from the values given by [Equations (1)] and [(2)]. As the height of the wall increases, say to 25 or 50 ft., the influence of cohesion, in diminishing the thrust, becomes very small, and it is better to ignore it altogether. In fact, as we know very little, and that imperfectly, of the coefficients of cohesion, it is perhaps safer, at present, to use [Equations (1)] and [(2)] in all cases. It is very evident, though, that for most cases in practice, the formulas give a very appreciable excess over the true thrust, and that the true plane of rupture never coincides with the natural slope.
From all that precedes, it is seen that the results of experiments on small models in the past have proved to be very misleading, and that experiments on large models are desirable, and can alone give confidence. Leygue has made such experiments on retaining boards, from 1 to 2 m. (3.28 to 6.56 ft.) in height, simply to determine the surface of rupture. This is really the essential thing, for, as soon as the prism of rupture is known, the thrust is easily found. In a general way, the results agree with theory when the cohesion is neglected, though the curved surfaces of rupture were very irregular, particularly for the stone filling. The first two experiments were made with both dry and damp sand as a filling; the next six, with stones varying from 1.5 to 20 in. in diameter. In another series of five experiments, sand was used. In all the foregoing experiments, the surface of the material was horizontal. In three additional experiments, the walls were surcharged with sand as a filling. In one experiment, the wall was 6.56 ft. high and the surcharge was 3.28 ft.; in another experiment, the wall was 3.28 ft. high, and the sand, sloping from its top at the angle of repose, as in the former case, extended to 3.28 ft. above the wall, where the surface was horizontal.
Applying the construction of [Fig. 1], it was found that the plane of rupture passed, say, 2° above that given by experiment in the first case and about 3° below in the second. It will be evident from the construction of [Fig. 11], omitting cohesion, that trial planes of rupture differing by 2 or 3° from the true one, give nearly the same thrust. Taking the average, these experiments on large models, tend, in a general way, to sustain the theory.
In a paper by the late Sir Benjamin Baker, Hon. M. Am. Soc. C. E., “The Actual Lateral Pressure of Earthwork,”[Footnote 8] ] two experiments by Lieut. Hope and one by Col. Michon, on counterforted walls, are given. Although such walls do not admit of precise computation, on account of the unknown weight of earth carried by the counterforts, through friction caused by the thrust of the earth in a direction perpendicular to the counterforts, still the computation was made, as the conclusions are interesting. Therefore, the first vertical wall of Lieut. Hope was examined, especially as Mr. Baker, using the Rankine theory, found, for this wall, the greatest divergence between the actual and the Rankine thrust, of any retaining wall examined.
At the moment of failure, the wall was 12 ft. 10 in. high, the thickness of the panel was 18 in., and the counterforts were 10 ft. from center to center, projecting 27 in. from the wall, or 3 ft. 9 in. from the face, as inferred from the next example. As it is stated that the wall had the same volume as the 10-ft. wall previously examined in this paper ([Fig. 4]), the counterforts must have been 2 ft. thick. Assuming these dimensions, and using the values given;
, or
(say