If we consider concrete, the main ingredient is aggregate: rocks, stones and sand. I briefly discussed this here on this blog.
Of real importance is the particle size distribution in the aggregate mix. The goal in good concrete is to get a complete space filling by using different sized particles.Aggregate (stones, rocks and sand) is generally not spherical, but has a longer dimension and a shorter dimension. This results in a “tip” which is located at the ends of the longer dimension, and a “face” which is located at the end of the shorter dimension. One of the keys to good concrete is tip-to-face contact between larger aggregate.
One of the other keys to good concrete is that the gaps between large aggregate are filled with smaller aggregate, so that there are not empty spaces, or gaps, or interstitial sites between aggregate. This is what is meant by “space filling.”
There is a field of science which concerns itself with space filling between particles. My own exposure to this science came in studying ceramics, wherein scientists are typically looking at very small particles. One of the insights into space-filling came about in 1930, and was proposed by two scientists (A.E.R. Westman and H.R. Hugill) who worked together to develop a diagram which represented space filling as a percentage of volume based on different sized particles, and is known as a Westman-Hugill diagram.
Here is a quote from an abstract of their paper “The Packing of Particles” published by the Journal of the American Ceramic Society, June 12, 1930: “It is axiomatic that the mode of packing of very large volumes of particles of uniform shape and size is independent of the size of the particles, provided they are large enough for the effect of electrostatic forces, air films, etc., to be negligible. An apparatus is described, in which equal true volumes of approximately spherical particles, ranging in diameter from 0.2 to 0.0035 inch, pack practically to the same apparent volume. This apparatus was used in studying the packing of mixtures of two and three sues of particles. By plotting the data so obtained in diagrams of a particularly convenient character, it is shown that the apparent volumes of mixtures containing unit real volume of solid fall between limiting values which can be calculated from simple assumptions, and that their deviation from these limits depends in a definite manner upon the diameter ratios of the component particles. The conditions governing the application of the results of the study to ceramic technology are pointed out.”
While Westman and Hugill were considering spherical particles for their model, the basic ideas hold for irregular shapes, which is what one encounters in concrete mix.
Here is what I find interesting about this whole concept. If you go outside and scoop up a shovel full of rocky, sandy mix (not soil, but aggregate, such as one finds in a stream or creek bed) then the mix is very close to the ideal particle size distribution one would design if starting from “scratch.”
I find this incredible! Nature has provided us with a close to ideal particle size distribution for very good concrete. Almost everyone fails to appreciate this fact. Everything we make from concrete would be much more difficult to make if this were not the case. If we lived in a world of only tiny sand, we would be making large rocks to provide large aggregate. If we lived in a world of only large rocks, we would be making sand (at a huge cost of time and energy). As it is, nature has provided us with a very close to ideal concrete mix in terms of aggregate particle size distribution.
There is a commercial brand of concrete known as “quikcrete” which is sold in dry bags. Friends of mine who are aware that a creek bed provides an ideal mix of aggregate particle size also live in the country, where a creek is known as a “crick”. They call their homemade concrete “crickcrete” and chuckle and guffaw like country bumpkins.
So grab a shovel, head to the creek and make some of nature’s own crickcrete.