, which has been driven by shield or by use of timbering, so that an appreciable settlement of the roof occurs; then the weight of the earth vertically over the tunnel is partly carried by the adjacent walls of earth, by friction and cohesion, and it would seem that such walls can be supposed to take the place of vertical grain bin walls, and that the theory of bin pressures corresponding may be made to apply. The theory that will be developed, which includes the influence of cohesion, is simply a modification of that used in developing Janssen’s formula, as given by Mr. Ketchum,[Footnote 19] ] and, for a ready comparison of results, his notation will be used.
In [Fig. 20], let
be the distance from the roof of the tunnel to the surface of the earth. Compute
from [Equation (3)] and lay it off from the top down.
