The pressure on the subsoil, which is less than 2,1 tons per square foot, is less than that usually allowable on a good subsoil. There is therefore but little danger that the subsoil will be crushed and that the wall will tip over bodily on account of the failure of the subsoil. Since the line of pressure is likewise two feet back of the toe of the wall, there is no danger that the wall will tip over around its toe. The accuracy with which these calculations have been carried out should not lead to the idea that the pressures will necessarily be exactly as stated, since the calculations are based on assumptions which are at the best very doubtful, but which, as previously stated, are probably excessively safe.
The form chosen for this wall is also so simple that a purely numerical calculation was the easiest and most satisfactory method. If the shape of the wall had been more irregular, it would have been easier to adopt the graphical method for the determination both of the center of gravity of the wall and of the resultant pressure on the subsoil. For in stance, if the rear face of the wall had been inclined, the line of pressure would have been drawn perpendicular to the rear face and through a point at one-third the height of the wall. The position of the center of gravity of the wall would have been deter mined by the purely graphical method of determining the center of gravity of a trap ezoid; and then the amount, direction, and intersection of the resultant with the base of the wall would have been determined by purely graphical methods.
228. Empirical Rules. On account of the unsatisfactory nature of theoretical calculations, retaining walls are usually built by the application of purely empirical rules. Trautwine recommends that for a wall of cut stone or of first-class large ranged rubble in mortar, the thickness should be .35 of its vertical height. For a good common mortar rubble or brick, the thickness should be .4, and for a dry wall .5, of the height. Military engineers who have a very extensive experience in constructing retaining walls as a feature of fortification work, use a rule giving much less thickness than this, and make it depend on the batter of the wall. The thickness at the base in pro portion to the height, is as follows: The fact that experience has shown that the above proportions are usually safe, provided that the subsoil is sufficiently hard, is another proof that the assumptions made in the problem worked out above are excessively safe, since Fanshawe's rule would have required a ratio of base to height of only 24 per cent, while the ratio chosen for the problem was 40 per cent.
229. Failure of Retaining Walls. It is a significant fact that a retaining wall may apparently withstand the pressure against it for a period of several years, and may then slowly and gradually fail. This is sometimes due to
the action of frost on the soil behind the wall. The water ac cumulates behind the wall in the early winter, and, if it is unable to drain away, may freeze, ex pand, and exert a pressure on the wall which forces it out. One great precautionary feature in the construction of retaining walls is to place drain-pipes through the wall at sufficient in tervals so that water cannot ac cumulate and remain behind the wall. The gradual failure of walls may also be due to the undermining and weakening of the sub soil, which makes it unable to resist the concentrated pressure on the toe of the wall. Faulty construction and the violation of the ordinary rules of good masonry work—the latter being sometimes done with the idea that anything is good enough for a retaining wall—are also responsible for some failures, since they prevent the body of the wall from acting as a unit in resisting a tendency to overturn.
The tendency to slide outward at the bottom, and even the tendency to overturn, may be materially resisted by making the lower course with the joints inclined toward the rear. This method of construction is all the more logical, since it makes the joints nearly perpendicular to the line of pressure. In fact, the line of pressure is really a curved line which is more nearly vertical toward the top of the wall, and more and more inclined to the horizontal toward the bottom of the wall. The recognition of this principle has sometimes resulted in designing retaining walls on the principle illustrated in Fig. 69, which is somewhat similar to a section of an arch set on end. Such curved outlines, of course, are more expensive, and are sometimes inconvenient, and for that reason are but seldom adopted.
A detail which is frequently adopted in the design of retaining walls, is to use what is virtually a batter to the rear face of the wall, but to accomplish this by a series of steps on the rear of the wall. This not only per mits the use of rectangular blocks of stone and the employment of ver tical joints, but also adds considerably to the stability of the wall, since the vertical pressure of the earth on the horiz-ou t a I -steps adds considerably to the resistance to overturning. In Fig. 70 is shown a design for a retaining wall made to support a railway embankment in a location where the natural surface was so steep that the embankment would not readily obtain sufficient sup port. Although this use of a retaining wall is somewhat special, the general outline of the design not only conforms to the standards on that railroad, but represents good practice and is an illustration of many of the points referred to above. It should be noted that in this case the total width of the base of the wall is nearly one-half the height.