Note Return to text — DISCUSSION.

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, (as given by Equation (8)), below it, and regard this line as the free surface of non-coherent earth of the same specific weight and angle of repose as the given earth; compute the thrust against the wall for such earth, devoid of cohesion, by methods pertaining to such earth; the thrust thus found is assumed to be approximately the true thrust on the wall for the original coherent earth. It is proper to state that Résal rejects the sliding-wedge theory for non-coherent earth, and uses a method of his own, which involves elaborate tables given in his book. The wedge theory is admittedly imperfect, mainly because the surface of rupture is a curve, but we have seen that it agrees with experiments on model walls or retaining boards, when properly interpreted, and it will be used, as before, in computing the earth thrusts, , below, for earths devoid of cohesion. The graphical method has already been indicated.[Footnote 28]