, respectively,
being equal to the height of the wall.
It must be noted especially, however, that if the original earth thrust, when combined as usual with the weight of wall, gives a resultant which passes outside of the middle third of the base of the wall as computed above, then the thickness must be increased, so that the resultant will at least pass through the outer middle-third limit. This ensures compression over the whole base and no opening of part of the joint under normal conditions. With regard to the thickness above of about one-third of the height, Mr. Baker states that hundreds of brick revetments have been built by the Royal Engineer officers, with a thickness of only
for a vertical wall. He advises, as the result of his own extensive experience, that the thickness be made one-third of the height for level-topped earth of average character, and that the wall be battered 1½ in. to the foot. He states, further, that, under no ordinary conditions of surcharge on heavy backing is it necessary to make the thickness of a retaining wall on a solid foundation more than one-half the height. The thicknesses computed above agree fairly well with those recommended by Mr. Baker, and it would seem that a table of thicknesses computed on the above basis should correspond to safe walls under ordinary conditions.
It has been noted above that [Equation (1)], corresponding to a slope of indefinite extent, probably gives too great a thrust; besides, there are no embankments with such a slope. An embankment from 100 to 150 ft. high, supported by a low wall, may approximate the conditions assumed, but, before it is finished, the earth has consolidated to such an extent that the actual thrust is doubtless much less than the computed one. The truth is that, in nearly all back-filling of ordinary earth, the cohesive and chemical affinities commence their work very soon after the filling is deposited, and consolidation is gradually effected; so that, as has been stated, the actual thrust is often much less than is estimated in the design of the wall, where cohesive forces are neglected. In many old walls, as has been observed, the consolidation has gone so far that the backing has shrunk away from the wall altogether. It would be hazardous, though, to allow for cohesion, in a wall backed by fresh earth, unless the surcharge was high and was a long time in building. Finally, it should be observed that the footing of a retaining wall should be wide, and should always be tilted at such an angle that sliding is impossible.
A glance at [Figs. 4], 5, and 6, will make it apparent that the Rankine and other theories differ in their results mainly because of the assumed difference of inclination of the earth thrust. In the design of walls, however, the method proposed ([Fig. 15]) will approximate in results those given by the Rankine theory, where, say, the earth thrust, whether inclined or not, is multiplied by the factor of safety. The writer [does not advocate the middle-third] limit method in design, as it gives variable factors of safety for different types of walls. Besides, if the actual resultant on the base passes one-third of its width from the outer toe, there is no pressure at the inner toe, and the unit pressure at the outer toe is double the average. If vibration or other cause increases the thrust, the joint at the inner toe opens, and the pressure is concentrated too much near the outer toe. In the reinforced concrete wall, the earth thrust on a vertical plane through the inner toe is required. As this plane lies well within the earth mass, the thrust on it must be taken as acting parallel to the top slope, and its amount will be the same as that given by the Rankine theory.
Although it is highly desirable to have more precise experiments on large models in order to draw sure conclusions, yet, as far as the experiments go—those which have been analyzed and discussed in this paper—the following conclusions may be stated: