Sand Heap Research Articles

Fundamental study on the effect of grain size distribution on angle of repose

In this study, the authors developed a new sidewall velocity-controlled cylindrical angle of repose measurement apparatus that can capture images of a sand heap continuously using two orthogonal cameras in order to reduce the cost of photography. The developed apparatus was used to measure the angle from formation to repose of sand heap using different grain sizes distribution and to assess the effect of grain size distribution on the angle of repose. The formation process of the sand heap was continuously measured using the experimental apparatus, and it was found that the sand heap became steady state when it reached a certain height. It is inferred that the angle of repose measured in a stationary state indicates the inclination angle of the sand heap at a certain point in time, suggesting the possibility of obtaining a highly accurate angle of repose with fewer experiments by using this experimental apparatus to continuously acquire and average the inclination angle of a sand heap in a steady state. For samples with a stepped grain size distribution, the angle of repose was found to be higher than for samples with a gentle grain size distribution at the same 20% grain size D20 and mean grain size D50. It was found that the angle of repose increased logarithmically with increasing coefficient of uniformity. Based on these results, it is clear that for a well-graded sand, it is the grain size rather than the coefficient of uniformity that has an effect on the angle of repose.

Numerical investigation of sand sliding methods for hydro-morphodynamic modelling

In numerical modelling of scour around riverine and coastal structures using a hydro-morphodynamic model, a discrete sand sliding procedure needs to be implemented to avoid the occurrence of unrealistic bed profiles. In this study, two commonly employed sand sliding techniques, namely, the artificial transport rate method (ATRM) and the geometry-based method (GBM), are implemented in OpenFOAM and their performances are evaluated for five three-dimensional test cases. The test cases are classified into cases with and without sediment transport induced by a flow field. In the first three test cases, in the absence of a flow field, sand heap avalanches for different geometries and bed boundary grid structures are modelled to compare the methods in terms of simulation time and mass continuity. In test cases 4 and 5, in the presence of a flow field, the sensitivity of the sand sliding methods coupled with a hydro-morphodynamic model to different bed mesh structures is evaluated in modelling scour. The results of the analysis demonstrate that modelling of the sand sliding procedure using ATRM requires higher computational time, while its results are highly independent of the bed mesh structure with lower mass continuity error, <0.2% in all test cases, in comparison with GBM.

Continuous to intermittent flows in growing granular heaps.

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

A MIMO Radar System based on Fractal Antenna Arrays for Level Measurement Applications

Abstract. In this contribution, the design of a multiple-input multiple-output (MIMO) radar system in 77–81 GHz range with 18 transmitting antennas and 24 receiving antennas for measuring the height profile of bulk solids in silos, is presented and discussed. The antenna array topologies are optimized by utilizing space filling fractals in order to approximate a circular shaped antenna array on a hexagonal grid. The proposed MIMO radar system achieves an angular resolution of 3.1∘ for a maximum scanning angle of ±45∘ and a side lobe suppression of 12.6 dB. The performance of the system has been evaluated by test measurements on a sand heap, showing an improved measurement accuracy compared to conventional radar level systems.

Cellular automata modeling of rockfill dam failure caused by overtopping or any other extreme throughflow

A cellular automaton for the study of the progressive failure of rockfill dams caused by overtopping flows is presented. The celebrated Bak, Tang and Wiesenfeld’s model, proposed in 1987 to reproduce sand avalanches on the surface of a sand heap is adapted to a rockfill dam with an impervious central core that is subjected to extreme throughflow caused by overtopping flow or by failure of the watertightness of the core, or the dam foundation. The downstream rockfill shoulder is represented by a set of cells whose states (elevation and submergence) evolve according to a set of fixed transition rules. These rules, which are affected by the instantaneous throughflow, are based on widely used hydraulic and geotechnical approaches to mass sliding and particle dragging mechanisms. The CA model has been validated with laboratory experiments performed on a U-shaped channel. Albeit the apparent simplicity of the underlying formulation, this model not only sheds light on a complex phenomenon but also provides a way for quantifying the overtopping throughflow needed to threaten the central core or upstream face, which can lead to a catastrophic failure.

