THEORY OF THE QUANTITY OF CEMENT IN MORTAR AND CONCRETE.—All sand contains a large percentage of voids; in 1 cu. ft. of loose sand there is 0.3 to 0.5 cu. ft. of voids, that is, 30 to 50 per cent. of the sand is voids. In making mortar the cement is mixed with the sand and the flour-like particles of the cement fit in between the grains of sand occupying a part or all of the voids. The amount of cement required in a mortar will naturally depend upon the amount of voids in the particular sand with which it is mixed and since a correct estimate of the number of barrels of cement per cubic yard of mortar is very important, and since it is not always possible to make actual mixtures before bidding, rules based on various theories have been formulated for determining these quantities. In this volume the rule based on the theory outlined by one of the authors in 1901 will be followed. The following is a discussion of the authors' theory:
When loose sand is mixed with water, its volume or bulk is increased; subsequent jarring will decrease its volume, but still leave a net gain of about 10 per cent.; that is, 1 cu. ft. of dry sand becomes about 1.1 cu. ft. of damp sand. Not only does this increase in the volume of the sand occur, but, instead of increasing the voids that can be filled with cement, there is an absolute loss in the volume of available voids. This is due to the space occupied by the water necessary to bring the sand to the consistency of mortar; furthermore, there is seldom a perfect mixture of the sand and cement in practice, thus reducing the available voids. It is safe to call this reduction in available voids about 10 per cent.
When loose, dry Portland cement is wetted, it shrinks about 15 per cent, in volume, behaving differently from the sand, but it never shrinks back to quite as small a volume as it occupies when packed tightly in a barrel. Since barrels of different brands vary widely in size, the careful engineer or contractor will test any brand he intends using in large quantities, in order to ascertain exactly how much cement paste can be made. He will find a range of from 3.2 cu. ft. to 3.8 cu. ft. per barrel of Portland cement. Obviously the larger barrel may be cheaper though its price is higher. Specifications often state the number of cubic feet that will be allowed per barrel in mixing the concrete ingredients, so that any rule or formula to be of practical value must contain a factor to allow for the specified size of the barrel, and another factor to allow for the actual number of cubic feet of paste that a barrel will yield—the two being usually quite different.
The deduction of a rational, practical formula for computing the quantity of cement required for a given mixture will now be given, based upon the facts above outlined.
| Let | p | = | number of cu. ft. cement paste per bbl., as determined by actual test. |
| n | = | number of cu. ft. of cement per bbl., as specified in the specifications. | |
| s | = | parts of sand (by volume) to one part of cement, as specified. | |
| g | = | parts of gravel or broken stone (by volume) to one part of cement, as specified. | |
| v | = | percentage of voids in the dry sand, as determined by test. | |
| V | = | percentage of voids in the gravel or stone, as determined by test. |
Then, in a mortar of 1 part cement to s parts sand, we have:
| n s | = | cu. | ft. | of | dry sand to 1 bbl. of cement. |
| n s v | = | " | " | " | voids in the dry sand. |
| 0.9 n s v | = | " | " | " | available voids in the wet sand. |
| 1.1 n s | = | " | " | " | wet sand. |
| p - 0.9 n s v | = | " | " | " | cement paste in excess of the voids. |
Therefore:
1.1 n s + (p - 0.9 n s v) = cu. ft. of mortar per bbl.