A reexamination of the friction circle method for the stability analysis of slopes

Summary

The stability of earth slopes according to the friction circle method, as normally employed, is based on the condition of equilibrium of forces, and on the condition that at limit equilibrium the actuating and resisting forces are concurrent at one point. This particular condition, assumed in place of the general one of equilibrium of moments at the said stability limit, is not in accordance with the fundamental hypotheses of the kinematics of motion; it gives rise as well to the indetermination of the couple of values of the soil resistance parameters c (cohesion) and ϕ (friction) at limit equilibrium.

Therefore the problem is taken up again and resolved on the basis of rational equilibrium conditions and assuming that at failure in any point along the sliding circle the maximal strength of the material is developed and therefore limit values of c and ϕ proper to failure of the particular soil are uniformly reached along the circle itself.

On this basis the condition of equilibrium of forces determines one parameter of the distribution pattern of the normal components of stresses along the circle; the value of a second parameter of the said distribution, involved in the condition of equilibrium of moments, can be easily determined in an approximate way.

It is therefore possible to determine easily and speedily the arm of the total actuating force which realizes the limit condition of the supposed sliding movement along the considered circle. The comparison of this arm with the real one of the aforesaid force indicates the degree of stability for any considered circle.

The extension of the method to an embankment made up of two zones of different materials is also examined.