. The friction (acting vertically downward) caused by this thrust is
on the panel and
on the counterfort. The moment of these forces about the outer toe of the wall, totals 39 800 ft‑lb. The resisting moment of 10 ft. in length of combined panel and counterfort, about the outer toe, assuming the wall to be vertical, is 29 800 ft‑lb. If, to the latter, we add the moment of 17% of the weight of earth between the counterforts, supposed to be held up by the sides of the latter, the total moment exactly equals the first. However, at the moment of failure by overturning, the panels had bulged 4½ in. and the overhang at the top was 7½ in. Taking the moment of stability of the wall at 26 000 ft‑lb. (Mr. Baker’s figure), it is found that, for equilibrium, 24% of the weight of earth between the counterforts must be carried by them, When the earth was 8 ft. high, a heavy rain was recorded, so that, doubtless, some appreciable cohesion was exerted, though necessarily omitted in the computation.
The experimental wall of Col. Michon was 40 ft. high, with very deep counterforts, only 5 ft. from center to center. The very heavy and wet filling between the counterforts, being treated as a part of the wall, a construction (made on the printed drawing) shows that the resultant of earth thrust and weight of wall passes through the outer toe. Doubtless the cohesion factor in this wall was large. In the paper mentioned, the details as to Gen. Burgoyne’s experimental walls are given. There were four of these walls, each 20 ft. long, 20 ft. high, and with a mean thickness of 3 ft. 4 in. Two of the walls were perfectly stable, as in fact theory indicates for all four walls if they were monolithic. The other two walls fell, one bursting out at 5 ft. 6 in. from the base, and the other (a vertical wall), breaking across, as it were, at about one-fourth of its height. As these walls consisted of rough granite blocks laid dry, it is highly probable that the breaks were due to sliding, owing to the imperfect construction; besides, “the filling was of loose earth filled in at random without ramming or other precautions during a very wet winter.”
From a consideration of all the observations and experiments (some of them unintentional), Mr. Baker concludes that the theoretical thrust is often double the actual lateral pressure. He used the old theory, which neglects both cohesion and wall friction. If he had included them, the resulting theory would not have been so deficient “in the most vital elements existent in fact” as he charges against the “textbook” theory.
However, the writer must be clearly understood as not recommending that cohesive forces be considered in designing a retaining wall backed by a granular material, such as fresh earth, sand, gravel, or ballast. It has been the main object of this paper to show that, although cohesive forces must be included in interpreting properly the results on small models and many retaining walls, yet, for walls more than 6 or 10 ft. in height, backed with dry fresh material, not consolidated, the cohesive forces can be practically neglected in design. Hence, experimenters are strongly advised to leave small models severely alone and confine their experiments to walls from 6 to 10 ft. high, backed by a truly granular material, such as dry sand, coal, grain, gravel, or ballast, where the cohesive forces will not affect the results materially. Further, it is evident that walls of brick in wet sand, or walls of granite blocks, etc., laid dry, are very imperfect walls. The overhang, just before falling, is large, and the base is often imperfect. For precise measurements, a light but strong timber wall on a firm foundation, seems to be best; and the triangular frame of [Fig. 8] seems to meet the required conditions very well, especially if the framing is an open one, with a retaining board only on one leg. The base thus becomes wider, and the overhang less, than with any rectangular wall.
When the design of a wall to sustain the pressure of consolidated earth is in question, even if a perfect mathematical theory existed, it would still prove of little or no practical value, because the coefficients of friction and cohesion are unknown. The coefficient of friction at the surface can be easily found, but it is a difficult matter to find the coefficient of cohesion, which doubtless varies greatly throughout the mass.