The preceding shows that the assumption that the surface of rupture is a plane is not in accordance with ordinary practical con ditions. At the time the earth is deposited behind a retaining wall, it has the least cohesion and most nearly conforms to the theory; and hence the theory most nearly represents the most dangerous condition. But as the soil is deposited, the weight of the upper portion and the rain consolidate the lower strata and thereby in creases the cohesion; and hence, unleas the bank is built rapidly of dry earth during a dry time, the assumption that the surface of rup ture is a plane does not closely represent the facts.
All theories assume that the coefficient of friction in the interior of the earth mass is the same as on the exterior slope; or in other words, all theories assume that the coefficient of internal friction is equal to the tangent of the angle of the natural surface slope. Experiments show that the angle of internal friction differs materially from the angle of surface slope, and probably varies some what with the pressure.* The resistance of particles of earth or sand to moving on an exposed slope is probably rolling friction rather than sliding, while the resistance involved in the lateral pressure of earth is sliding friction. This is the reason why there is a difference between surface friction and internal friction.
Table 76 shows the values of the tangent of the angle of internal friction and also of the angle of the surface of repose for identical materials by the same observer.t There seems to be no constant relation between the two sets of values; but Table 76 shows that the angle of internal friction for most materials is considerably smaller than the angle of natural slope. The angle of internal friction seems to depend upon the size of the particles and to increase with the pressure and the moisture; but additional experiments are required to determine the law of its variation.
Table 77 gives various values of the angle of internal friction, including those in Table 76. The angle of internal friction (Table 77) rather than the angle of repose (Table 75) should be used in formulas for the lateral pressure of earth.
not been proved beyond question that the pressure varies as the square of the height, and hence it can not be concluded that the point of application is certainly at of the height.
In deducing the formula for the amount of the pressure, it was assumed that the prism of earth between the plane of rupture and the back of the wall acted like a solid wedge sliding on the plane of rupture; and hence there is reason for claiming that the pressure on the back of the wall is uniformly distributed, and that the resultant is applied at the center of the height.
Since earth is neither a liquid nor a solid, it is probable that neither of the above assumptions is correct, and that the true position is somewhere between these two extremes.
Experiments with Sand. Experiments show that clean dry sand under pressure does not act even approximately as a liquid. For example, in one experiment* fine, clean, dry sand under a pres sure of 2,250 lb. per sq. ft. in a box 4 ft. by 6 ft. by 6 ft. would not flow through a horizontal hole tapering from 3 inches at the inside to 2 inches at the outside; a hole at 30° with the horizontal would flow only about one third full; and a hole at would flow nearly full. A vertical hole in the bottom discharged freely, but a slight pressure of the hand was sufficient to stop the flow. In another experiment t substantially the same results were found under a pressure of 22i tons per sq. ft. Since clean sand did not act as a liquid in these experiments, it should not be assumed that earth supported by a retaining wall acts as a liquid; and consequently it should not be assumed that the point of application of the resultant is at of the height from the base.