applicable to spherical grains cannot be transposed to more complex shapes. The tests carried out by Djelal et al. [22] on small plates representing kaolin particles revealed that a rotational plate motion requires more energy to overcome the interparticle friction. Consequently, this rotational motion raises frictional force at the plate-rough wall interface. Moreover, Djelal et al. [22] identified the existence of a minimum friction corresponding to a roughness of the same order of magnitude as the average kaolin particle size. 5.2. Influence of the normal force applied on the rod Fig. 13 shows both the variation in tangential force (a) and number of beads leaving the box (b) as a function of normal force applied on rods R1, R2 and R3. The rod displacement speed has been set at 5 mm/s. During shear, bead movements under the lid prevent this latter from remaining horizontal, thus indicating that the load applied to the granular medium is not uniform. Each point on the curve and each error bar of Fig. 15 represent respectively the average and standard deviation for three measurements. Regardless the rod roughness, tangential force increases with normal force. For a normal force almost 275 N (equivalent normal pressure: 7.5 kPa) due to beads being blocked from leaving the box, the error bar becomes significant relative to the average tangential force value (40% for rod R2, 30% for rod R3). For measurements corresponding to a normal force almost 275 N, the measurements dispersion becomes very wide, hence only values of normal force less than 275 N will be included during results interpretation. For normal forces applied to the rod of below 275 N, results suggest that regardless of the normal force, the tangential force exerted on rod R3 is greater than that exerted on either R1 or R2. However, Fig. 15a shows that the variation in tangential force for rods R1
and R2 does not reveal any significant influence of roughness on tangential force. Fig. 15b shows that the number of beads leaving the box remains independent of the normal force applied on the rod. Note that in the case where no bead is able to become completely interlocked in the hollow spaces (R1), only the first layer of beads is able to leave through the opening. For the other two rough rods (R2 and R3), in addition to this first layer, the beads interlocked in the rod hollow spaces can also exit through the opening. This explains the fact that the number of beads interlocked in the hollow spaces of rod R3 is greater than that of rod R2; consequently, the number of beads leaving the box for rod R3 is higher than that for rod R2. Due to experimental limitations, some parameters cannot be measured during the test. As a case in point, it was mentioned in Section 5.1 above that for roughness R3, it is difficult to observe whether the broken beads are a sign of blocking at the box exit or obstacles at the rod surface. At this stage, it would be worthwhile to verify whether the increase in tangential force for R3 is due to blockage near the opening or bead movements near the notches. Such a hypothesis may be examined by means of numerical modeling. The study conducted on the experimental device can thus be complemented by a numerical study.
6. Numerical modeling of the experimental device The objective of this section is to compute the force being exerted by grains in the medium on the grains simulating the opening, which would allow us to conclude whether or not the opening constitutes a significant artefact. The approach selected herein is the smooth discrete element method (or smooth DEM) [24]. The simulations are performed using the ‘‘DemGCE” numerical computation code developed in-house by the Civil and Environmental Engineering Department at the Douai School of Mines. In this numerical tool, a grain is represented by a sphere with several interaction law models being feasible [23,25–29]. In this paper, Hertz-Mindlin contact laws implemented and tested in [30] are used in order to focus exclusively on interactions existing in dry granular medium.
6.1. Boundary conditions In the experimental device, two types of walls are used: a rough and mobile wall (rod), and four plane and stationary walls (Plexiglass sidewalls). A plane wall is modeled in the DemGCE code by a sphere with infinite radius. The rough wall is simulated by an assembly of spheres bonded to a flat surface (Fig. 14b). The distribution of spheres on the rough wall, along with their diameter and the distance separating two successive spherical assemblies, serves to simulate the rod notches used for purposes of the experimental device. The opening is modeled by another assembly of spheres 2.5 mm in diameter; this diameter was set at the same order of magnitude as the rough wall spheres. The spheres for the opening are positioned 12 mm from the simulated notches so as to comply with the experimental device configuration.
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Fig. 13. Variation in tangential force (a) and number of beads leaving the box (b) vs. normal force applied on rods R1, R2 and R3; Rod speed 5 mm/s.
6.2. Simulation stages In order to fully comply with the experimental protocol adopted, all grains in the granular medium must settle on the rough wall under their own weight. Once grains are settled and in order to confine the granular medium, a normal pressure is applied on its upper surface. Next, the granular medium is sheared by a horizontal displacement at constant speed of the rough wall. (A) Preparation of the confined granular medium The preparation of a granular medium initially involves generating grains within the computed volume. The algorithm used for grains generation is RSA (Random Sequential Addition) [31], which enables preparing a granular stacking similar to that intended for experimentation. Grains are randomly and sequentially generated in the computed volume, without any overlap with the grains already placed. Using this procedure, the packing density of generated grains does not exceed 0.38, in our case a packing density of 0.3 is targeted. The number of grains (6450), their diameter (10 mm) and the volume dimensions (250 mm high, 300 mm long, and 80 mm deep) are all equal to those used in experiments. The micromechanical characteristics of the generated spheres are similar to those of the glass beads used in experimental testing. After randomly placing the required number of grains (6450), the grains are released from their stationary positions and settle onto the rough wall under
Fig. 15. Example of controlling normal pressure (r) on the granular medium: Roughness R1.
their own weight in order to constitute a stable granular stacking with a packing density near that of the experimental one (0.62). In order to confine the medium, a horizontal plane is placed on the upper surface of the granular medium. The normal pressure applied on this medium is controlled by computing the vertical displacement speed (V) to be imposed on the plane (Eq. (2)).
V ¼ sign
r r req a
r rreq min 1;
r
ð2Þ
Fig. 14. (a) Schematic depiction of both the rod notches and opening of the experimental device; (b) DEM numerical modeling of the notches and opening.
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Fig. 16. Displacement of the rough wall: (a) beginning of simulation, and (b) end of simulation (non-confined granular medium).
Table 3 Primary micromechanical parameters used in the simulations. Parameter symbol (unity)
Value
Diameter of grains d (mm) Density of grains q (g/cm3) Young modulus E (Pa) Poisson’s ratio m () Friction coefficient l () Rolling coefficient lr () Damping coefficient A (s1) Restitution coefficient e () Time step Dt (s)
10 mm 2.6 1.0E+8 0.29 0.15 0.002 4.5E5 0.85 1.0 E6
where r is the normal pressure exerted by grains in the medium on the upper plane, r_req the desired normal pressure, and a a constant set equal to 30. Fig. 15 displays an example of the normal pressure r evolution for a desired pressure r_req of 8 kPa. An 8 kPa normal pressure applied on the granular medium is equivalent to an 11.5 kPa normal pressure applied on the rough wall, which accounts for adding the weight of the grains (3.5 kPa). During the experimental tests, the normal pressure is not uniformly distributed along the stacking surface. Indeed, the level of the masses added on the upper surface of the granular medium is influenced by the level of the latter, which does not remain horizontal under the effect of beads leaving through the opening. However, by numerical modeling, the normal pressure may be controlled during the simulation. (B) Displacement of the rough wall Fig. 16 presents an example of modeling the experimental test for rod R2 and for a normal force almost 85 N applied to the rod
(normal pressure: 3.5 kPa). The rough wall is moved by imposing a constant speed in the shear direction on all packets of bonded grains, as well as on the lower plane. The motion of the bonded grains is not determined by resolving the fundamental law of dynamics, as is the case for the other grains in the granular medium. By default, the sidewalls and mobile rough wall have the same material parameters as the grains in the granular medium. The primary micromechanical parameters used in the simulations are listed in Table 3. The values of Young’s modulus and time step were chosen to reduce the computational expense of simulation, while the values of the other parameters were fixed according to parametric study and most used values in the literature for glass beads. 6.3. Comparison between numerical simulations and experiments In this section, the experimental tests are compared to the numerical simulations. Fig. 17 shows the variation of the tangential force as a function of the normal force for the rods R1, R2 and R3. The bars shown on the experimental measurements represent the standard deviation of 5 tests. On one hand, for a given rod roughness, both numerical and experimental measures show that the tangential force increases with increase in the normal force. As well experimental and numerical curves describe similar evolution except for R1 when the normal force increases, the numerical tangential force increases faster than the experimental one and the deviation between numerical and experimental measures becomes greater. On the other hand, regarding the normal force, a deviation of 5 N is found between numerical and experimental measures for rods R2 and R3. This shows that the numerical model is able to represent approximately the tangential force for a given confinement. The obtained deviation can be explained by the fact that the posi-
Fig. 17. Numerical – experimental comparison of the variation of the tangential force as a function of the normal force for rods R1 (a), R2 (b) and R3 (c).
