Packaging of stones

One of the common issues posed in the practice of civil engineering is how to estimate the volume of holes - porous volume - between more or less regular solid particles. Sometimes this hot topic originates long debates with reluctant contractors and picky consultants.
Recently, I have needed to give a number for the spare space in a stone wall like that in the image below. In the project, the interstitial space was required to be filled with cement mortar until certain height to ensure the stability of the base. A bit of mathematics and Wikipedia were useful to justify the necessary amount of the concrete.













Left: Masonry wall in a Roman path somewhere in Germany. Right: Well, needless to say that those are oranges.

The majority of the stones in a wall have similar weight and appearance and, in fact, they are usually defined by a characteristic diameter. If we assume that stones are like oranges -I mean spheres- and that the maximum density of packaging is achieved, the problem can be transformed into the Kepler's conjecture that was proved by Prof. Thomas Hales a decade ago.
It is clear that stones are not spheres -ellipsoids would be a better approximation- but this value of the porosity is close to experiments referred for coarse non-graded gravel in several books. At least, if the on-site engineer asks for the origin of the famous 25% of holes I will have something interesting to say.