Copying nesting attempts in a new site may be the wrong choice. A case in the European Bee-eater (<em>Merops apiaster</em>)

Insistent nesting attempts by a group of European Beeeaters in a new site, a pebbly bank of the middle course of Trebbia River, northern Italy, mostly failed because of the unmovable pebbles encountered during tunnel excavation. The birds later nested in an artificial sand heap, with full success that time. Various considerations suggest that birds insisted in the unsuitable site because they copied the nesting activity of model conspecifics. Finding social attraction and “public information” from conspecifics in a place where no breeding attempt was previously made would allow disentangling social philopatry from spatial philopatry.

Plastic behaviors of asymmetric prismatic sand heaps on the verge of failure

The geometric properties accompanying a priori stress conditions determine the physical behaviors of a sand heap. In this study, the incipient failure solution, obeying the Mohr-Coulomb criterion, was successfully applied to an asymmetric planar sand heap under active condition. The shooting technique, based on the 5th order Runge-Kutta method in association with Brent's method, was put in place. Moreover, Sokolovskii's theory of active planar heaps was extended to facilitate the numerical stress solution by refining the boundary conditions. The new integration scheme was handled with appropriate numerical perturbations to cope with the singularity problem. Regarding the experimental validation, the active condition in an asymmetric prismatic sand heap was experimentally triggered by seismic loading. The results revealed that the distribution of vertical stress was uneven before shaking; however, the vertical stress conformed to the theory after the first period of shaking. Furthermore, the deformation threshold of the limit equilibrium state was also revealed. On the other hand, the trajectory of the major principal stress characterizing the load transfer mechanism in an asymmetric planar heap were seen to be different from those in a symmetric planar heap.

Study on the Establishment and Optimization of Sandcastle Infrastructure Model

Sand castle was created by the tourists on the beach for fun, then how to set up a stable sand castle under the condition of waves and tidal waves to get the honor of “sandcastles builder” has been their main concern. In this paper, considering the formation principle of sandcastle and the effect of the uncertain factors and the effect on the stability of the sand castle, the sandcastle infrastructure model is established and the 3D geometric model of the sand pile is optimized step by step. We start with sand heap discretization, the impact process of waves and tides is regarded as the external force acting on the sand, and the stress analysis shows that there are three kinds of stress conditions: no external force, one external force and two external forces. Then from the point to surface, the stress energy of the whole layer of sand is analyzed according to the two aspects of energy transfer dissipation and internal force failure dissipation. The optimal bearing capacity plane is approximately pentagon by annealing algorithm. Finally, from the surface to the solid, taking the self-weight of the sand pile, the effective external force action and the seawater erosion action as the constraint conditions, the optimal tilt angle of the plane stack is calculated to be 36.87° by measuring the risk degree of the overlaying slope Angle. Therefore, the oblique pentagonal body with an inclination angle of 36.87° is relatively stable.

Experimental realization of incipient active failure in sand heap by seismic loading

Sand heaps avalanche when a static angle of repose is exceeded, and freeze at a dynamic angle of repose. The stress distribution in a planar sand heap stabilized at the angle of repose with an incipient active failure condition, by which the material is on the verge of failure everywhere, was examined. At the time of construction, the vertical pressure was initially not in the incipient failure. A slight amount of seismic loading using the sinusoidal motions of a shaking table was set up with just enough energy to rearrange the sand particles, to erase the formation history, and to fluctuate local density inside a sand heap without an excessive loss of mass. During the experiments, laser displacement sensors and pressure gauges were employed to monitor the vertical displacements above and the vertical pressures below the sand heap respectively. The non-linear differential equations, characterizing the stress distribution in an active sand heap, were formulated under the Mohr–Coulomb failure criterion and numerically solved by the Newton method. Bulk solids started flowing after the state of incipient failure; therefore, the experimental vertical pressure profiles were found to gradually conform to the theoretical vertical pressure profiles if the sand heap was subjected to sufficient excitation.

