stone for the reason that, by the laws of the survival of the fittest and by process of elimination, nature has supplied us with the most durable. Short-time tests for compression strength usually show broken stone concrete to be superior, but long-time tests of from six months to a year show gravel concrete on an average to be equal if not stronger. In construction work where tensile or other stresses are to be cared for, as may occur in reinforced concrete, crushed gravel should be used. The cement will adhere more readily to crushed than to the rounded, polished surface of the gravel. CHAPTER VI HOW TO PROPORTION THE MATERIALS Nature of the Problem.-Voids in Concrete.-Methods of Proportioning.-Tables for Proportioning. Nature of the Problem.-A great deal of study has been given to the question of proportioning the materials of concrete, and most of the study has been directed to one end; viz., to find a mixture that will give the maximum density and strength with a minimum amount of cement. The difficulties in arriving at any definite rules for obtaining this result arise from the great variation in the various elements affecting the work, no two materials being exactly alike, and rules deduced from one set of experiments being of very doubtful value when applied to other conditions. Although a good deal of care in proportioning is warranted, to obtain the best mix with any given material, too great refinement is unnecessary and the theoretical methods which have been gone into with such great detail in many of the books on concrete work have more of an academic interest than a practical value. The principal thing to bear in mind in order to obtain the densest possible mixture is to eliminate the voids in the concrete mass, and to do this, it is desirable that the sand and gravel be well graded from coarse to fine and enough cement be used to obtain a rich mixture. Plenty of water, to obtain a wet mix, should be employed, as water will drive out the air entrained between the particles of the aggregates. The density, strength, and watertightness of concrete will be increased in accordance with the richness, variation in size of aggregate, and with the plasticity of the mixture. Mix rich and mix wet to obtain the best work. The question of proportioning is, of course, also dependent upon the use to which the concrete is to be put and in many locations density and strength may not be the prime requisites, and then a very small percentage of cement will suffice to obtain a hardened mass; as low as 5 per cent has given a strong concrete. Voids in Concrete.-American engineers proportion concrete mixtures by measure, thus a 1:2:4 concrete is composed of 1 volume of cement, 2 volumes of sand, and 4 volumes of broken stone. Both the sand and the coarse aggregates employed for concrete contain voids or empty spaces between their particles. In a perfect mixture the cement would fill the voids in the sand and coat each grain, while the sand with its coating of cement would fill the voids in the aggregate and also cover each stone with a film of mortar. In practice, it is impossible to fill all of the voids in concrete. In the first place, the cement and sand cannot be perfectly distributed, and in the second place, the water used in the mixing causes the sand to swell, thus increasing the voids about 10 per cent. This swelling is due to a film of water between the grains, and this film cannot be entirely displaced by the cement. When the water evaporates after a wall of concrete has set, voids always remain throughout the mass, and some shrinkage of the mass occurs. A rich mixture is obtained when the cement is somewhat in excess of the quantity that would, theoretically, be sufficient to fill the voids in the sand. Sand and gravel contain from 30 to 50 per cent of voids, while the voids in broken stone range from 40 to 50 per cent. The proportion of voids may be approximately determined in either sand or broken stone in the following way: Wet the loose aggregate thoroughly; fill a vessel of known capacity with the material, and then pour in all the water the vessel will contain. Measure the volume of water required and divide this by the volume of the vessel. The quotient represents the proportion of voids. Method of Proportioning.—The ordinary mixture for watertight concrete is about 1: 2: 4 which requires 1.32 barrel of cement per cu. yd. of concrete. The most scientific method for proportioning the ingredients is that known as the Mechanical Analysis. In this method the available materials, including the cement, are separated into various sizes by means of a series of sieves. Curves. are then plotted on cross-section paper which indicate the percentages of the whole mass that pass the several sieves. From a study of these curves, the proportions of the different ingredients are determined. This method is, however, not available in the usual course of concrete work. In hand-mixing, cement is generally measured by specifying the number of bags to a batch. Machine mixers frequently have automatic measuring devices. When removed from the bag or barrel, cement occupies about 15 per cent more space than when in the original package; or a 1:2:4 mixture measured by counting the number of bags will be 15 per cent richer than a 1:2:4 mixture, which is proportioned by measuring the cement loose. Hence in determining the proportions, the methods of measuring the cement should be considered and specifications should clearly provide how this shall be done. Volume of Barrel of Cement.-The difference between the volume of a barrel of cement when measured packed and loose, and variations in size and weight have been subjects of extended controversy and often bitterness between engineer and contractor, and has resulted in much friction and litigation. The tendency now is to fix an arbitrary but average value for the volume of the cement barrel as a standard, and have this used as a basis on all concrete work. The value of 4 cu. ft. to the barrel is preferred, the actual volume being about 3.75 cu. ft. packed and 4.2 cu. ft. loose. The fixing of such a standard of value is highly desirable, and would be of great benefit to engineers and contractors alike. Proportions by Formula.-A number of formulas have been introduced for proportioning the sand, cement and stone and it is worth the cement user's while to take note particularly of the one here given, as it is exceedingly simple and may save much trouble in proportioning. While proportioning by formula is not employed as frequently as proportioning by rule of thumb, the method has been employed to work out some excellent tables for proportioning concrete and these tables are extremely useful in estimating the amount of cement required on any particular job as well as for other construction purpose. The simplest formula for this purpose is: B = number of barrels of cement per cu. yd. of concrete. S= number of parts of sand to I part of cement as specified. This formula assumes that the voids in the gravel are filled by the sand and the voids in the sand are filled by the mortar, and therefore the results are approximate. Thus for a 1:2: 4 concrete, when I bbl. cement is specified as 4 cubic feet, The following table was computed by Gillette's formula, giving the quantities of cement, sand, aggregate, and water required to produce one cubic yard of wet concrete: TABLE II.-INGREDIENTS IN ONE CUBIC YARD OF CONCRETE. Voids in Sand, 40 per cent. Voids in Stone, 45 per cent. In Table II, the approximate amount of water required for a wet mixture is expressed as a percentage of the combined weight of sand and cement. These percentages are, however, only approximate. More water is required in dry than in moist atmospheres, and more in summer than in winter. A wetter mixture is also required when the material cannot be tamped. While a dry mixture is theoretically the stronger when carefully deposited and |