This method is very valuable £1.9 an easy and practicable means of determining the best proportions in which to combine natural mixtures of a sand and an aggregate; but it is impracticable for an exhaustive study to find the very best proportions attainable by screening the sand and the stone and making artificial combinations of the several portions. The only practical method of determining the best possible artificial mixtures of sand and stone is by the use of sieve-analysis curves (Q 302-307).
"The objects of sieve-analysis curves as applied to concrete aggregates are: (1) to show graphically the sizes and relative sizes of the particles; (2) to indicate what sized particles are needed to make the aggregate more nearly perfect, and so to enable the engineer to improve it by the addition or substitution of another material; and (3) to afford means for determining the best proportions of different aggregates." * "The experience which the writer [Fuller] has had and the various experiments which he has made indicate that concrete which works the smoothest in placing and gives the highest breaking strength for a given percentage of cement, is made from an aggregate whose sieve analysis, taken after mixing the sand and the stone, forms a curve approaching a parabola having its beginning at the zero of co ordinates and passing through the intersection of the curve of the coarsest stone with the 100 per cent line, that is, passing through the upper end of the coarsest stone curve."t In Fig. 12, the parabola OCPA represents a theoretically perfect combination of sizes of that particular sand and crusher-run stone. This curve shows, for example, that for the best combination of the above materials 93 per cent of the mixture should pass the 11-inch sieve, 76 per cent should pass the 1-inch sieve, 54 per cent the i-inch, and so on.
"Where, as in Fig. 12, the materials to be mixed are represented by only two curves no combination of which will make a curve as close to a parabola as is desirable, there is another limiting condition which was brought out by the experiments, viz., that for the best
results the combined curve shall intersect the parabola on the 40 per cent line, at C, and that the finer material shall be assumed to include the cement."$ The curve DBKLA, Fig. 12, may be transformed so that it will pass through C, by changing the distances from the top of the diagram to the line DBKLA in the proportion EC = 60 _ 61 per cent, FB 98 which shows that 61 per cent of the dry materials should be broken stone. In a similar manner the line OF is replotted in the position OJ. The line OJCGA is. assumed to represent the best possible combination of sizes of this sand and stone. For example, with the best possible combination of sizes of this stone and sand, 89 per cent would pass the 1.50-inch sieve, 67 per cent would pass the 1-inch sieve, 46 per cent_the i-inch sieve, and so on.
The proportion of cement to be used to give the required strength of concrete must always be assumed; and in this example it will be assumed that the cement is to constitute one eighth of the dry mate rials (measured before the sand and stone are mixed together), which will make the cement one ninth or 11 per cent of the total dry mate rials. Since the diagram shows that the sand and cement are to con stitute 39 per cent of the dry materials, the sand must then be 39 11= 28 per cent.
The proportions of concrete for 1 part cement to 8 parts of sand and stone, measured separately, then are: 11 per cent cement, 28 per cent sand, and 61 per cent broken stone, or 1 : 2.5 : 5.5 by weight. If the proportions are required by volume and the relative weights of the sand and the stone differ from their relative volumes, the pro portions should be corrected accordingly.
An important feature of the sieve-analysis curves is that they show how the materials may be improved by 'adding or sub tracting some particular size. For example, if the stone represented by the curve DBKLA in Fig. 12 had contained more pieces 0.5 and 1.0 inch in diameter, its curve would have more nearly approached the parabola in the region SG. If a stone giving the line DRHA were used, the ratio for transforming the line to make it pass through C would be 91 EC = 91 =66 per cent, which shows that with the assort ment of sizes of broken stone represented by this line the best con crete is made by using 66 per cent of broken stone. For a 1 : 8 mixture as before, the proportions would be 11 : 23 : 56, or 1 : 2 : 6, —a cheaper, stronger, and denser concrete than that made with the stone represented by the line DBKLA.