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tion). These results allow concluding that the opening has greater influence with roughness R1 than R2 and R3. These results lead also to the conclusion that the beads broken during experimental testing with roughness R3 do not provide an indication of blockage upon leaving the box.
7. Conclusion
Fig. 18. Evolution in force Fh for rough surfacesR1, R2 and R3: 85 N normal force, and 10 mm/s rough wall displacement speed.
tion of the lid added on the upper surface of the granular medium is influenced by the level of the latter, which does not remain horizontal under the effect of beads leaving through the opening. This means that the confinement is not uniformly applied on the rod. However, by numerical modeling, the normal pressure may be controlled and uniformly applied on the rod during the simulation. In addition the parameters chosen for the simulations which are not calibrated according to the experiments can explain the difference obtained between numerical and experimental measures. However, for experiments conducted under different conditions, it has been highlighted that the tangential force increases with the rod roughness (highest value for R3). On the contrary, numerical simulations show that for a given value of normal force, the tangential force of rod R3 is less than those obtained for R1 and R2. We suppose that this result is due to the fact that the notches (flat surface and acute edge) are modeled by spheres (rough surface and rounded edge). Rough surface has tendency to increase the value of the tangential force while rounded edge has tendency to decrease the latter with comparison to experiments. The overall result depends on which parameter is dominant, and the tangential force can increase or decrease. In general the comparison between experiments and numerical simulations shows a good agreement. Thus, the numerical code is able to give a good indication of the frictional force between the rod and the beads but it is not fully able to capture the specific influence of different types of roughness. 6.4. Evaluation of the force exerted upon the device opening The force Fh exerted on the grains composing the opening is computed in the rough wall displacement direction. Fig. 18 shows the variation in force Fh during the rough wall displacement under the granular medium. In order to reduce computation time, the rough wall displacement speed is set at 10 mm/s. The weight of the grains applies a 85 N normal force on the rough wall. For a higher normal force, the medium becomes more confined, which in turn promotes blockage. The results shown in Fig. 18 highlight that for roughness R3, the 0.15 N average value of force Fh is negligible when compared to the force being exerted on the notches (27 N for experiment and 21 for numerical simulation). However, for roughness R2, force Fh varies quite significantly once the wall has been displaced a distance of 40 mm, to reach a value of 40 N, which is twice that of the tangential force exerted on the notches (21 N for experiment and 26 for numerical simulation). Then, the average value of force Fh becomes negligible (0.3 N) relative to the tangential force exerted on the notches. For roughness R1, the average value of force Fh equals 5 N, which represents almost 20 % of the average tangential force on the notches (22 N for experiment and 26 for numerical simula-
An experimental device has been designed in order to study the influence of roughness on friction at the granular medium-rough wall interface. The trial principle consists of displacing a notched plate under a confined monodisperse granular medium. First, the influence of roughness and normal force on the set of measurable magnitudes is studied. The experimental study, showed that: – Regardless of the rod roughness, the force exerted on the rod in its displacement direction increases with the normal force being applied on it. – The main parameter controlling the frictional force acting between the granular medium and the rod is the beads interlocking depth within the hollow spaces formed by two successive notches. In order to determine at which level of system (Fig. 4) the beads actually broke, the experimental study was complemented by a numerical study using an in-house DEM code. – The comparison between experiments and numerical simulations is quite coherent. – Results revealed that for roughness R3, to the case of major force noticed in the dynamic regime during the experimental test, the force applied by grains in the medium on spheres simulating the opening proves to be negligible compared to the average tangential force exerted by grains on the rod notches. Consequently, the beads that broke during the experimental test with roughness R3 do not provide an indication of blockage at the box opening. In further studies beads failure under mechanical loadings will be conducted to compare this value to the amount of the pic in the dynamic regime. Experiments in more realistic configurations will be performed. Such studies must be carried out on polydisperse granular medium (spherical or angular in shape) and irregular roughness. As well, the device will be improved in such a manner to prevent encountered problems (broken beads) by designing flexible opening and wavy rough wall. Or by moving vertically rough rod into a container full of beads and then the force exerted by the beads on the rod will be measured. References [1] I. Albert, P. Tegzes, B. Kahng, R. Albert, J.G. Sample, M.A. Pfeifer, A.L. Barabasi, T. Vicsek, P. Schiffer, Jamming and fluctuations in granular drag, Phys. Rev. Lett. 84 (2000) 5122. [2] R.M. Nedderman, Statics and Kinematics of Granular Materials, Cambridge University Press, Cambridge, 1992. [3] N. Bell, Y. Yu, P. J. Mucha, Particle-based simulation of granular materials in ACM SIGGRAPH/ Eurographics Symposium on Computer Animation, August 2005. [4] G.D.R. MiDi, On dense granular flows, Eur. Phys. J. E 14 (2004) 341–365. [5] O. Pouliquen, F. Chevoir, Dense flows of dry granular materials, C. R. Acad. Sci. Phys. 3 (2002) 163–175. [6] S. Volpato, P. Canu, A.C. Santomaso, Simulation of free surface granular flows in tumblers, Adv. Powder Technol. 28 (2017) 1028–1037. [7] S.H. Chou, H.J. Hu, S.S. Hsiau, Investigation of friction effect on granular dynamic behavior in a rotating drum, Adv. Powder Technol. 27 (2016) 1912– 1921. [8] K.A. Dahmen, Y. Ben-Zion, J.T. Uhl, A simple analytic theory for the statistics of avalanches in sheared granular materials, Nat. Phys. 7 (2011) 554–557.
