The inaccuracies involved in proportioning cement to sand by determining the voids in the sand is explained in Art. 7. When determinist, the ratio of fine to coarse aggregates by the method of voids, it is usual to proportion cement to sand by adopting an arbitrary ratio between the two, although some users of concrete have used the void method for this purpose also.
75. Proportioning by Mechanical Analysis Curves.—Mr. William B. Fuller I has devised a method of proportioning concrete by plot ting the curves of mechanical analysis of the aggregates to be used, then combining them in such proportions as to give a curve which corresponds as nearly as possible with a certain ideal curve. This ideal curve is supposed to represent the combination of sizes which will give maximum density for the given materials.
Mechanical Analysis Curve.—The method of plotting the curves of mechanical analysis is shown in Fig. 44. The analyses are made by the method outlined in Section 72. In the Curves, the ordinates represent p.reentages of the samples (by weight) which pass through openings whose sizes are shown by their distances from the origin. Fig. 44 shows a sample of stone and one of sand which are to be used in forming concrete.
From these curves, others may be drawn showing the grading of sizes in various combinations of cement, sand, and stone. Thus for the 1 : 3 : 6 concrete, we will have percentages passing openings as follows: This curve, corresponding to 10 per cent cement, 30 per cent sand, and 60 per cent stone, is shown on the diagram, as is the curve for l : 2 1 : 6 concrete.
The ideal curve is found by sifting the stone and sand into a number of sizes, and then recombining these sizes in varying pro portions and comparing the results, until the condition of maximum density is obtained. In an extended series of experiments, Messrs. William B. Fuller and Sanford E. Thompson t found that the curve of most desirable grading of materials was a smooth curve, consist ing of an ellipse at the fine end with a straight line tangent to the ellipse and passing through the point where 100 per cent is reached. The materials tested in these experiments consisted of broken stone, gravel, and sand used in the construction of the Jerome Park Reser voir, at New York. The equation for the ellipse as determined
from these experiments is x and y being the horizontal and vertical coordinates of points on the ellipse measured from the origin of the diagram.
The values of a and b vary for the different materials and are as follows: D in the above formulas is the maximum diameter of the coarse • aggregate.
To use this method of proportioning rt is first necessary to determine the ideal curve. Sufficient data are not available to indicate whether the formulas given above are generally represent ative of broken stone and gravel respectively. To determine the curve in a particular case, the sand and stone should each be sifted into about three sizes. A trial curve may then be assumed and the materials mixed in proportions to agree with the curve and the density of the. mixture tested. Curves above and below the first one can be tried until an approximate density is located.
76. Proportioning by Trial.—The simplest and usually the most accurate way of determining the ratios of quantities of materials for concrete is that of mixing batches in different proportions and comparing the densities of the resulting concrete. The object should be to secure the mixture of aggregates which will give the greatest density when mixed with the cement and water.
For making these tests, it is convenient to use a cylindrical measure S or 10 inches in diameter and 12 or 15 inches high. A batch of concrete is mixed in assumed proportions to the consistency to be used in the work, and the height to which it fills the cylindrical measure is noted. Other batches are then prepared with the same total weight of materials, but differing in proportions of aggregates, and measured in the same manner. The greatest density is that which occupies the least volume for the same weight. It is necessary to use a uniform method of filling the cylinders, and is usually desir able to compact the concrete by light ramming in rather thin layers to prevent voids being left where the concrete is in contact with the surface of the cylinder.