The Generalized Coefficients of Earth Pressure: A Unified Approach

This paper offers an extension of Cauchy’s first law of motion to deformable bodies with internal resistance with application to earth pressures. In this respect, a unified continuum mechanics approach for deriving earth pressure coefficients for all soil states, applicable to cohesive-frictional soils and both horizontal and vertical pseudo-static conditions is proposed. Adopting Jaky’s (1944) sand heap hypothesis, modified suitably to accommodate the needs of the present research, the analysis led to generalized, yet remarkably simple in form, expressions for the “at rest”, active and passive earth pressure coefficients. The validity of the proposed coefficients is strongly supported by the fact that, under static conditions they are transformed into the well-known Rankine’s expressions for cohesive-frictional soils for the active and passive state. Comparisons with widely used solutions (e.g., Rankine’s and Mononobe–Okabe’s), design code practices (Eurocode 8-5; AASHTO), and results from centrifuge tests further support the validity of the proposed coefficients. In the framework of the present work, analytical expressions for the calculation of the depth of neutral zone in the state “at rest”, the depth of tension crack in the active state, the required wall movement for the mobilization of the active or passive state, as well as the mobilized shear strength of soil (for all states) are also given. Finally, following the proposed approach, the earth pressure can be calculated for any intermediate state between the state “at rest” and the active or passive state when the allowable wall movement is known.

Stress distribution in conical sand heaps at incipient failure under active and passive conditions

Stress discontinuity plays an important role in both planar and conical heaps of granular materials. The aim of this study is to reveal the numerical solutions for the stress distribution in fully plastic conical sand heaps that obey the Mohr-Coulomb yield criterion under both passive and active conditions. Levy's circumferential stress assumption was added to the system of equilibrium equations to formulate a pair of ordinary differential equations that were integrated by the 5th order adaptive Runge–Kutta method. Moreover, the numerical perturbations of the initial conditions were put in place to overcome the singularities of the integrations. Trial-and-error iterations were implemented under the passive condition to indicate the location of the stress discontinuity in conjunction with the application of the stress jump condition. Meanwhile, the shooting technique was employed to facilitate the integration under the active condition. The results of the passive conical sand heaps exhibit a local minimum pressure at the center, thus initiating arch action. In addition, the trajectories of principal stresses visually elucidate the mechanisms of load transfer in the conical sand heaps. The linear-fitting relationship between the location of the stress discontinuity and the repose angle in a conical sand heap under the passive condition was also elaborated.

Experimental Investigation on the Bearing Capacity of Cold-Formed Thin-Walled Steel-OSB Composite Floor

An experiment was performed about the bearing capacity of cold-formed thin-walled steel-OSB composite floor by the sand heap. The strain and deflection response of OSB board and steel beam is analyzed under the load; then the test process is simulated by ANSYS, the results of simulation are agreed with the experiment basically. Through the analysis of experiment and finite element simulation, the results indicate that the composite floor has enough bearing capacity and meets the requirement of the residential building completely.

Geometric effect of angle of repose revisited

We report on a universal pattern observed in the collapse dynamics of a sand heap. Collapse dynamics of a three-dimensional sand heap were studied through experiments and numerical simulations. A phenomenological law that describes the shape of a collapsed sand heap was found, we call this the geometric constitutive law of friction. The law is summarized as the linear relation between the frictional coefficient and the local horizontal curvature.

Coupled CFD–DEM simulation of fluid–particle interaction in geomechanics

This paper presents a coupled Computational Fluid Dynamics and Discrete Element Method (CFD–DEM) approach to simulate the behaviour of fluid–particle interaction for applications relevant to mining and geotechnical engineering. DEM is employed to model the granular particle system, whilst the CFD is used to simulate the fluid flow by solving the locally averaged Navier–Stokes equation. The particle–fluid interaction is considered by exchanging such interaction forces as drag force and buoyancy force between the DEM and the CFD computations. The coupled CFD–DEM tool is first benchmarked by two classic geomechanics problems where analytical solutions are available, and is then employed to investigate the characteristics of sand heap formed in water through hopper flow. The influence of fluid–particle interaction on the behaviour of granular media is well captured in all the simulated problems. It is shown in particular that a sand pile formed in water is more homogeneous in terms of void ratio, contact force and fabric anisotropy. The central pressure dip of vertical stress profile at the base of sandpile is moderately reduced, as compared to the dry case. The effects of rolling resistance and polydispersity in conjunction with the presence of water on the formation of sandpile are also discussed.

Numerical modeling of fluid-particle interaction in granular media

Fluid-particle interaction underpins important behavior of granular media. Particle-scale simulation may help to provide key microscopic information governing the interaction and offer better understanding of granular media as a whole. This paper presents a coupled computational fluid dynamics and discrete element method (CFD-DEM) approach for this purpose. The granular particle system is modeled by DEM, while the fluid flow is simulated by solving the locally averaged Navier–Stokes equation with CFD. The coupling is considered by exchanging such interaction forces as drag force and buoyancy force between the DEM and CFD. The approach is benchmarked by two classic geomechanics problems for which analytical solutions are available, and is further applied to the prediction of sand heap formation in water through hopper flow. It is demonstrated that the key characteristic of granular materials interacting with pore water can be successfully captured by the proposed method.