Please cite this article in press as: K. El Cheikh et al., Experimental and numerical study of granular medium-rough wall interface friction, Advanced Powder Technology (2017), https://doi.org/10.1016/j.apt.2017.10.020
12
K. El Cheikh et al. / Advanced Powder Technology xxx (2017) xxx–xxx
[9] H. Yang, R. Li, P. Kong, Q.C. Sun, M.J. Biggs, V. Zivkovic, Avalanche dynamics of granular materials under the slumping regime in a rotating drum as revealed by speckle visibility spectroscopy, Phys. Rev. E 91 (April 2015) 042206–42230. [10] P. Wang, L. Zhu, X. Zhu, Flow pattern and normal pressure distribution in flat bottom silo discharged using wall outlet, Powder Technol. 295 (2016) 104– 114. [11] A. Qadir, N.A. Ispalove, A. Ali, R. Chand, M.A. Shah, A. Khan, K. Hussain, Experimental and numerical determination of apparent mass variation of granular media confined in silo geometry, Acta Phys. Polonica A 129 (2016). [12] R. Balevicˇius, R. Kacˇianauskas, V. Vadluga, Investigation of three-dimensional granular stresses in pyramidal container after filling, Mechanika 74 (2008) 1392–11207. [13] O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, sixth ed., Butterworth-Heinemann, 2005, ISBN 0750663200. [14] J.N. Reddy, An Introduction to the Finite Element Method, third ed., McGrawHill, 2006, ISBN 9780071267618. [15] F. Radjai, F. Dubois, Discrete-element modeling of granular materials. London: Wiley-ISTE, 2011, ISBN 978-1-84821-260-2. [16] J.R. Williams, G. Hocking, G.G.W. Mustoe, The Theoretical Basis of the Discrete Element Method. NUMETA 1985, Numerical Methods of Engineering, Theory and Applications. Rotterdam: A.A. Balkema [17] C. Djelal, Y. Vanhove, A. Magnin, Tribological behaviour of self compacting concrete, Cem. Concr. Res. 34 (2004) 821–828. [18] W. Rasband, imageJ. National Institutes of Health, Bethesda MD, USA, imagej. nih.gov/ij/. [19] G.D. Scott, D.M. Kilgour, The density of random close packing of spheres, Br. J. Appl. Phys. (J. Phys. D) 2 (1969). [20] G.D. Scott, Packing of spheres, Nature, Lond 188 (1960) 908–909. [21] A.E.R. Westman, H.R. Hugill, Packing of Particles, Am. Ceram. Soc. 13 (1930) 767–779.
[22] C. Djelal, Designing and perfecting a tribometer for the study of friction of a concentrated clay-water mixture against a metallic surface, Mater. Struct. 34 (1) (2001) 51–58. [23] K. El Cheikh, S. Rémond, P. Pizette, Y. Vanhove, C. Djelal, Discrete Element study of granular material - Bumpy wall interface behavior, Physica A 457 (2016) 526–539. [24] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Géotechnique (1979) 47–65. [25] S. Rémond, DEM simulation of small particles clogging in the packing of large beads, Physica A 389 (2010) 4485–4496. [26] S. Rémond, P. Pizette, A DEM hard-core soft-shell model for the simulation of concrete flow, Cem. Concr. Res. 58 (2014) 169–178. [27] A. Kimbonguila Manounou, S. Rémond, Discrete element modeling of the microstructure of fine particle agglomerates in sheard dilute suspension, Physica A 412 (2014) 66–83. [28] P. Pizette, S. Rémond, DEMGCE Code, Discrete element modeling of Granular materials for Civil Engineering, MINES DOUAI, Civil & Engineering Departement, FRANCE, InterDeposit Digital Number, 2013, IDDN. FR.010.0118996.000.R.A.2013.035.30000. [29] K. Wu, P. Pizette, F. Becquart, S. Rémond, N.E. Abriak, W. Xu, S. Liu, Experimental and numerical study of cylindrical triaxial test on mono-sized glass beads under quasi-static loading condition, Adv. Powder Technol. 28 (2017) 155–166. [30] P. Pizette, S. Rémond, Experimental and numerical studies of the effect of rolling friction for sandpile formation, in: 11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI) July 20–25, 2014, Barcelona, Spain. [31] B. Widom, Random sequential addition of hard spheres to a volume, J. Chem. Phys. 44 (1966) 3888–3894.
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Contents lists available at ScienceDirect
Advanced Powder Technology journal homepage: www.elsevier.com/locate/apt
Original Research Paper
Experimental and numerical study of granular medium-rough wall interface friction Khadija El Cheikh a,b,⇑, Chafika Djelal a, Yannick Vanhove a, Patrick Pizette b, Sébastien Rémond b a b
Univ. Artois, EA 4515, Laboratoire de Génie Civil et géo-Environnement (LGCgE), Béthune F-62400, France IMT Lille Douai, Univ. Lille, EA 4515 – LGCgE – Laboratoire de Génie Civil et géoEnvironnement, département Génie Civil & Environnemental, F-59000 Lille, France
a r t i c l e
i n f o
Article history: Received 24 April 2017 Received in revised form 11 July 2017 Accepted 23 October 2017 Available online xxxx Keywords: Granular medium Shear Friction Rough wall DEM
a b s t r a c t Wall roughness plays a crucial role in granular medium - rough wall interface friction. In this study, an experimental device has been designed to study the influence of boundary conditions, more specifically wall roughness, on the behavior of sheared granular medium. The study is based on use of an analog model, and consists of simulating roughness by means of notches and grains in the medium by monodisperse beads and on use of a numerical model based on the discrete element method. The test protocol entails displacing at fixed speed notched rods under confined granular medium. Movement of the beads layer near the rods as well as friction of the beads against the rods are both studied herein. Results indicate that the parameter controlling friction at the granular medium - rough wall interface is primarily the depth of beads embedment in surface asperities. The objective of the associated numerical modeling is to supplement the experimental results. Ó 2017 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
1. Introduction Whether in natural form like agricultural products (e.g. rice, corn), sand or aggregates used in concrete production or in a more elaborate form like bitumen, bricks or pharmaceutical powders, granular media are essential to our environment. The geometric and mechanical characteristics of the grains composing these materials are highly diverse, as are the loads potentially acting upon these media during the phases of fabrication, transportation, storage and/or use. Literature offers valuable information towards an in-depth understanding of the statics and dynamics of granular media, as obtained through both physical experimentation and numerical simulations [1–7]. When studying their flow, granular materials were found to rub against a surface that can be a substrate formed by grain assemblies (avalanche) [8,9] or else a wall (grain flow in a silo) [10–12]. Most research conducted on the rheology of granular media imposed a non-slip condition near the wall. This condition is fulfilled by bonding grains of the same size as mobile grains onto the wall [4]. In this case, the influence of wall roughness on granular medium behavior is not being studied. Nonetheless, an understanding of the phenomena involved at the rough wall contact may ⇑ Corresponding author at: Univ. Artois, EA 4515, Laboratoire de Génie Civil et géo-Environnement (LGCgE), Béthune F-62400, France. E-mail address: [email protected] (K. El Cheikh).
