Condition for the onset of bifurcation in en echelon crack arrays

Emergence and evolution of en echelon crack arrays play an essential role in the failure of geomaterials, regardless of the scale of deformation. This paper derives analytically an approximation for the critical crack size/spacing ratio at which a uniformly growing en echelon crack array yields to a non-uniform growing pattern of crack growth. Numerical results show that the critical crack size/spacing ratiocr(= a/d where a is the half crack length and d is the distance between the centres of two adjacent cracks) depends on the orientation of the crack array ø, the number of cracks N in the array, as well as the loading conditions. In general,crdecreases with N, but depends non-linearly on ø. When en echelon crack arrays are under far-field shearing along the direction of the crack array, our prediction forcris about 0.5715, comparing to the experimental observation of about 0.5. For rock joints containing en echelon cracks, the interpreted critical crack size at the onset of the alternating evolution of crack growth are 0.66 and 0.89 for ø = 26 and 6°, comparing to our predictions of 0.5695 and 0.6112, respectively.