, for earth devoid of cohesion and having a free surface,
. The importance of these conclusions lies in this: that for the wall vertical, the earth surface horizontal, the earth thrust being horizontal or otherwise, the shorter method is available. If preferred, the thrust on the wall,
, for the earth devoid of cohesion, with the free surface,
, for either direction of the thrust, can be evaluated by the graphical methods ([page 404]) hitherto given.
Since this paper was written, Résal’s “Poussée des Terres,” Deuxième Partie, on Coherent Earths, has appeared.[Footnote 27] ] In it the author gives an exhaustive discussion of lines of rupture for a great number of cases. The equivalent of [Equation (7)] is found for the case of the horizontal pressure on a vertical plane when the free surface of earth is horizontal; but it was found to be impracticable to derive a formula for the earth thrust for the general case of the earth surface sloping at an angle to the horizontal, the wall being either inclined or vertical. In fact, for such cases, the intensity of the earth thrust at any depth is not a linear function of the depth, as obtains in the case shown by [Fig. 24]. Hence Résal resorts to the following approximation: Conceive a line drawn parallel to the surface, at a depth,