provide information on the bulk-related behavior of the granular medium. A conventional approach to reproduce the phenomena that may occur at the granular medium - rough wall interface is by developing experimental devices in the laboratory. Such experiments may be carried out on model materials, in most cases composed of glass beads. For such a study, the numerical modeling could be a complementary approach to explain physical phenomena from microscopic information that is either difficult or impossible to measure experimentally. To simulate the granular assembly, two numerical approaches are mainly used: a continuous medium [13,14] where the medium is described by finite elements or the use of discrete elements by individually modeling rigid grains of the medium [15,16]. Each of these approaches proves to be pertinent and adapted to a given situation. The continuous medium approach is better adapted to studying global behavior. However, when understanding the phenomena inherent in individual grain movements, the continuity hypothesis is no longer acceptable. This paper focuses on the granular medium-rough wall interface at the scale of grains capable of becoming interlocked in the wall surface asperities, by means of an experimental approach and then contributing additional information through a discrete numerical approach. On the experimental side, a modified plane/plane tribometer [17] was employed and an experimental device was specially designed in the Civil Engineering Department of
https://doi.org/10.1016/j.apt.2017.10.020 0921-8831/Ó 2017 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
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the IUT-Béthune institution (French regional laboratory LGCgE). Without seeking to replicate a granular medium at scale or the typical roughness of a wall, a simple model was developed based on the following premise: simulate the asperities of a wall by introducing ‘‘notches” machined perpendicularly to the shear direction on a rectilinear support (castellated rod), as well as the granular medium by using glass beads of the same dimension. The principle behind this test consists of shearing a granular medium via a horizontal rod displacement. This device enables not only applying a normal pressure on the granular medium and measuring the speed of rough wall displacement, but also assessing the influence of the ratio between bead size and rough wall asperities on friction at the interface. As for the numerical approach, the discrete element method is implemented in order to explain the experimentally observed blocking phenomena. This paper will initially provide a description of the device, along with the methodology adopted to conduct an experimental test and the measurements. Next, a study on test reproducibility will be discussed. A parametric evaluation of the choice of rod displacement speed will be presented in Section 4. The fifth section shares the results obtained with the experimental approach, while Section 6 is devoted to both experimental test modeling and the additional information derived by discrete numerical simulation. The concluding section will review both the work accomplished and primary results measured.
600 mm long with a 300 mm stroke length. During rod displacement, the force being exerted on it is measured by a compressive/tensile force sensor placed between the rod and the tribometer auger (Fig. 1). The sensor measurement range covers 2000 N, with an accuracy of ±10 N. The movement of beads in contact with the Plexiglas box walls is filmed with a color camera (at 25 images/s) positioned in front of the box wall. The height and spacing of the rod notches are selected such that the beads are able to interlock or not between two successive notches. Three configurations were examined, whereby greater or lesser roughness with respect to bead size was chosen (Fig. 2.
2. Experimental program
Note that In order to reduce the friction between the plate and the lateral walls of the container, the plate width is made slightly smaller than the width of the container (less 2 mm than the width of the container 800 mm) (Fig. 2a).
2.1. Experimental device The experimental device is composed of a rectangular parallelepiped-shaped box (250 mm high by 300 mm long by 80 mm deep) filled with 10 mm glass beads (Fig. 1). The dimensions of this box are imposed by those of both the tribometer stroke length and its space constraints. The observation of beads movements in the three-dimensional configuration is facilitated by a 10 mm beads dimension. The box has been fitted at its base with an interchangeable brass rod that serves to simulate the asperities of a surface. The upper surface of the granular medium may be left exposed or subjected to normal pressure. A ‘‘T”-shaped steel lid with dimensions slightly less than those of the box, to ensure no friction with the box, may be added to the upper part of the medium while simultaneously authorizing dilatation of the latter. This set-up allows simulating the pressures being exerted by the granular material against a wall (e.g. the case of silos). On this lid, masses may be placed to enable varying the normal pressure. The entire assembly is then positioned on the tribometer [17], a device that makes it possible to move the rod at constant speed and measure the force bearing on the rod. In order to mobilize friction, the rod shifts into a translational motion beneath the granular medium. The rod is
Roughness R1: The beads are unable to completely interlock between two notches, as both the notch height and distance separating two successive notches measure 5 mm. This case represents a roughness of less than the grain size in the medium. Roughness R2: Only one bead is able to completely interlock between two notches. The notch height is 10 mm while the spacing separating two consecutive notches equals 15 mm. This case represents a roughness of the same size as that of the grains in the given medium. Roughness R3: Two beads are able to completely interlock within a hollow space. Notch height is 10 mm, and the spacing between two notches equals 25 mm. This is the case where roughness exceeds the medium grain size.
2.2. Test methodology In its initial configuration, the medium is composed of an assembly of 6450 glass beads 10 mm in diameter with a mass density of q = 2.6 gcm3. A box filling procedure has been devised in order to track the shear profile of the medium during the displacement of the rough rod. For this purpose, the beads are introduced in three columns of two distinct colors (Fig. 3). To prepare the initial configuration of three columns, two plastic plates remaining 100 mm apart are vertically placed in the box (Fig. 3a). Next, 2150 beads are inserted into each column in five layers in order to maintain the vertical plates during filling (Fig. 3b). After introducing the 6450 beads, both plastic plates are carefully removed (Fig. 3c). Then the medium is confined (Fig. 3e) and sheared (Fig. 3f). 2.3. Conducted testing The shear of the granular medium has been studied for various rod roughnesses, imposed rod speeds and levels of confinement
Fig. 1. Experimental device.
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applied to the medium. The roughness thresholds evaluated are R1, R2 and R3, as presented in Section 2.1. The imposed rod displacement speeds are 1, 5 and 10 mm/s. The investigated speed range was determined so as to measure the force being exerted by the rod and then to observe the phenomena taking place at the beads/rod interface. Indeed, for a speed value larger than 10 mm/ s, the shear force recording time is insufficient to compute an average force (short time measurement). Moreover, rapid beads movements interfere with the observation of interface mechanisms. The resultant of beads weight and vertical forces applied by the T-shaped lid and the masses positioned on the granular medium constitutes the normal force applied on the rod. The normal pressure values are chosen according to the masses used to confine the medium. The normal force values are listed in Table 1. 2.4. Measures Tangential force, shear profile, initial packing density, and total number of beads leaving the box have systematically been measured. The tangential force is measured in order to study effects of rod displacement speed, normal pressure applied on the medium, and rod roughness on the friction at the granular mediumrough wall interface. In addition, tangential force, shear profile, initial packing density and number of beads leaving the box all serve as measurements for assessing test reproducibility. During motion, the rod placed at the bottom of the device rubs against both the beads in the medium and the base of the device. The frictional force between the beads and the rod is referred to as the tangential force: it is the force required for the beads to cross both the notches and the other beads remaining interlocked during rod displacement. This force is computed as the difference between the force measured by the sensor and the frictional force between rod and device base. The initial beads arrangement and sequences of images obtained during the test are analyzed using the FIJI/ImageJ image analysis software [18] for the purpose of measuring the initial packing density of the medium and tracking shear profile formation throughout the test. As the rod is moving some beads become locked and then broken between the lateral wall and the notches as shown in Fig. 4b. To enable the beads to exit without being blocked, the end of the front wall is cut open (Fig. 4a). The height of the opening can be
3
adjustable (Fig. 4c). After many tests conducted for different opening height, a height of 12 mm (2 mm more than the bead size) has been chosen in order to ease the exit of the beads and prevent jamming to occur. The number of beads leaving denotes the total number of beads exiting through the box opening once the rod has been displaced a 300 mm distance. 3. Test reproducibility The objective of the test reproducibility is to study the effect of the initial state (initial arrangement of beads) on the measurements. The reproducibility study consists of performing each test three times by keeping the same test conditions (confining pressure, rod roughness and speed, number of beads in the medium) and varying the initial state. For brevity, only the reproducibility of tests conducted for rod R1, with a 175 N normal force and a 5 mm/s rod displacement speed, is presented herein. The results obtained under other conditions are comparable to those discussed and depicted in the following using error bars. 3.1. Packing density Packing density is defined as the volume occupied by the beads divided by total volume (Eq. (1)):
Packing density ¼
Volumebeads Volumetotal
ð1Þ
Total volume is computed as the stacking height multiplied by the box width (300 mm) and depth (80 mm). The stacking height is determined with the FIJI/ImageJ image analysis software [18] by drawing a line whose length can be measured between the stacking base (excluding notch height) and its upper part (Fig. 5). The uncertainty on this height measurement, due to unevenness of the free surface, equals 2 mm. The average packing density and standard deviation of three measurements is 0.597 and 0.003 (0.5%), respectively. Overall, for the various roughness and normal force conditions, the packing density varies between 0.590 and 0.606 (Table 2). The measured packing density values are close to those of a monodisperse stacking laid out without any special arrangement in a large container relative to the bead diameter, which lies on the order of 0.6 with a variability of a few hundredths [19–21]. The low disper-
Fig. 2. Notched rods : R1, R2 and R3.
