Mr. E. P. Goodrich* by using a box 3 ft. by 3 ft. square and 6 ft. deep, found the point of application for slightly moist bank sand to be 0.38 of the head, and by measuring the deflection of the sheeting of a trench in fine beach sand 0.39 and 0.40 for two different days. In discussing these and the preceding results, Goodrich says that these experiments "tend to show that for retaining walls from 6 to 10 ft. high, the resultant should be considered as applied at a point 0.4 of the head from the bottom; and with walls less than 6 ft. high, the resultant should be applied still higher; while with walls more than 10 ft. high, the point of application will approach the one third point." Another conclusion from these experiments was that the lateral thrust decreased with time and with repeated applications of the load.
A further conclusion, but one not so well established, was that in building a wall to restrain quicksand it is necessary to provide only for the pressure of the water.
Dr. H. Miiller-Breslau, Professor in the Technical High School, Berlin, in an elaborate series of experiments t used the most scientific and most sensitive apparatus yet devised. He made his experiments with sand in a box 40 inches wide and 80 inches long, having one end 30 inches high and the opposite one 75 inches. He measured the pressure against the low end, which was 30 inches by 40 inches. The sand was such as is used for building purposes in Berlin, and was sharp and thoroughly dry. The apparatus gave, simultaneously and with great accuracy and for practically an infinitesimal movement, the horizontal pressure at the top and the bottom of the pressed surface and also the vertical 'component of the pressure, from which he could deduce the amount, the direction, and the point of application of the resultant pressure. Observations were made (1) with the upper surface of the sand sloping down from the top of the "wall" at the angle of repose and (2) at half the angle of repose, (3) with the upper surface horizontal, (4) with the upper surface horizontal and carrying a vertical load both near to and remote from the wall, and (5) with the upper surface sloping up at the angle of repose.
Since the head was so small, i.e., since the observations were made so near the origin of the curves shown in Fig. 110 and 111, pages 500 and 501, the results are not of much value as showing the amount of the thrust; but the experiments give important information con cerning other features of the problem.
These experiments are very valuable as showing the position of the point of application of the resultant. For sand sloping down
from the wall at the angle of repose, the point of application was 0.313 h from the bottom; when sloping down at half the angle of repose, 0.331 h; when level, 0.352 h; when level and carrying a vertical load remote from the wall, varied from 0.380 h to 0.420 h; and when level and carrying a load near the wall, varied from 0.360 h to 0.466 h. In other ways, the observations show that as the head increases the point of application rises, which is in accordance with the results recorded in Fig. 110 and 111, pages 500 and 501.
Dr. Muller-Breslau says: "It is especially important to notice that, contrary to the Rankine theory, the slope of the upper surface of the sand has no effect upon the direction of the resultant." Another interesting feature of these experiments was that the angle of friction of the sand against a sheet of plate glass was about three fourths of the angle of repose of the sand, which shows that with a very smooth back to the wall, the resultant makes a considerable angle with the normal.
The experiments also show that as an external load is succes sively applied and removed, the point of application rises.
The experiments are to be continued with the view of deter mining (1) the pressure upon oblique walls for different inclinations of the upper surface, (2) the pressure for different kinds of soils, (3) the effect of repeatedly loading the back filling, (4) the influence of moving loads, and (5) the effect of shocks.
Rankine's theory assumes that the pressure is always parallel to the earth slope; but this does not seem reasonable, since the direction of the pressure should be the same as that of the motion, which is parallel to the plane of rupture and nearly independent of the surface slope. According to this theory, a wall may be more stable with a surcharge than with a level top surface, because of the difference in direction of the thrust. Experiments with sand (1 1008) and with grain (1 1003-4) show that the surcharge has little or no effect upon the lateral pressure, except for small heads; and hence for this reason Rankine's theory is not general. M6ller-Breslau's experiments (1 1008) with very sensitive apparatus show that the slope of the upper surface has no appreciable effect upon the direction of the pressure.