Grading is the science of particle size distribution and packing density.

Grading is used in civil engineering in concrete technology, soil compaction and road construction.   In refractories , grading is used to find the optimal density of materials, and also to provide specific rheology or flow properties of materials.   Different particle size distributions are required for  different placement methods, for example; vibration casting, pouring, gunning, plastering, pressing, plastic placement, pumping etc.   

The theory of grading starts with the mathematics of packing spheres of a particular diameter so that they touch each other and then filling the spaces between them with smaller spheres and filling the resulting voids with still smaller spheres and so on ad infinite until you approach a solid mass.   This theory, developed by Fuller, can be illustrated on a log-normal distribution curve, but in practice it does not yield the highest density.   This is because, firstly, we cannot get the spheres to find their exact best positions in the structure.  Secondly, refractories are not made out of spheres.   Bolomey developed a more practical curve which gave better results.    The author added a modification to accommodate grain shape and proudly called it the “Onderstall curve” until one of his colleagues (I think it was Tony Bubb) showed him the identical formulation published ten years earlier by an Australian named Hughan.   The next problem arising is that the specific gravities of the particles varies from mineral to mineral.   Strictly speaking, one should work with the volume, not the mass of the particles, if the formulation contains different minerals.   Concrete technologists think refractories technologists are crazy to use mass percent instead of volume percent, and they are correct from their perspective.   If you design an insulation material containing perlite or vermiculite and alumina and you fail to take into the difference in density of the components, you will get a disastrous result.

The author in his youth wasted a lot of time designing materials for their ultimate densities, but found that his super dense mixes were totally impractical, because they spalled, suffered from steam explosions and drying problems and spherical particles do not yield high cold crushing strengths.   If you want good thermal shock resistance, it has been shown that deliberate deviation from the ideal packing curve is needed.

Paul Rothenbuehler told me about a gunning mix grading which contained a fairly fine material but a small percentage of 20mm diameter tabular alumina convertor discharge balls.   The “CD balls” had nothing to do with packing density at all, their function was to clear obstructions in the gunniting hose.   

Now that I have trashed the theory of grading, why bother with it?   I have found it very useful in designing the fines.   Use only materials of which of the supplier can give a reliable particle size distribution and by packing them well you get good results.   Dirk Kotze taught me to develop “from the bottom upwards”.   Start with your water, add your finest component until saturated, then the next finest etc.   For dense ceramic slips this is magic.   For refractories, don’t get carried away with gradings on the coarse end, I only work to the nearest  5%, and suspect that even that is too accurate.   Spend your efforts on the fines, work all the way to the sub-micron level.   Remember that the densest is not necessarily the best.   One application of grading is to get the same properties of a formulation using a different mineral composition.    An important application is to utilize an off spec. raw material to adjust the percentages in your formulation to get the original grading.   30 years ago “fines” were lumped together below 200 micron size.   Today we have very sophisticated ultrafines which must be engineered into your grading.   Fitting cements into a theoretical grading has always been a nightmare.   The particles dissolve and shrink during placement, and sometimes we see the rheology changing as time progresses.   You cannot cater for this in mix design.   Of course there are chemical effects and particle attractions and repulsions which have a dramatic effect on rheology, which are not related to grading.

In specifying grading for quality control, the gradings must be cumulative.  A grading spec. which reads “-6 +4mm = 5-15%, -4+2mm = 10-20%, -2+1mm = 15-25%, -1+0,5mm = 20-30% etc. all the way down looks pretty sophisticated, but actually generates a grading envelope very wide.   It is a “spec. that you can drive a bus through.”   A two point cumulative spec. such as “+1mm = 40-50% and -50micron = 20–30% is a far tighter control, with much less work in testing.

Illustration;  log cumulative curve showing Fuller curve, Bolomey curve, Hughan curve, two types of grading spec.

Back in the “good old days” of Cullinan refractories boom time, Jean Taylor was looking for a way to improve the performance of “CLD” periclase bricks.   She found a paper showing that periclase refractories with a fine pore size distribution gave better performance.   She asked me to make bricks with systematically varied gradings, fire them and examine pore size distributions.   The best fired results were obtained from a fine grading fired at 1600C, better than those fired at 1700C.   I put it down to experimental error, but, being a better scientist than me, Jean insisted I find out why these samples were better.   I spent days investigating them under a microscope, and eventually recognized a pattern.   The coarse pores had 3 origins; cracking, parting and packing.   Cracking was the actual breaking of the coarse grains during pressing, parting was the sintering of the matrix away from the aggregate, because there was not enough matrix.  Packing was the pores left as a result of incorrect grading.   The best bricks had enough fines to overcome these three problems.   These very fine bricks did not give the best “Pressing factor”, which is the density of the green bricks out of the press.   Unfortunately I left Cullinan before I could implement the changes to CLD and similar products.   I hope somebody somewhere can make use of this discovery.