Force networks and elasticity in granular silos

Abstract

We have made experimental observations of the force networks within a two-dimensional granular silo similar to the classical system of Janssen. Models like that of Janssen predict that pressure within a silo saturates with depth as the result of vertical forces being redirected to the walls of the silo where they can then be carried by friction. We use photoelastic particles to obtain information not available in previous silo experiments --the internal force structure. We directly compare various predictions with the results obtained by averaging ensembles of experimentally obtained force networks. We identify several differences between the mean behavior in our system and that predicted by Janssen-like models: We find that the redirection parameter describing how the force network transfers vertical forces to the walls varies with depth. We find that changes in the preparation of the material can cause the pressure within the silo to either saturate or to continue building with depth. Most strikingly, we observe a nonlinear response to overloads applied to the top of the material in the silo. For larger overloads we observe the previously reported "giant overshoot" effect where overload pressure decays only after an initial increase (G. Ovarlez et al., Phys. Rev. E 67, 060302(R) (2003)). For smaller overloads we find that additional pressure propagates to great depth. Analysis of the differences between the inter-grain contact and force networks suggests that, for our system, when the load and the particle weight are comparable, particle elasticity acts to stabilize the force network, allowing deep propagation. For larger loads, the force network rearranges, resulting in the expected, Janssen-like behavior. Thus, a meso-scale network phenomenon results in an observable nonlinearity in the mean pressure profile.

Behavior of grains in contact with the wall of a silo during the initial instants of a discharge-driven collapse

“…Janssen's saturated stress profile may not be found before the discharge when the system is in a state of undetermined mobilization of friction, but may be produced by fully mobilizing the friction during the preparation of the system or by allowing it to evolve during the discharge. Previously, Wambaugh et al [14] studied the force chains inside a two dimensional silo controlling the initial mobilization and showed that when mobilization at the wall is not uniform, Janssen's screening effect is not produced. From these results regarding the stresses in the silo, even though these where obtained under experimental conditions different from ours, we arrive at the conclusion that in the cases under study in this paper the collapse is triggered by forces on the wall that may not produce a saturating stress profile as would be expected from the classical Janssen model.…”

“…Finally, to monitor the movement of individual grains we use a software, developed using Python package SciPy, that identifies the position of individual grains through each frame of the video using a centroid technique. The image processing is very similar to the one used by Choi et al [8] and Wambaugh et al [18]. We use the observed fluctuations in the position of the grains before the discharge to estimate the uncertainty in their position after the discharge starts (±0.03d).…”

“…This redistribution of the weight of a static granular column to the silo wall produces a screening effect, that allows the pressure in the bottom of the silo to be independent on the height of the granular column when this height exceeds a certain value, called the screening length. This effect was first described by Janssen [11] in 1895 and, more recently, has been the subject of several studies [12,13,14,15,16,17]. In particular, Perge et al [15] studied how the vertical force exerted by static grains on the silo wall increases as the grain-to-wall friction is mobilized.…”

Evolution of grain contacts in a granular sample under creep and stress relaxation

“…A direct consequence of this is the strong local heterogeneity of the stress distribution within the medium [7]. Since Dantu [8] and De Josselin de Jong [9], we already know that the distribution of the contact forces, resulting from an externally applied load, is very inhomogeneous [10,11], as shown in experiments by photoelastic visualization [9,11,12] and via simulations [10,13]. The contact network determines most salient mechanical properties of a dense granular medium such as its ability to bear load, its nonlinear elastic response, and flow behavior.…”

Distribution of static pressure of seeds in a shallow model silo

“…To overcome this discrepancy the Eurocode (EN 1991(EN -4, 2006 recommends using the overpressure factors to raise Janssen pressures to real experimental values. For small depths the profile of wall pressure is nearly linear (Wambaugh et al, 2010) and therefore some design standards (ANSI/ASAE EP446.3, 2013; ANSI/ASAE EP545, 2015) recommend calculating pressures in a shallow silo as the hydrostatic pressure for storage and flowing conditions. Janssen (1895) assumed that the vertical pressure across the radius of the bin is uniform.…”