Trautwine’s wall consisted of a central portion of uniform height, from which it tapered to the ends, the upper surface being at the angle of repose for the tapered ends. In this case no side friction was developed. The results agree in a general way with the others.
In the many experiments on high grain bins, the enormous influence of the friction of the grain against the vertical walls or sides of the bin has been observed. In fact, the greater part of the weight of grain, even when running out, is sustained by the walls through this side friction. This furnishes another argument for including wall friction in retaining-wall design.
In connection with this subject, it may be observed that many experiments, made to determine the actual lateral pressure of sand or its internal friction angle, are inconclusive, because an unknown part of the vertical pressure applied to the sand in the vertical cylinder or box was sustained by the sides of the cylinder or box. The ratio of lateral to vertical pressures, or the friction angle, cannot be precisely found until the proportion of the load sustained by the sides of the containing vessel has been ascertained experimentally. The writer is of the opinion that the best experiments to aid in the design of retaining walls are those relating to the rotation of retaining walls or boards. The few given herein are the best recorded, though some of them were on models which were too small. In fact, for the small models of Leygue and others, the effect of cohesion is so pronounced that some of the results are very misleading.
As the experiments by Leygue[Footnote 4] ] were very extensive, and evidently made with great care, they will be considered carefully in what follows.
As preliminary to the discussion, however, it is well to give the essentials of Leygue’s experimental proof that cohesion and friction exist at the same time. A box without a bottom, about 4 in. square in cross-section and 4 in. high, was made into a little carriage by the addition of four wheels. The latter ran on the sides of a trough filled with sand which the bottom of the box nearly touched. The box was partly filled with sand, and the trough and box were then inclined at the angle at which motion of the box just began, the sand in the box resting on the sand in the trough, developing friction or cohesion or both, just before motion began. Only friction was exerted after motion began. The solution involves the theory of the inclined plane, but, to explain the principles of the method, it will suffice to suppose the trough and the sand in it to be horizontal, and that the bottomless box filled with sand is just on the point of moving, due to a horizontal force applied to it. The weight of the box and a part of the weight of the sand in it held up by the friction of the sides, is directly supported by the wheels resting on the sides of the trough; so that only a fraction of the weight,
, of the sand in the box is supported directly by the sand in the trough. Call this amount
. Then, for equilibrium, calling
