THEORY O! $TABII.ITY or AN ABIIrnENT. The abutment of an ordinary bridge has two offices to perform, viz.: (1) to support one end of the bridge, and (2) to keep the earth embankment from sliding into the water. In Fig. 126, the portion DEGF serves both these purposes, while the wings ADF and BEG act only as retaining walls. In Fig. 127 and 128, the portion DE performs both offices, while the wings AD and BE are merely retaining walls. In Fig. 129 the head DE supports the bridge, and the tail, or stem, AB carries the train; hence the whole structure acts as a retaining wall and also supports the load. The abutment proper may fail (1) by sliding forward, (2) by overturning, or (3) by crushing.
The top dimensions of the body of the abutment must be sufficient for the bridge seats, which will vary with the style and the span of the bridge, and must also allow room for a vertical wall on the back edge of the abutment to sustain the roadway, which wall is variously called a dirt wall, a parapet wall, or a back wall. Theoretic ally, the bottom dimensions of the body may be determined by a consideration of the lateral pressure of the earth; but the mathe matical theory of the pressure of earth is a much less perfect guide for designing bridge abutments than for simple retaining walls owing to the effect of the moving load—both on account of its weight and its motion, particularly of a railway train—to increase the lateral pressure against the abutment. Obviously, the effect of the weight of the bridge in resisting the overturning of the abutment is greater for low abutments than high ones, and for long spans than short ones.
Again, the bridge acts more or less as a strut between the two abutments to prevent sliding or overturning, the exact effect depend ing upon the weight of the bridge and upon whether one end rests upon sliding plates or expansion rollers. Further, the wings assist in preventing overturning, except in the straight abutment.
In view of the uncertainties of the mathematical theory of the pressure of earth (§ 998-1013), it is not customary to attempt to com pute the stability of an abutment, but to take the thickness of the body at the top of the footing at 0.40 or 0.45 of the height of the earth fill. In applying this empirical rule, little or no distinction is made between highway and railway bridges, i.e., little or no account is taken of the effect of the moving load; and no account is ever taken of the difference in weight of different bridges, or of the strut like action of the bridge. Apparently, it is more common to make
the thickness 0.40 of the height than 0.45; but the latter is em ployed by some of the largest and best railway systems in this country (see Fig. 132, page 541). In several cases, abutments having a thickness of the height have failed. The thickness of wing walls is frequently made 0.3 of the height of the earth above the point, and seem to stand satisfactorily.
Ordinarily, only comparatively little dif ficulty is encountered in securing a foundation for a bridge abutment. Frequently, by doing the work at the time of low water, the founda tion can be put down without the use of a coffer-dam or at most by the use of a light curbing. When the ground is soft or likely to scour, a pile foundation and grillage may be employed. For the method of procedure in such cases, see Art. 4, Chapter XV; and for examples of this kind of foundation, see Fig. 134 (page 544), Fig. 136 (page 546), Fig. 148 (page 561), Fig. 149 (page 562).
Where there is no danger of underwashing, and where the foun dation will at all times be under water, the masonry may be started upon a timber platform consisting of timbers from, say, 8 to 12 inches thick, laid side by side upon sills, and covered by one or more layers of timbers or thick planks, according to the depth of the foundation and the magnitude of the structure. For an example of a foundation of this class, see Fig. 149 page 562. For a discussion of the method of failure by sliding on the foundation, see § 930 and 1043.
Experience has determined the safe thickness of an abut ment at the top of the footing within comparatively narrow limits; but the width of the footing is subject to wide variation, as it depends upon the bearing power of the soil. Since the moment tending to overturn the abutment is not definitely known, neither the dis tribution of the pressure on the soil under the footing nor the max imum pressure can be found with any considerable accuracy; and therefore, if the soil is even slightly compressible, the dimensions of the footing must be determined with the utmost care. The decision to what will be a safe and not extravagant area of the footing, or rather what will be a safe and not extravagant projection of the footing in front of the wall, is a matter of judgment based upon past experience and a careful study of all the conditions of the particular case in hand. For a few suggestions, applicable in this connection, see § 1025-28.