On the other hand, in the case of an embankment the normal load upon the earth is not affected, but an additional weight is superimposed; consequently, to prevent slips or subsidence from overweighting, there is a limit to the height of an embankment, apart from economical considerations of its deposition. The problem to determine is, therefore, the limit of the height to which an embankment may be deposited without exceeding the safe load that the natural ground will permanently sustain. The safe load upon the earth of which an embankment is composed is referred to in due course.
Let
S = the safe load in tons per square foot upon the original ground or earth not artificially deposited.
H = the theoretical limiting height in feet of an embankment.
W = the weight in tons of a cubic foot of the deposited earth.
Note.—When the earth is of a mixed character, the safe load should be that of the weakest soil.
The condition of equilibrium is that the height is not greater than the safe load divided by the weight of the ground, and is consequently given by the expression—
H = S
W.
In order to prevent a reference to other books, a table is appended of the approximate weights of different earths in their ordinary condition, compiled from the best authorities.
The weights are those of solid rock, therefore, when it is deposited they will be lighter according to the volume of the interstices.