THEORY OF STABILITY.
A retaining wall proper may fail (1) by sliding on the plane of any horizontal joint, or (2) by over turning about the front edge of any horizontal joint, or (3) by crushing at the front edge of any horizontal section. The preceding methods of failure refer to the body of the wall and not to the foun dation.
A wall which is held at the top may fail by bulging out near the center; but such a wall is not rightly called a retaining wall, and is not considered in this connection. Such a wall acts as a masonry beam, and not by its weight as a true retaining wall.
In the discussion of the stability of dams, it was shown that in order to determine the effect of the thrust of the water against the wall, it is necessary to know (1) the amount of the pressure, (2) its point of application, and (3) the direction of its line of action. Similarly, to determine the effect of the thrust of a bank of earth against a wall, it is necessary to know (1) the amount of the pressure, (2) its point of application, and (3) its line of action.
In the present state of our knowledge but little is known con cerning the amount, the point of application, or the line of action of the lateral pressure of earth against a retaining wall. The difficulties in the matter may be briefly explained as follows: AC, Fig. 107, resents the back of a retaining wall, and AD the surface of the ground. The earth has a tendency to break away and come down some line, as CD. The force
ing to bring the earth down is its weight; and the forces tending to keep it from coming down are the friction and the cohesion along the line CD, and the sistance of the wall. The pressure against the wall depends upon the form of the line CD. If the constants of weight, friction, and cohesion of any particular ground were known, possibly the form of CD, and also the amount, point of application, and line of action of the thrust on the wall could be determined; but at present there are no adequate experi mental data on this subject.
Notwithstanding the fact that since the earliest ages constructors have known by practical experience that a mass of earthwork will exert a severe lateral pressure upon a wall or other retaining structure, there is probably no other subject connected with the constructor's art in which there exists the same lack of exact experimental data. On the other hand, there is almost no other phase of construction in which there is proportionally an equal amount of theoretical mathematical investigation. Apparently, each new investigator has recognized the inadequacy of former theories, and has sought to present a new one with the hope that it might be more satisfactory. Of course, mathematical investigations unsupported by experiments or experience are a very uncertain guide.