The voids in Table 27 are for the wet concrete. As the concrete dries out the air-filled voids will increase, since all the water employed in making the concrete does not enter into chemical combination with the cement (g 365); and consequently when the concrete has dried out the space occupied by the free water will be filled with air.
The details of the method of determining the relative quan tities of the several ingredients will be illustrated by the following example. Assume the aggregate to be broken stone, unscreened except to remove the dust, containing 33 per cent of voids when loose and 28 when rammed (see No. 10, Table 20, page 99). Also assume that the sand has 45 per cent of voids when measured loose and 37 when rammed. Further assume that a concrete of maximum density is desired; and that therefore the mortar should be equal to about 140 per cent of the voids (see Table 27).
To determine the reduction in volume by ramming the broken stone, use the relation: the solid material in 1 cu. yd. of rammed stone is to the volume of 1 cu. yd. of rammed stone as the solid material in 1 cu. yd. of loose stone is to the equivalent volume of rammed stone; or 0.72 is to 1.00 as 0.67 is to 0.93, the volume of a cubic yard of loose stone after ramming. The aggregate compacts 7 per cent in ramming, and a yard of loose material will equal 0.93 of a yard rammed. Adding mortar equal to 140 per cent of the voids increases the volume to about 114 per cent (Table 27); and therefore adding the mortar will increase the volume of the rammed aggregate to 0.93 X1.14=1.06 cu. yd., which is the volume of concrete produced by a yard of loose aggregate. To produce a yard of concrete will therefore require 1=1.06=0.94 cu. yd. of loose broken stone.
Since the mortar is to be equal to 140 per cent of the voids in the rammed stone, a yard of concrete will require 0.94 X 0.93 X 0.28 X 1.40 = 0.34 cu. yd. of mortar. To determine the relative amounts of sand and cement in the mortar proceed as follows: The solid material in a cubic yard of loose sand is to the volume of 1 cu. yd. of loose sand as the solid material in 1 cu. yd. of rammed sand is to the equivalent volume of loose sand; or 0.55 is to 1 as 0.63 is to 1.14, the volume of loose sand required to make a cubic yard of rammed sand. Since the mortar is to have cement paste equal to the voids in the rammed sand, the composition of the mortar is as follows: 0.37 is to 1.14 as 1 is to 3 nearly; or the mortar is 1 part cement paste to prac tically 3 parts of loose sand. The 1 part cement paste will require an equal volume of packed cement. Hence, from Table 22, page 120, a cubic yard of this mortar will require 2.36 bbl. of packed port land cement and 0.95 cu. yd. of loose sand; and consequently 0.34 cu. yd. of mortar will require 0.80 bbl. of packed cement and 0.32 cu. yd. of loose sand.
The composition of the concrete then is: 0.80 bbl. of cement, 0.32 cu. yd. of sand, and 0.94 cu. yd. of stone. Since it is assumed that 1 bbl. of cement is 0.13 cu. yd., the composition is 0.10 cu. yd.
of cement, 0.35 cu. yd. of sand, and 0.94 cu. yd. of stone; or 1 volume of packed portland cement, 3 volumes of loose sand, and 8i volumes of loose broken stone.
The method of proportioning a concrete with reference to the voids is objectionable, since the per cent of voids in the sand may be greatly affected by a small per cent of moisture (1 196), and also owing to possible errors in determining the voids by a direct measure ment by the use of water (§ 195). However, this method is more scientific than the first method mentioned in * 295, and is more simple but less scientific than either the third or fourth method.
To apply this method procure a vessel of uniform cross section, say a cylinder, 10 or 12 inches in diameter and 12 or 14 inches deep, its strength being such that its volume will not be changed in tamping it full of concrete. Weigh out a unit of cement, and any number of units of sand, say two, and also weigh out any number of units of broken stone, say five, taking care that the quantities are such that when the ingredients are thoroughly mixed and placed in the cylinder, the mixture will fill it only partly full, say three quarters full. Make a concrete of any desired consistency by mixing the cement, sand and stone with water on a sheet of steel; and tamp the concrete into the cylinder leaving the upper surface smooth and horizontal, and then measure the depth of the concrete from the upper end of the cylinder. Next empty the concrete from the cylinder, clean it and the tools; and make another batch with different proportions of sand and stone, but keeping the quantity of cement and the plasticity of the concrete the same as before. If this batch, when tamped into the cylinder, gives a less volume of concrete, this proportion is better than the first. Continue the trials until the proportions have been found which will give the least depth i ii the pipe. The proportions can be varied almost infinitely by the sand and the stone, and trying different combinations of the several portions.* The following principles will serve as a guide in selecting the proportions to be tried. 1. The larger the maximum size of the aggregate, the denser and stronger the concrete; but it is not practi cable to use larger fragments than 21 or 3 inches in diameter in plain concrete or / to 1 inch in reinforced concrete. 2. The greatest density will be obtained with an aggregate graded nearly uniformly from fine to coarse. 3. An excess of fine or medium sized particles decreases the density. 4. The coarser the stone the coarser the sand must be; and vice versa, the finer the stone the finer should be the sand.