(5) Proportions based on the surface area of the aggregates.
(6) Proportions based on the water-cement ratio and the fineness modulus.
(7) Proportions based on mortar-voids and cement-voids ratio.
Arbitrarily selected proportions are in quite general use; they are intended to apply to the materials most commonly used in the vicinity of the work. The most common practice is to use twice as great a volume of coarse aggregate as fine aggregate, as for instance 1 part cement, 2 parts fine aggregate, and 4 parts coarse aggregate. Decreasing the ratio of coarse aggregate to fine aggregate may give a more easily worked mix or require relatively less water for a given workability, and in some cases it will be proper to increase this ratio and thus secure an increase of strength. Judgment and experience with given materials may warrant changes from a stated ratio. The proportions are now frequently given as one part cement to a certain number of parts of the mixed aggregate, leaving the proportions of the fine to coarse to be determined otherwise, since small variations in the relation of these will not greatly affect the strength. Proportions in common use are:[[55]]
| Mortar for | |||
| Laying brick and stone masonry | from | 1 : 0 to 1 : 3 | |
| Filling joints in sewer pipe | 1 : 0 to 1 : 2 | ||
| Surfaces, floors, sidewalks, pavements | 1 : 0 to 1 : 2 | ||
| Waterproof linings | 1 : 0 to 1 : 2 | ||
| Cement, bricks, and blocks | 1 : 2½ to 1 : 4 | ||
| Concrete for | |||
| Gravity retaining walls, heavy foundations, structures needing mass more than strength | from | 1 : 3 : 6 to 1 : 4 : 8 | |
| Retaining walls, piers, sewers, pavements, foundations, and work requiring strength. (Compressive strength in 28 days, 1,500 to 2,000 pounds per square inch) | from | 1 : 2 : 4 to 1 : 3 : 6 | |
| Floors, beams, pavements, reinforced concrete, arch bridges, low-pressure tanks. (Compressive strength in 28 days, 2,000 to 3,000 pounds per square inch) | from | 1 : 1½ : 3 to 1 : 2½ : 4½ | |
| Reinforced concrete columns, conduit pipe, impervious concrete. (Compressive strength in 28 days, 3,000 to 4,000 pounds per square inch) | from | 1 : 1 : 2 to 1 : 1½ : 3 | |
The usual method of proportioning based on minimum voids is to assume that the particles of fine aggregate should fill the voids in the coarse aggregate and that the particles of the cement will fill the voids in the fine aggregate. About 5 to 10 per cent additional fine aggregate is generally added to push the particles of the coarse aggregate apart and thus give a more easily worked concrete and one freer from void spaces. This method is inaccurate, principally because of the effect of the moisture on the volume of the voids, and because the effect on the volume by the addition of water is unknown.
Trial mixtures may be made by carefully weighing each of the ingredients and then combining them to give a workable concrete. Using a given amount of cement, the proportion of ingredients, of the same total weight, which will give the least volume and therefore the densest concrete is adopted. When making the comparison the consistency of the mixes must be maintained constant.
Proportioning may be based on an ideal sieve analysis curve of the mixed cement and aggregates. The sieve analysis of the aggregates is made by screening a predetermined weight of the sample through a series of 5 to 8 sieves graded in size from slightly below the size of the largest particle to slightly above the smallest particle of the aggregate. The analysis is then expressed in the form of a curve. The ideal curve, according to Fuller,[[56]] is shown in Fig. 77.
Fig. 77.—Gravel Analysis.
The dotted line indicates the ideal combination of the coarse and fine portions. The heavy full line indicates the combination attained.