Crack growth is a major mechanism of f?acture in brittle rocks and rock masses. Since

laboratory cannot be directly used to determine of f?acture parameters pertinent to field situations

due to the different scales, it is important to analyze the mechanisms of crack propagation in situ.

Crack propagation is governed in many cases by interaction with microcracks. In the context

[ 1], the term microcracks is reserved for sufficiently small cracks capable of forming the fracture

process zone. The propagation of the microcracks within the material of the process zone can

model its strain-softening (post-peak softening) which simulates the cohesive forces (e.g., [2]).

However, the strain-softening is the stress-strain relationship characterizing volume elements

(VEs) of the material, whereas the conventional models of a crack with the process zone require

the knowledge of relationship between stresses and displacements. Therefore the explicit

introduction of the process zone thickness is necessary. This paper is a follow-up to a previous

one by the same authors [ 1], whose names are listed alphabetically.


Crack growth can be considered as successive fracturing of the VEs at the crack front (Fig. 1).

The fractured VEs form either the process zone or immediately the crack itself. Since the VEs are

not infinitesimal, their f?acture makes the crack effectively "thick". Its effective thickness is

assumed to equal the VE size H. Since any step of the real 3-D crack propagation requires

crushing the majority of the VEs along the crack front, the crack growth can be described in terms

of the average VE strength.

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