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Fig. 3. Experimental protocol for preparing and shear a confined granular medium.
Table 1 Normal forces applied to the rod.
Normal force [N] Equivalent pressure [kPa]
Beads weight
Beads weight + T-shaped lid
Beads weight + T-shaped lid + mass of 5 kg
Beads weight + T-shaped lid + mass of 15 kg
85 3.5
125 5
175 7.5
275 11.5
Fig. 4. Diagram depicting the experimental device.
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initial state. While, over the dynamic regime, the average value of the tangential force varies between 27 and 33 N. Unlike its maximum value, the average tangential force value within this dynamic regime does not depend on the initial state of the stacking. For this reason, only the average tangential force value in the dynamic regime will be discussed in the paper. Regarding the number of beads leaving the box for the three reproducibility tests, the results demonstrate that this number varies between 173 and 179. Thus, this number is considered independent of the initial state. Fig. 7 exhibits the shear profiles for the three reproducibility tests. These results indicate that the difference among the three profiles is insignificant. Indeed, in the initial state, the three columns remain vertical, whereas in the final state, the first layer of beads in contact with the rod has been horizontally moved (along the rod displacement direction) by a distance of almost 90 mm. When moving, the first layer drags the upper layers, which then slide on the first one without creating any major disorder in the bulk. The influence of roughness on beads movements near the rod will be discussed in what follows.
Fig. 5. Example of a stacking height measurement using the FIJI software: example for Roughness R1, and a 175 N applied normal force applied on the rod.
sion in initial packing density values indicates that the latter does not seem to be affected by roughness or by the normal force applied on the granular medium.
3.2. Initial state of beads stacking Fig. 6 displays the recording of force applied to rod R1 as a function of its displacement distance for the same test repeated three times. The normal force applied on the rod equals 175 N with a displacement speed of 5 mm/s. For the set of curves shown in Fig. 6, three distinct zones can be identified: A rapid increase in force until reaching a maximum value (first peak). The peak value of the force exerted by the rod is the force required to produce a granular rearrangement by moving the beads from their initial positions (i.e. static friction). A rapid decrease in the force to reach a dynamic regime. Upon moving the rod, each bead needs a sufficient free space in order to initiate its movement. To create this free space, the beads initially lying in a static state (i.e. packing density 0.6) move apart which leads in decrease in the friction between beads and rod, thus causing a drop in the tangential force. A dynamic regime (i.e. characterized by dynamic friction) formed by irregular oscillations. The beads rearrange themselves during rod movement. The oscillations observed within this dynamic regime reflect the bead movements needed to overcome obstacles (whether interlocked beads or notches). Fig. 6 shows that the maximum value of the tangential force varies between 68 and 98 N across the three reproducibility tests. The tangential force mainly depends on the layout of beads in their
4. Parametric study: selection of rod displacement speed The study of the influence of rod displacement speed on tangential force has been conducted on rod R1. The normal force applied on this rod equals 175 N while the studied displacement speed are 1, 5 and 10 mm/s. In the dynamic regime, results reveal that the average tangential force computed over this regime increases slightly with the speed being imposed on the rod. Indeed, the average value of tangential force and their standard deviation lie on the order of 32 (±3.5 N), 33 (±3 N) and 40 N (±10 N) for speeds of 1, 5 and 10 mm/s, respectively. At a 10 mm/s speed, the increase in average tangential force may be explained by a displacement distance not long enough to attain the dynamic regime. Indeed, only for the curve corresponding to a 10 mm/s speed a peak in value (64 N) near that of the first peak (65 N) appears in the dynamic regime. This observation allows stating that for a 10 mm/s displacement speed, a longer rod displacement distance is required. In order to choose between 1 and 5 mm/s, oscillations within the dynamic regime are described by the standard deviation at the various measurement points. These oscillations are more intense at speeds of 1 mm/s (37%) and 10 mm/s (26%) than at 5 mm/s (20%). The 5 mm/s speed has thus been selected for the following experimental study. 5. Results and discussion The influence of roughness is first investigated for a normal force of 85 N. Afterwards, the influence of the normal force on beads/rod interface friction is presented for each rod. 5.1. Influence of rod roughness The variation in tangential force for rods R1, R2 and R3 (85 N normal force and 5 mm/s displacement speed) is measured. The average tangential force values corresponding to R1 (22 ± 1.1 N) and R2 (21 ± 1.3 N) are similar. As well, nearly identical force evo-
Table 2 Initial packing density values measured for various normal forces applied on the granular medium. Normal force [N]
85
125
175
275
R1 R2 R3
0.599 ± 0.008 0.593 ± 0.002 0.593 ± 0.001
0.600 ± 0.004 0.600 ± 0.001 0.598 ± 0.002
0.597 ± 0.003 0.600 ± 0.002 0.598 ± 0.002
0.596 ± 0.001 0.597 ± 0.005 0.602 ± 0.004
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Fig. 6. Recording of force applied on the rod as a function of its displacement distance: Roughness R1, 175 N normal force applied on the rod, and 5 mm/s rod displacement speed.
Fig. 7. Shear profiles for the reproducibility tests: Roughness R1, 175 N normal force applied on the rod, and 5 mm/s rod displacement speed.
lution described by oscillations standard deviation for the two rods R1 (4.4%) and R2 (3.8%) are observed. However, the average tangential force value rises for R3 (27 ± 2.9 N) and higher oscillations (7%) with comparison to R1 and R2 are detected. The influence of rod roughness on tangential force has been explained by observing the mechanisms at the vicinity of the beads/rod interface. To simplify the schematic representation of these phenomena, the motion of an individual bead observed through the Plexiglas wall during rod displacement has been studied for each rod. Bead rotation has been highlighted by means of a white bead marked with red1 lines and initially placed near the rod (Fig. 8). Note that the marked bead allows only to describe its rotation by observation under different test conditions but the rotation speed variation can not plotted. For rod R1, in the initial state, each bead in contact with rod notches is positioned inside a hollow space 1 mm deep (Fig. 9a). When a speed is imposed on the rod, the bead systematically crosses both the hollow spaces and notches. The number of hollow spaces and notches crossed by the bead depends on its initial position on the rod. For rod R1, a 250 mm displacement distance corresponds to 25 hollow spaces and 25 notches. During rod displacement, regardless of its initial position, the bead can either move (sliding motion) at the same speed as the rod (Fig. 9b), undergo rotation (Fig. 9c) or cross the notch ridge by simultaneously sliding and rotating motions (Fig. 9d). The examples shown in Figs. 9–12 correspond to beads placed in their initial state near the intermediate column. For rod R2, bead dimension equals the depth of hollow spaces (10 mm). In the initial state, the first beads layer (black beads in
1 For interpretation of color in Fig. 8, the reader is referred to the web version of this article.
Fig. 8. White bead marked in order to observe its rotation.
