Where a sand contains 30 per cent voids, the table shows that only 2.5 parts of it should be mixed with 1 part of cement. And if coarser material is also available, say stone containing 45 per cent of voids, then parts of such ag gregate should be added. The proper mixture would be 1:2.5:4.5; and if this mixture had been used on the job, the amount of cement necessary would have been only one-eighth the total volume, instead of the one-fifth called for by the 1:4 mixture—a saving of 37.5 per cent.
When a natural mixture of sand and gravel is available, the most reliable results will be ob tained by screening it, and then remixing the fine and coarse material in the proper definite proportions. But if this cannot be done and un screened gravel has to be used, the proportion of cement can be roughly determined in the fol lowing manner: Take a portion of the gravel, and screen out the sand through a screen. If the volume of sand that passes the screen bears to that retained on the screen the ratio, of, say, 3 to 5, then the mixture to use is 1 part cement to 3+5=8 parts of the unscreened gravel, since this practically amounts to a mix ture of 1 part cement, 3 parts sand, and 5 parts gravel.
The proportions for a mixture can also be cal culated, though but roughly, from the voids in the sand and stone. Assume, for example, a sand with 33 per cent and a gravel with 40 per cent of voids. Then, to fill the voids in 100 volumes of gravel, we shall need 40 volumes of sand. To fill the voids in the sand with cement, we shall need 33 per cent of 40 volumes; but, allowing an extra 10 per cent for thorough coating of the particles and to avoid results of possible errors made in determining the voids, we shall take 43 per cent of 40 volumes, that is, 17.2 volumes of cement. The proportions of the mixture will then be 17.2 ce ment to 40 sand to 100 gravel, or, approximately, 1:2.3:5.8.
Any great variation in the relative propor tions of sand and gravel may convert a good, strong concrete into a weak and inferior one, even though the proportion of the cement be not changed. Strength may ordinarily be in creased by adding to the proportion of cement, but a simultaneous increase of the sand would defeat the purpose in view, possibly weakening the concrete as much as the increase of cement would strengthen it.
It is a widely accepted conclusion among engineers, that a determination of the voids in sand affords at best only an approximate indica tion of the amount of cement that should be mixed with the sand in making mortar or con crete. Safety, it is true, may always be con served, where this method is followed, by making due allowance for errors of calculation, imperfect mixing, etc.; yet this, they point out, may be at an unnecessary sacrifice of economy, and, for a determination of the ideal proportions, some other method is to be preferred.
That the voids in sand are an uncertain and variable factor, is shown by several considera tions. When water is added to sand and thor oughly mixed with it, the sand swells in volume, so that a cubic foot of the damp sand will weigh less, and will contain a f4r larger amount of voids, than a cubic foot of the same sand when dry. At the same time, the available voids in the damp sand are different from the available voids in the dry sand. Fine sand takes up more water than coarse, and increases con siderably more in volume.
Moreover, the volume of any measured quan tity of cement will be considerably reduced by the addition of water so as to work the cement into a thick paste. A cubic foot of packed ce ment does not signify a cubic foot of void-filling capacity when the cement is wetted and made into a thick paste.
In view of such considerations as these, many engineers prefer to base their proportioning of mixtures, so far as the cement and sand are con cerned, not on the measured or computed volume of voids in the sand, but on the density and plasticity of the mortar produced by differently proportioned mixtures of cement and sand. The sample mixtures for examination (say five sam ples in proportions 1:2; 1:2.5; 1:3, etc.) are very carefully proportioned out by weighing, and are made to approximate as nearly as possible the conditions that will exist in actual work, as to compactness, amount of moisture absorbed, etc. The tests are taken in finely graduated measur jug tubes which show accurately the relation be tween the original volume of the sand and that of the resulting mixture, and also the slightest variations in volume of the mixture due to the different proportions. The density of the mortar increases with the amount of the cement, up to that point where a further increase of .cement will cause an increase in the volume of the mor tar. If the conditions of the work do not require a very dense or strong mortar, the proportions to be adopted will be indicated by one of the samples containing the least cement, but show ing sufficient plasticity to insure a good bond in the concrete.
In principle this method of determining pro portions is very similar to that depending on the "yield" or "volumetric test" for sand, which has already been described. Table VIII is a working table based on this method, compiled by Albert Moyer from the results of many tests. It shows the proportions of aggregates which will give maximum density with a minimum of cement. The voids in the stone, and the eco nomic proportions of cement to sand which will give the density and plasticity of mortar re quired on the particular concrete job, should first be determined; and the table may then be applied to show the amount of coarse aggregate to be used.
For example, suppose that a mortar mixture of 1 part cement to parts sand is decided upon, and that the available coarse ag gregate contains 33 per cent of voids. Then, looking at the table, starting at 33 in the void column at the left, and passing over to the right until we come to the proportion column headed 'we find which is the number of parts of stone to be added to the mortar mixture.