Theories of Lateral Pressure

Conclusion. It

is generally conceded that for a level earth surface and a vertical back, the most common case, the ordinary theories do not greatly differ, and that all give results that are safe. Not infrequently a wall is designed according to some one of the common theories without any factor of safety on the assumption that the errors in the theory amount to a sufficient factor of safety. Apparently, the ordinary formulas give a value for the lateral pressure that is much greater than the real pressure, and assume the point of application lower than it is in fact, the error in the one case neutral izing, in part at least, that in the other; but apparently the first error is so great that the net overturning moment by the ordinary theories is two or three times greater than the real moment.

The ordinary theoretical formulas are of but little value in design ing retaining walls. The problem of the retaining wall is not one that admits of an exact mathematical solution, since the conditions can not be expressed in algebraic formulas. Something must be assumed

in any event, and it is far more simple and direct to assume the thickness of the wall at once than to derive the latter from equa tions based upon a number of uncertain assumptions.

Theoretical investigations of many engineering problems which in every-day practice need not be solved with extreme accu racy, are useful in determining the relations of the various elements involved, and thus serve as a guide to the judgment and as a skeleton upon which to group the results of experience; but the preceding discussion shows that the present theories of the stability of retain ing walls are not sufficiently exact to serve even this purpose. Furth ermore, the stability of a retaining wall is not a purely mathematical problem. Often the wall is designed and built before the nature of the backing is known; and the variation of the backing, due to rain, frost, shock, extraneous loads, etc., can not be included in any formula.