Fig. 10) lie completely inside the hollow spaces between notches. The (white) beads of the next layer above may adopt a position: in a 1 mm deep hollow space (Fig. 10a), on the notches (Fig. 10b), or on a bead interlocked between two notches (Fig. 10c). As the rod is being displaced, 3 cases may happen. The white bead (in the beads layer lying directly above) may: The nearly identical force evolution for the two rods R1 and R2 may be explained by the fact that the phenomena observed solely on rod R2 and not on R1 are: rod sliding beneath the bead, and bead rotation on the notch. These motions do not generate additional force in comparison of that of R1. In the case of rod R3, an additional mechanism is observed, in comparison with R2, it is the possibility that beads embed within a 2 mm deep hollow space to then extend beyond the bead interlocked in the hollow space of the rod (Fig. 12). Note that this depth may be greater in the medium further from the Plexiglas wall but it cannot be observed.
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Fig. 9. Mechanisms observed on rod R1.
Fig. 10. R2 - Initial configuration.
-
Be immobile, while the rod slides underneath the bead:
-
Rotate on the notches:
-
Become partially interlocked in the rod hollow space and extend beyond the bead interlocked in this space:
Fig. 11. Mechanisms observed on rod R2.
To disengage from a 2 mm deep hollow space, the given bead must push the bead already interlocked inside the rod hollow space. In this case, the white bead applies a force on the notch
ridge and/or the black interlocked bead. The notch then applies the same magnitude of force on the bead (known by reaction force). If the magnitude of the reaction force exceeds the bead’s
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Fig. 12. Mechanism observed on rod R3.
rupture limit, then the bead breaks, which is reflected by a peak within the dynamic regime equals to that of the static value. The tangential force value corresponding to this peak is thus removed from the average tangential force computation. In the case of roughness R3, higher oscillations with comparison with R1 and R2 in tangential force overtime reveal that the phenomena occurring in this case are more complex (crossing of a 2 mm deep hollow space) than those encountered for rods R1 and R2. Broken beads were only observed in the case of rod R3. It is impossible however to observe whether these broken beads indicate blockage at the box exit or obstacles on the rod surface. The various mechanisms observed regarding R1, R2 and R3 show that crossing more challenging obstacles (crossing of a 2 mm deep hollow space) requires a greater force than that needed to overcome multiple obstacles of lesser severity (case of rods R1 and R2). These results are in agreement with our previous study conducted on a discrete modeling of symmetrical shear of a monodisperse granular medium under periodic conditions [23]. In fact, it was demonstrated that for a given normal pressure and imposed displacement speed, the tangential force at the granular medium-rough surface interface depends on the depth of grain interlocking into the surface asperities. This study also found that for an interlocking depth of less than 0.25d (where d is the diameter of grains in the medium), the tangential force increases with interlocking depth. Yet these various observations applicable to spherical grains cannot be transposed to more complex shapes. The tests carried out by Djelal et al. [22] on small plates representing kaolin particles revealed that a rotational plate motion requires more energy to overcome the interparticle friction. Consequently, this rotational motion raises frictional force at the plate-rough wall interface. Moreover, Djelal et al. [22] identified the existence of a minimum friction corresponding to a roughness of the same order of magnitude as the average kaolin particle size. 5.2. Influence of the normal force applied on the rod Fig. 13 shows both the variation in tangential force (a) and number of beads leaving the box (b) as a function of normal force applied on rods R1, R2 and R3. The rod displacement speed has been set at 5 mm/s. During shear, bead movements under the lid prevent this latter from remaining horizontal, thus indicating that the load applied to the granular medium is not uniform. Each point on the curve and each error bar of Fig. 15 represent respectively the average and standard deviation for three measurements. Regardless the rod roughness, tangential force increases with normal force. For a normal force almost 275 N (equivalent normal pressure: 7.5 kPa) due to beads being blocked from leaving the box, the error bar becomes significant relative to the average tangential force value (40% for rod R2, 30% for rod R3). For measurements corresponding to a normal force almost 275 N, the measurements dispersion becomes very wide, hence only values of normal force less than 275 N will be included during results interpretation. For normal forces applied to the rod of below 275 N, results suggest that regardless of the normal force, the tangential force exerted on rod R3 is greater than that exerted on either R1 or R2. However, Fig. 15a shows that the variation in tangential force for rods R1
and R2 does not reveal any significant influence of roughness on tangential force. Fig. 15b shows that the number of beads leaving the box remains independent of the normal force applied on the rod. Note that in the case where no bead is able to become completely interlocked in the hollow spaces (R1), only the first layer of beads is able to leave through the opening. For the other two rough rods (R2 and R3), in addition to this first layer, the beads interlocked in the rod hollow spaces can also exit through the opening. This explains the fact that the number of beads interlocked in the hollow spaces of rod R3 is greater than that of rod R2; consequently, the number of beads leaving the box for rod R3 is higher than that for rod R2. Due to experimental limitations, some parameters cannot be measured during the test. As a case in point, it was mentioned in Section 5.1 above that for roughness R3, it is difficult to observe whether the broken beads are a sign of blocking at the box exit or obstacles at the rod surface. At this stage, it would be worthwhile to verify whether the increase in tangential force for R3 is due to blockage near the opening or bead movements near the notches. Such a hypothesis may be examined by means of numerical modeling. The study conducted on the experimental device can thus be complemented by a numerical study.
6. Numerical modeling of the experimental device The objective of this section is to compute the force being exerted by grains in the medium on the grains simulating the opening, which would allow us to conclude whether or not the opening constitutes a significant artefact. The approach selected herein is the smooth discrete element method (or smooth DEM) [24]. The simulations are performed using the ‘‘DemGCE” numerical computation code developed in-house by the Civil and Environmental Engineering Department at the Douai School of Mines. In this numerical tool, a grain is represented by a sphere with several interaction law models being feasible [23,25–29]. In this paper, Hertz-Mindlin contact laws implemented and tested in [30] are used in order to focus exclusively on interactions existing in dry granular medium.
6.1. Boundary conditions In the experimental device, two types of walls are used: a rough and mobile wall (rod), and four plane and stationary walls (Plexiglass sidewalls). A plane wall is modeled in the DemGCE code by a sphere with infinite radius. The rough wall is simulated by an assembly of spheres bonded to a flat surface (Fig. 14b). The distribution of spheres on the rough wall, along with their diameter and the distance separating two successive spherical assemblies, serves to simulate the rod notches used for purposes of the experimental device. The opening is modeled by another assembly of spheres 2.5 mm in diameter; this diameter was set at the same order of magnitude as the rough wall spheres. The spheres for the opening are positioned 12 mm from the simulated notches so as to comply with the experimental device configuration.
