Determining mortar mix ratios visibly.

Imagine four snooker balls arranged in a pyramid, 3 on the bottom one on top.

There is a small pyramid like gap in the middle of this arrangement. The volume of this gap can be arrived at by some simple geometry – find the volume of the spheres, the volume of a pyramid with sides equal to the distance between the centres of the spheres and subtract the volume of the parts of the spheres that are in this theoretical pyramid. The gap is the bit in the pyramid that the spheres do not occupy. This can be expressed as a percentage or ratio of the total volume of the spheres. Move the spheres apart and this ratio changes. At 2.5 : 1 the spheres are at an optimum distance apart so that the gap between the  four snooker balls is as even as it can be.

Repeating the pattern of four balls to create say a room full of snooker balls with this spacing maintained will result in a matrix of space within the balls that is as consistent in thickness as it can be, fill this with a binder like calcium hydroxide and you achieve a mortar that is a compromise between strength and economical use of binder. Increase the lime and the tendency to shrink is increased.

Of course we don’t use snooker balls, and we don’t like sands that are uniform in shape or size. But the same pattern can be used in my model by reducing the size of the balls, so lets introduce some marbles arranged in the same way and some footballs as well and we see that the matrix is maintained but the now groups of spheres can fit in that gap between the four balls we first mentioned. This then creates an even more regular matrix and thereby reduces further the tendency to shrink.

The finer the sand, as we all know, the greater the shrinkage, this is because there is less opportunity for there to be groups of sand grains between other larger grains – all the grains of sand are much closer in size.

By using geometry it is shown that two and a half parts sand to 1 part calcium hydroxide makes a good mix for course stuff.

A visual inspection of a section of mortar, therefore, can be used to determine the probable mix ratio of the mortar simply by measuring the distance between the grains of aggregate.

Q. Why does fine sand require more lime?

A. Because the surface area is greater.

This can be easily illustrated by a box of OXO cubes. If you paint the box you will need x amount of paint. If you paint all the OXO cubes as well you will need more paint!

Therefore the smaller the sand grains the more lime is required. Now if we return to the snooker balls that I mentioned at the start and imagine they represent say silver sand or, in fact, finishing plaster (fine stuff). It is known that there is a concentration of lime at the gap between the four balls. But, whereas, I introduced smaller and larger balls to inhabit each others ‘gaps’ now I can’t. This now introduces a possibility of shrinkage occurring – as the water in the lime evaporates the binder shrinks and pulls groups of grains apart creating cracks in the plaster. It is interesting to ponder why the cracks occur just where they do, is it random or the result of a weakness of some sort within the plaster?

By using very thin coats and floating or scouring the surface of the plaster we reduce the incidence of cracking.

But why does any of this matter? Well, by understanding why we use say 3 to 1 we can make adjustments to suit the situation, understand failures, and create mortars that are targeted at the job in hand.