optimal stability of binary granular mixtures

when mixtures form steeper slopes than either of its components

Several techniques have been employed to create a steeper pile out of a granular material. The most intuitive idea is to wet a granular medium to make it form a steeper pile.

Imagine experimenting with sand, as you may have done in the beach in the previous summer months. When very little amount of water is used to wet a pile of sand, the pile is still dry, and no significant increase in stability is observed. Add a little more water and the pile significantly becomes steeper; you can now form walls and towers of your sand castle. Upon reaching this point, you don't add more water to the pile; when more water is added, its behavior dominates and the pile is washed away.

In an experiment recently published in the journal Physica A, a team of scientists from the Complex Systems Group of the Instrumentation Physics Laboratory, National Institute of Physics was able to find an analog to such phenomenon of granular material stability; instead of using water, they used another granular medium, but this time of smaller grain sizes than the one in consideration [1]. The team is headed by Christopher Monterola, a pioneer in granular materials research in the country.

Experimental design

A plexi-glass box container with a motor-controlled opening wall carries the granular medium. The medium is mixed well, and upon opening the wall, some of the granular mixtures fall off to the edge. The resulting pile is stable and the angle of its inclination with respect to the floor of the container is taken as a quantitative measure of its stability.

The experimental setup. Click on image for larger view.

The procedure is done multiple times for different granular mixture types and different concentrations of the smaller particle. It was found out that the speed of opening the container does not affect the result much, so it was not included in the parameters under consideration.

The experiment revealed that steepest pile is formed also under optimal conditions: (1) The size difference of the materials is significantly large; (2) The larger grain must occupy about 50-70% of the available volume, and the smaller grain the remaining 30-50%. When these conditions are met, the pile is most stable because the smaller grains fill in the voids between larger grains, supporting its weight and avoiding more slippage, resulting in a pile with a higher angle of inclination.

Some configurations even show vertical slopes, perfect 90-degree regions near the top of the pile. This is not attained for granular-water mixtures, because water, as a liquid, cannot support weight.

Cellular automata (CA) model

The experimental results are further complemented by a lattice model. A 128 by 128 square grid is used as a 2D representation of the granular medium inside the container. By employing a probabilistic slipping rule and a condition for stopping the update, the model resulted in slopes that are similar to the ones observed experimentally.

Even more important is the fact that the CA model captured the vertical slope regions, also near the top of the heap. This is an important advantage of CA over continuum models, because continuum models require infinite coefficients of friction to achieve a 90-degree inclination, which is not realistic.

Implications to large-scale stability

Water content is the primary concern in assessing landslide risk zones such as cliffs and mountain slopes. The study hints to the possibility that the material sizes and their relative concentrations in the medium may be a crucial factor in determining stability of the slopes in these hazard-prone areas.

The group has recently provided evidence that small scale models have similar statistical signatures as empirical landslide surveys [2, see highlight]. The researchers hope that scaled-down approach, such as studies of these kind, could prove useful for studying the complex dynamics of landslide hazards.

1. R.Batac, M.Pastor, M. Arciaga, J. Bantang and C. Monterola, Kinks, logarithmic tails, and super-stability in bi-disperse granular media, Physica A 388, 3072-3082 (2009).
2. D. Juanico, A. Longjas, R. Batac and C. Monterola, Avalanche statistics of driven granular slides in a miniature mound, Geophys. Res. Lett., 35, L19403, doi:10.1029/2008GL035567, 2008.