RELIEVING ARCHES. In extreme cases, the pressure of the earth may be sustained by relieving arches. These consist of a row of arches having their axes and the faces of their piers at right angles to the face of a bank of earth. There may be either a single row of them or several tiers; and their front ends may be closed by a vertical wall,— which then presents the appearance of a retaining wall, although the length of the archways is such as to prevent the earth from abutting against it. Fig. 113 represents a front view and a vertical transverse section of such a wall, with two tiers of relieving arches behind it.
To determine the conditions of stability of such a structure as a whole, the horizontal pressure against the vertical plane OD may be determined, and compounded with the weight of the combined mass of masonry and earth OAED, to find the resultant pressure on the foundation.
The resistance to slid ing depends only upon the weight of the wall and the coefficient of friction, and hence is independent of the form of the vertical cross section. The resistance to crushing depends upon the relative position of the center of pressure and the center of the base, and varies approximately as the stability against rotation; and hence the form of the vertical cross section that gives greatest stability against rotation also gives the greatest stability against crushing. The resistance to overturning depends upon the moment of the weight of the wall, and for a given amount of masonry the longer the moment arm the greater the stability; and hence the nearer the center of gravity of the wall is to the earth to be supported, the greater is the economy of material, which requires that the back of the wall shall lean toward the earth. But in order that the wall may be self-sup
porting before the back-filling is deposited, the center of pressure should preferably fall within the base, although with care, particu larly with monolithic concrete, the center of pressure may safely fall a little outside of the base. However, in localities where the ground freezes, it would not be wise to build a retaining wall leaning toward the earth, on account of the heaving action of the frost— unless the back-filling is thoroughly drained.
The above shows that in discussing the stability of a retaining wall, it is not sufficient to give simply the thickness at the base in terms of the height, as is usually done. A wall whose vertical cross section is a right-angled triangle has exactly twice as much stability when the earth is against the vertical side as when it against the hy potenuse, if the vertical component of the earth pressure be neglected.
Sometimes attention must be given to the available area above and behind the retaining wall, and then the .cost of land also must be considered.. It may be that the price of land is such as to make a wall with vertical front and inclined back on the whole the most economical, for the saving in the cost of land may more than balance the expense of the extra masonry.
It is usual to build the face of the wall with a small batter and to step or slope the back so as to maintain a constant ratio between the width at any point and the height of the wall above that point. Re taining walls usually have a top width of 18 inches or 2 feet to give resistance against frost and lateral blows.