Granular Materials in Civil Engineering: Recent Advances in the Physics of Their Mechanical Behavior and Applications to Engineering Works - Multiscale Geomechanics: From Soil to Engineering Projects - page 65

Figure 3.14. Combined impacts on rockfill embankments safety factors, of size effects and
other key parameters: rockfill granulometric size, embankment height, and slopes

The results published by Charles and Soares [CHA 84] on rockfill slope stability
using Bishop's method for shallow circular failure lines including a power law shear
strength relation can be combined with our results on scale effects in order to
establish such a method.

3.3.2.2. Explicit scale effect in safety factors
Charles and Soares have demonstrated that the mathematical structure of the
static equilibrium equations leads to the following expression of the safety factor,
defined as the ratio between the available shear strength and the shear stresses
mobilized at equilibrium along the potential failure line:

Γ A.

( )

[3.36]

b,β

F=

S

(1-b)

γ.H

This expression put in separate factors, height H , coefficient A of the power law
expression of the shear strength envelope (see Figure 3.14) and an adimensional
stability coefficient Γ , depending on the slope β and on exponent b of the power law.

Furthermore, the computed values of coefficient Γ appear to be almost linearly
dependent on the slope coefficient cot β , as shown in Charles and Soares' diagram
presented in Figure 3.15, at least for usual slopes between 1.2 h/1v and 2.0 h/1v
(outlined zone in the diagram).