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Fig. 13. Variation in tangential force (a) and number of beads leaving the box (b) vs. normal force applied on rods R1, R2 and R3; Rod speed 5 mm/s.
6.2. Simulation stages In order to fully comply with the experimental protocol adopted, all grains in the granular medium must settle on the rough wall under their own weight. Once grains are settled and in order to confine the granular medium, a normal pressure is applied on its upper surface. Next, the granular medium is sheared by a horizontal displacement at constant speed of the rough wall. (A) Preparation of the confined granular medium The preparation of a granular medium initially involves generating grains within the computed volume. The algorithm used for grains generation is RSA (Random Sequential Addition) [31], which enables preparing a granular stacking similar to that intended for experimentation. Grains are randomly and sequentially generated in the computed volume, without any overlap with the grains already placed. Using this procedure, the packing density of generated grains does not exceed 0.38, in our case a packing density of 0.3 is targeted. The number of grains (6450), their diameter (10 mm) and the volume dimensions (250 mm high, 300 mm long, and 80 mm deep) are all equal to those used in experiments. The micromechanical characteristics of the generated spheres are similar to those of the glass beads used in experimental testing. After randomly placing the required number of grains (6450), the grains are released from their stationary positions and settle onto the rough wall under
Fig. 15. Example of controlling normal pressure (r) on the granular medium: Roughness R1.
their own weight in order to constitute a stable granular stacking with a packing density near that of the experimental one (0.62). In order to confine the medium, a horizontal plane is placed on the upper surface of the granular medium. The normal pressure applied on this medium is controlled by computing the vertical displacement speed (V) to be imposed on the plane (Eq. (2)).
V ¼ sign
r r req a
r rreq min 1;
r
ð2Þ
Fig. 14. (a) Schematic depiction of both the rod notches and opening of the experimental device; (b) DEM numerical modeling of the notches and opening.
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Fig. 16. Displacement of the rough wall: (a) beginning of simulation, and (b) end of simulation (non-confined granular medium).
Table 3 Primary micromechanical parameters used in the simulations. Parameter symbol (unity)
Value
Diameter of grains d (mm) Density of grains q (g/cm3) Young modulus E (Pa) Poisson’s ratio m () Friction coefficient l () Rolling coefficient lr () Damping coefficient A (s1) Restitution coefficient e () Time step Dt (s)
10 mm 2.6 1.0E+8 0.29 0.15 0.002 4.5E5 0.85 1.0 E6
where r is the normal pressure exerted by grains in the medium on the upper plane, r_req the desired normal pressure, and a a constant set equal to 30. Fig. 15 displays an example of the normal pressure r evolution for a desired pressure r_req of 8 kPa. An 8 kPa normal pressure applied on the granular medium is equivalent to an 11.5 kPa normal pressure applied on the rough wall, which accounts for adding the weight of the grains (3.5 kPa). During the experimental tests, the normal pressure is not uniformly distributed along the stacking surface. Indeed, the level of the masses added on the upper surface of the granular medium is influenced by the level of the latter, which does not remain horizontal under the effect of beads leaving through the opening. However, by numerical modeling, the normal pressure may be controlled during the simulation. (B) Displacement of the rough wall Fig. 16 presents an example of modeling the experimental test for rod R2 and for a normal force almost 85 N applied to the rod
(normal pressure: 3.5 kPa). The rough wall is moved by imposing a constant speed in the shear direction on all packets of bonded grains, as well as on the lower plane. The motion of the bonded grains is not determined by resolving the fundamental law of dynamics, as is the case for the other grains in the granular medium. By default, the sidewalls and mobile rough wall have the same material parameters as the grains in the granular medium. The primary micromechanical parameters used in the simulations are listed in Table 3. The values of Young’s modulus and time step were chosen to reduce the computational expense of simulation, while the values of the other parameters were fixed according to parametric study and most used values in the literature for glass beads. 6.3. Comparison between numerical simulations and experiments In this section, the experimental tests are compared to the numerical simulations. Fig. 17 shows the variation of the tangential force as a function of the normal force for the rods R1, R2 and R3. The bars shown on the experimental measurements represent the standard deviation of 5 tests. On one hand, for a given rod roughness, both numerical and experimental measures show that the tangential force increases with increase in the normal force. As well experimental and numerical curves describe similar evolution except for R1 when the normal force increases, the numerical tangential force increases faster than the experimental one and the deviation between numerical and experimental measures becomes greater. On the other hand, regarding the normal force, a deviation of 5 N is found between numerical and experimental measures for rods R2 and R3. This shows that the numerical model is able to represent approximately the tangential force for a given confinement. The obtained deviation can be explained by the fact that the posi-
Fig. 17. Numerical – experimental comparison of the variation of the tangential force as a function of the normal force for rods R1 (a), R2 (b) and R3 (c).
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tion). These results allow concluding that the opening has greater influence with roughness R1 than R2 and R3. These results lead also to the conclusion that the beads broken during experimental testing with roughness R3 do not provide an indication of blockage upon leaving the box.
7. Conclusion
Fig. 18. Evolution in force Fh for rough surfacesR1, R2 and R3: 85 N normal force, and 10 mm/s rough wall displacement speed.
