9 in. deep.$ The pressures were measured with a rubber diaphragm and a mercury column. The line marked "fluid pressure" shows the press ure of a liquid having the same weight per cubic foot as the clean wheat. The work of other experimenters shows that these curves are typical of the results obtained with bins 12 to 24 feet in diameter and 60 to 80 feet high; and hence these results may be taken as representative of the pressure in large masses of a granular material which is devoid of cohesion.
shows the relation between the depth and the lateral and vertical pressures for wheat and also for clean sharp dry river sand.* These results were obtained from experiments with a model bin 12 inches in diameter and 6 ft. 6 in. high; but as the curves for wheat are representative of the values obtained with large bins, it is probably safe to assume that the curve for sand is representa tive of the pressure of sand in large masses.
Since all accurate experiments with such granular masses as wheat, corn, peas, flaxseed, and sand show that the pressure of such materials does not follow the law of liquid pressure, it is in correct to assume liquid pressure to determine the point of applica tion of the lateral thrust of earth. Several steel grain bins designed according to the former theories for the pressure of granular masses, failed by the buckling of the sides near the bottom, showing that the sides carried a considerable vertical component of the weight of the grain; and many wooden bins stand without any signs of failure in defiance of the ordinary formulas for the lateral thrust of granular masses.
In Fig. 110 and 111 the area between the curves for lateral pres sure and the vertical line through zero is proportional to the total pressure, and the center of gravity of the area gives the height of the point of application of the resultant; and consequently, the more nearly this area approaches a rectangle, the more nearly the lateral pressure is uniformly distributed and the more nearly the center of pressure approaches the center of the height.
The most instructive results of the experiments with high heads of grain are: (1) the pressure increases very little after a depth of 23 to 3 times the diameter of the bin has been reached; (2) the lateral pressure is from 0.3 to 0.6 of the vertical pressure according to the kind of grain, its moisture, the material of the bin, etc.; and (3) the vertical pressure on the bottom of the bin is greatest near the center and decreases toward the side of the bin, where it is practically equal to the lateral pressure on the aids of the bin. These results show that the only pressure on the bottom of the bin and also on the sides of the bin near the bottom is that due to a dome-shaped mass of grain immediately above the bottom, and that all grain above this mass is carried entirely by friction between the grain. and
the sides of the bin. The pressures depend upon the rise of this dome-shaped mass, which varies with the horizontal dimensions of the bin, the kind and the dryness of the grain, the material of the bin, etc. When grain is drawn out from below this dome, the space is filled by grains dropping from the under side of the dome, and as these drop others take their place in the dome.
The knowledge that a mass consisting of comparatively small and smooth particles is supported by arch-like action over the rela tively large space between the walls of a bin, is important in inter preting the results of experiments on retaining walls and on the pres sure of grain in bins, and also in designing structures to resist the pressure of earth.
Point of Application Determined Experimentally. Several direct experiments have been made to determine, among other things, the point of application of the resultant earth thrust against a retaining wall. M. Leygue,* Mr. George Darwin,t and M. Gobin$ have made such experiments, but their apparatus was upon such a small scale and of such a character that their results are not trust worthy, chiefly on account of the possible arch action of the sand and millet seed experimented with. However, according to Leygue's experiments, the point of application of the resultant for sand varies from 0.38 h to 0.50 h and for millet seed from 0.382 h to 0.450 h.
Mr. A. A. Steel¶ measured the pressure against two boards 12 inches square, due to earth in a pit which at the bottom was 6 ft. 6 in. from front to rear and 7 ft. long, and at the top was 7 ft. front to rear and 9 ft. long. The maximum head of earth against the upper board was 12.5 ft. The pressures were measured by a lever whose long arm acted against a spring balance. The curves for the lateral pressure for dry loam were uniformly of the same general form as the curves in Fig. 111, page 501. The observed pressures upon the upper board were from 70 to 80 per cent greater than those upon the lower board, probably owing to greater arch action at the lower board. The lower edge of one board was 0.5 ft. and of the other 1.5 ft. above the bottom of the pit. For dry loam weighing 80 lb. per cu. ft. and having an angle of repose of 35° 29', the point of application of the resultant pressure was 0.40 of the head above the bottom; for the same earth slightly moist 0.39, and when saturated 0.38.