**2.4 Damage evolution and failure in brittle rocks**

Over (geological) time, ductile deformation processes involve continuum mechanisms such as dislocation slip or migration of atomic vacancies within crystals resulting in distortion (pure or simple shear strain) [39]. However, in brittle materials, failure is controlled and governed by progressive damage driven by the pre-existing and new cracks initiation and evolution in the maximum load direction [40, 41]. **Figure 8** presents the four distinct stages during brittle deformability and failure: (i) closure of pre-existing cracks; (ii) linear elastic behavior; (iii) stable crack growth; and (iv) unstable crack growth, which leads to failure and the peak strength.

**Figure 8.** *Stress - strain response of brittle rock deformability and time-dependent behavior of creep and/or relaxation.*

#### *Engineering Geology*

Stress–strain curves for brittle rocks can be used to determine the: (i) crack initiation stress (CI); (ii) critical damage stress or axial yield stress (CD), and (iii) uniaxial compressive strength (UCS). While UCS strength can inhibit the loading rate and testing procedure influences, CD is the true upper bound yield strength when obtained in the lab, according to ISRM [42] standards [43]. In the limit CD, can drop in situ to the lower bound defined by CI. This lower bound is relatively insensitive to moderate pre-existing damage and other influences and is found to be 30–50% of standard UCS in brittle rocks as measured in the lab [44] or by in situ back analysis [45]. Below CI, the sample is genuinely elastic, with no new damage occurring in the sample.
