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 53

− these local failures result from sudden propagation of pre-existing microcracks
in the grains, controlled by the theoretical laws developed in fracture mechanics;

− these failures are mainly indirect tensile failures, similar to those that develop
in the “Brazilian test”. Failure mode is mainly Mode I, due to tensile stresses
induced in the grains by the loading of the granular assembly;
− in a grain with cracks of width c , the failure stress in Mode I is given by the
following expression:

K

[3.21]

σ ≈

Ic

ft

π c

where k 1c is the propagation threshold.

Figure 3.9. Principal features of grain breakage a) and b) basic sketches;
c) typical experimental results of Marsal (1973)