Percolation, self-organized criticality, and electrical instability in carbon nanostructures

The processes of avalanche formation, percolation, and electrical instability have been investigated experimentally using multi-walled and single-walled carbon nanotubes as an example. The performed investigations are based on the comparison of electrical conductivity dynamics in classical experiments, such as the “sand heap,” the two-dimensional grid of resistances with a stochastic node blocking, and the nanosecond percolation in a mode of electrical instability in nanotube tangles/granules. The regularities of mechanisms are revealed and the general concept is formulated.

Mathematical modelling of bottom evolution by particle deposition and resuspension

A two-dimensional numerical model for the evolution of a bottom due to particle deposition and resuspension by a fluid flow is here presented. A computational fluid dynamic approach is used to calculate the flow field and a Lagrangian particle tracking technique is applied to solve the dispersed phase. The evolution of the lower boundary is simulated taking into account the mass conservation of the solid phase and the geotechnical properties of the granular material. The model is characterized by two important features. First, fluid dynamics are coupled with the bottom evolution due to particle deposition and resuspension. This permits to use the model to simulate complex flow fields as well as complex time-evolving geometries. Second, the dispersed phase is calculated by a Lagrangian approach, which retains the discrete information of the individual particles of the granular bottom which may be of interest for some industrial processes (coating) and environmental flows (sediment stratification). First consistency checks have been performed for some deposition and resuspension test cases with fluid at rest. The model has also been tested by comparison with a physical experiment of deposition inside a cavity. Finally, as an example of possible applications of industrial and environmental interest, the model has been applied to investigate particle deposition in rectangular cavities and the evolution of a sand heap by a fluid flow.

Statics of loose triangular embankment under Nadai’s sand hill analogy

In structural mechanics, Nadai’s sand hill analogy is the interpretation of an ultimate torque applied to a given structural member with a magnitude that is analogously twice the volume of stable sand heap which can be accommodated on a transverse cross-section basis. Nadai’s analogy is accompanied by his observation of a loose triangular embankment, based on the fact that gravitating loose earth is stable if inclined just under the angle of repose. However, Nadai’s analysis of stress distribution in a planar sand heap was found to be inaccurate because the total pressure obtained from Nadai’s solution is greater than the self-weight calculated from the heap geometry. This raises a question about the validity of his observation in relation to the analogy. To confirm his criterion, this article presents and corrects the error found in Nadai’s solution by analyzing a radially symmetric stress field for a wedge-shaped sand heap with the purpose of satisfying both force balance and Nadai's closure. The fundamental equation was obtained by letting the friction state vary as a function of angular position and deduce it under the constraint that the principal stress orientation obeys Nadai's closure. The theoretical solution sufficiently agreed with the past experimental measurements.

Formation and transport of a sand heap in an inclined and vertically vibrated container

We investigate experimentally the formation and the transportation of a heap formed by granular materials in an inclined and vertically vibrated container. We observe how the transport velocity of heap up the container is related to the driving acceleration, the driving frequency, and the inclination of the container. An empirical law which governs the transport velocity of the heap is presented. An analogous experiment was performed with a heap-shaped Plexiglas block. We propose that the compressive force resulted from pressure gradient in ambient gas plays a crucial role in enhancing and maintaining a heap, and the ratchet effect causes the movement of the heap.

Ticking hour glasses: Experimental analysis of intermittent flow.

Fluctuations in the flow of sand in an hour glass have been investigated experimentally for the case when the interaction between grains and interstitial air is important. During the active phase of the flow, a plug is formed at the narrowest constriction of the hour glass. The plug is below the free-fall arch defining the lower ``edge'' of the sand heap in the upper chamber. The low-density region between the plug and the arch defines what we call a ``bubble.'' Early during the active (flow) phase, the position of the bubble is stationary, whereas later, it rises into the bulk of the sand and disappears. The position of the arch thus oscillates with a shorter period than the one associated with the active-inactive phase oscillation. \textcopyright{} 1996 The American Physical Society.