tion of the lid added on the upper surface of the granular medium is influenced by the level of the latter, which does not remain horizontal under the effect of beads leaving through the opening. This means that the confinement is not uniformly applied on the rod. However, by numerical modeling, the normal pressure may be controlled and uniformly applied on the rod during the simulation. In addition the parameters chosen for the simulations which are not calibrated according to the experiments can explain the difference obtained between numerical and experimental measures. However, for experiments conducted under different conditions, it has been highlighted that the tangential force increases with the rod roughness (highest value for R3). On the contrary, numerical simulations show that for a given value of normal force, the tangential force of rod R3 is less than those obtained for R1 and R2. We suppose that this result is due to the fact that the notches (flat surface and acute edge) are modeled by spheres (rough surface and rounded edge). Rough surface has tendency to increase the value of the tangential force while rounded edge has tendency to decrease the latter with comparison to experiments. The overall result depends on which parameter is dominant, and the tangential force can increase or decrease. In general the comparison between experiments and numerical simulations shows a good agreement. Thus, the numerical code is able to give a good indication of the frictional force between the rod and the beads but it is not fully able to capture the specific influence of different types of roughness. 6.4. Evaluation of the force exerted upon the device opening The force Fh exerted on the grains composing the opening is computed in the rough wall displacement direction. Fig. 18 shows the variation in force Fh during the rough wall displacement under the granular medium. In order to reduce computation time, the rough wall displacement speed is set at 10 mm/s. The weight of the grains applies a 85 N normal force on the rough wall. For a higher normal force, the medium becomes more confined, which in turn promotes blockage. The results shown in Fig. 18 highlight that for roughness R3, the 0.15 N average value of force Fh is negligible when compared to the force being exerted on the notches (27 N for experiment and 21 for numerical simulation). However, for roughness R2, force Fh varies quite significantly once the wall has been displaced a distance of 40 mm, to reach a value of 40 N, which is twice that of the tangential force exerted on the notches (21 N for experiment and 26 for numerical simulation). Then, the average value of force Fh becomes negligible (0.3 N) relative to the tangential force exerted on the notches. For roughness R1, the average value of force Fh equals 5 N, which represents almost 20 % of the average tangential force on the notches (22 N for experiment and 26 for numerical simula-
An experimental device has been designed in order to study the influence of roughness on friction at the granular medium-rough wall interface. The trial principle consists of displacing a notched plate under a confined monodisperse granular medium. First, the influence of roughness and normal force on the set of measurable magnitudes is studied. The experimental study, showed that: – Regardless of the rod roughness, the force exerted on the rod in its displacement direction increases with the normal force being applied on it. – The main parameter controlling the frictional force acting between the granular medium and the rod is the beads interlocking depth within the hollow spaces formed by two successive notches. In order to determine at which level of system (Fig. 4) the beads actually broke, the experimental study was complemented by a numerical study using an in-house DEM code. – The comparison between experiments and numerical simulations is quite coherent. – Results revealed that for roughness R3, to the case of major force noticed in the dynamic regime during the experimental test, the force applied by grains in the medium on spheres simulating the opening proves to be negligible compared to the average tangential force exerted by grains on the rod notches. Consequently, the beads that broke during the experimental test with roughness R3 do not provide an indication of blockage at the box opening. In further studies beads failure under mechanical loadings will be conducted to compare this value to the amount of the pic in the dynamic regime. Experiments in more realistic configurations will be performed. Such studies must be carried out on polydisperse granular medium (spherical or angular in shape) and irregular roughness. As well, the device will be improved in such a manner to prevent encountered problems (broken beads) by designing flexible opening and wavy rough wall. Or by moving vertically rough rod into a container full of beads and then the force exerted by the beads on the rod will be measured. References [1] I. Albert, P. Tegzes, B. Kahng, R. Albert, J.G. Sample, M.A. Pfeifer, A.L. Barabasi, T. Vicsek, P. Schiffer, Jamming and fluctuations in granular drag, Phys. Rev. Lett. 84 (2000) 5122. [2] R.M. Nedderman, Statics and Kinematics of Granular Materials, Cambridge University Press, Cambridge, 1992. [3] N. Bell, Y. Yu, P. J. Mucha, Particle-based simulation of granular materials in ACM SIGGRAPH/ Eurographics Symposium on Computer Animation, August 2005. [4] G.D.R. MiDi, On dense granular flows, Eur. Phys. J. E 14 (2004) 341–365. [5] O. Pouliquen, F. Chevoir, Dense flows of dry granular materials, C. R. Acad. Sci. Phys. 3 (2002) 163–175. [6] S. Volpato, P. Canu, A.C. Santomaso, Simulation of free surface granular flows in tumblers, Adv. Powder Technol. 28 (2017) 1028–1037. [7] S.H. Chou, H.J. Hu, S.S. Hsiau, Investigation of friction effect on granular dynamic behavior in a rotating drum, Adv. Powder Technol. 27 (2016) 1912– 1921. [8] K.A. Dahmen, Y. Ben-Zion, J.T. Uhl, A simple analytic theory for the statistics of avalanches in sheared granular materials, Nat. Phys. 7 (2011) 554–557.
Please cite this article in press as: K. El Cheikh et al., Experimental and numerical study of granular medium-rough wall interface friction, Advanced Powder Technology (2017), https://doi.org/10.1016/j.apt.2017.10.020
12
K. El Cheikh et al. / Advanced Powder Technology xxx (2017) xxx–xxx
[9] H. Yang, R. Li, P. Kong, Q.C. Sun, M.J. Biggs, V. Zivkovic, Avalanche dynamics of granular materials under the slumping regime in a rotating drum as revealed by speckle visibility spectroscopy, Phys. Rev. E 91 (April 2015) 042206–42230. [10] P. Wang, L. Zhu, X. Zhu, Flow pattern and normal pressure distribution in flat bottom silo discharged using wall outlet, Powder Technol. 295 (2016) 104– 114. [11] A. Qadir, N.A. Ispalove, A. Ali, R. Chand, M.A. Shah, A. Khan, K. Hussain, Experimental and numerical determination of apparent mass variation of granular media confined in silo geometry, Acta Phys. Polonica A 129 (2016). [12] R. Balevicˇius, R. Kacˇianauskas, V. Vadluga, Investigation of three-dimensional granular stresses in pyramidal container after filling, Mechanika 74 (2008) 1392–11207. [13] O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, sixth ed., Butterworth-Heinemann, 2005, ISBN 0750663200. [14] J.N. Reddy, An Introduction to the Finite Element Method, third ed., McGrawHill, 2006, ISBN 9780071267618. [15] F. Radjai, F. Dubois, Discrete-element modeling of granular materials. London: Wiley-ISTE, 2011, ISBN 978-1-84821-260-2. [16] J.R. Williams, G. Hocking, G.G.W. Mustoe, The Theoretical Basis of the Discrete Element Method. NUMETA 1985, Numerical Methods of Engineering, Theory and Applications. Rotterdam: A.A. Balkema [17] C. Djelal, Y. Vanhove, A. Magnin, Tribological behaviour of self compacting concrete, Cem. Concr. Res. 34 (2004) 821–828. [18] W. Rasband, imageJ. National Institutes of Health, Bethesda MD, USA, imagej. nih.gov/ij/. [19] G.D. Scott, D.M. Kilgour, The density of random close packing of spheres, Br. J. Appl. Phys. (J. Phys. D) 2 (1969). [20] G.D. Scott, Packing of spheres, Nature, Lond 188 (1960) 908–909. [21] A.E.R. Westman, H.R. Hugill, Packing of Particles, Am. Ceram. Soc. 13 (1930) 767–779.
[22] C. Djelal, Designing and perfecting a tribometer for the study of friction of a concentrated clay-water mixture against a metallic surface, Mater. Struct. 34 (1) (2001) 51–58. [23] K. El Cheikh, S. Rémond, P. Pizette, Y. Vanhove, C. Djelal, Discrete Element study of granular material - Bumpy wall interface behavior, Physica A 457 (2016) 526–539. [24] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Géotechnique (1979) 47–65. [25] S. Rémond, DEM simulation of small particles clogging in the packing of large beads, Physica A 389 (2010) 4485–4496. [26] S. Rémond, P. Pizette, A DEM hard-core soft-shell model for the simulation of concrete flow, Cem. Concr. Res. 58 (2014) 169–178. [27] A. Kimbonguila Manounou, S. Rémond, Discrete element modeling of the microstructure of fine particle agglomerates in sheard dilute suspension, Physica A 412 (2014) 66–83. [28] P. Pizette, S. Rémond, DEMGCE Code, Discrete element modeling of Granular materials for Civil Engineering, MINES DOUAI, Civil & Engineering Departement, FRANCE, InterDeposit Digital Number, 2013, IDDN. FR.010.0118996.000.R.A.2013.035.30000. [29] K. Wu, P. Pizette, F. Becquart, S. Rémond, N.E. Abriak, W. Xu, S. Liu, Experimental and numerical study of cylindrical triaxial test on mono-sized glass beads under quasi-static loading condition, Adv. Powder Technol. 28 (2017) 155–166. [30] P. Pizette, S. Rémond, Experimental and numerical studies of the effect of rolling friction for sandpile formation, in: 11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI) July 20–25, 2014, Barcelona, Spain. [31] B. Widom, Random sequential addition of hard spheres to a volume, J. Chem. Phys. 44 (1966) 3888–3894.
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