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 59

We notice that we find the same value of the exponent as the one already
obtained in section 3.1.3.3.
Figure 3.12. Evidence of scale effects in Charles and Watts compilation
3.2.2.3. The scale effect rule on the shear strength envelope
3.2.2.3.1. General case
In the above analysis, reasoning is based on the “central trend distribution”
where grain crushing resistances follow Weibull's theory with a parameter m = 6.
Therefore, the failure stresses vary with the grain diameter, according to a power
law with an exponent 3/ m = -1/2 (see section 3.2.1.3).
All the data reported by [MAR 72] and others on grain breakage show a
scattering in the values of parameter m for the different materials. This scattering
can be attributed to differences in the defect distribution within the grain material,
according to the nature and origin of these materials. A direct use of parameter m
determined on each material appears to improve the representation of particle
breakage statistics. So, the analysis presented above can be reconsidered with the
use of -3/ m instead of 1/2 in the effect of the characteristic grain diameter, which
leads to the following result that may be called the “scale effect rule on shear
strength envelope”.