# Creep Behavior of Rocks and Its Application to the Long-Term Stability of Deep Rock Tunnels
## 3 Mechanism of Rock Creep
Crack evolution is triggered in brittle rocks when the mode I fracture toughness (\(K_{IC}\)) is greater than the mode I stress intensity factor (\(K_{I}\)), and its rate can be expressed as [49]:  
\[\frac{dl}{dt}=\
u\bigg{(}\frac{K_{I}}{K_{IC}}\bigg{)}^{n} \tag{2}\]  
where \(l\): wing crack length; \(t\): time; \(n\): index related to stress corrosion; and \(\
u\): velocity characteristic of cracks. The ductile behavior of rocks is characterized by the exhibition of strong deformation before failure. It indicates the degree of plastic deformation of rocks. Generally, ductile creep provokes alteration of the stress state [58] and is characterized by a delocalized evolution [59]. Indeed, when closed microcracks develop by sliding friction and mode II failure, the deformation is ductile [60]. Specifically, over time, ductile deformation manifests as shear deformation and can be attributed to continuous events, namely the displacement of weak bonds in clay minerals, the displacement of interstitial atoms or atomic voids in crystals, or the sliding of dislocations [61]. A uniform stress distribution is generally observed in ductile creep rupture [50]. Ductile creep occurs mainly in soft rocks such as mudstone, sandstone, shale, or in other types of sedimentary rocks. Salt rocks are type of rocks that exhibit extraordinary ductile creep [22; 62]. Another creep failure mechanism is semi-brittle. In fact, when the contributions of the brittle and viscous deformation mechanisms to the adjustment of the strains are contemporaneous and notable during the deformation, there is the appearance of a semi-brittle creep [63]. Specifically, semi-brittle creep deformation is a type of strain mainly triggered when the creep strain rate is governed by pressure, applied stress, and temperature [64]. Semi-brittle creep can be either compact creep enduring rigid compaction or dilatant creep dealing with the highest differential stresses [54]. It is one of the predominant mechanisms in some rock types such as carbonate rocks [54]. More broadly, the creep mechanism of natural rocks can be described by the transition between brittle and ductile behavior. As at such depths there are usually increased pressures and temperatures, the brittle-ductile mutation is very common [59; 65]. The extent of microcracks inside rocks plays a key role in the brittle-ductile transition. Furthermore, as demonstrated by [PERSON] et al. [66], when microcracks and frictional slips are sufficiently distributed under the influence of increased confining pressures, the appearance of brittle-ductile fractures is possible in hard rocks. Basically, creep is a character common to any rock mass, but it is more prominent in clayey and organic rocks [67], as well as in weak rocks and in fractured rock masses [68]. As already mentioned, soft rocks, including salt rocks, exhibit high ductile creep deformation under loads. The creep deformations of these rocks are even greater with the complex general conditions of great depth. Furthermore, as reported by [PERSON] et al. [68], creep strain is large enough in jointed and fissured hard rocks. As the natural structure of rock masses usually contains many joints, fissures, fault zones [69], it can be understood that creep behavior is frequent in any type of rock mass. Therefore, understanding rock creep mechanism is essential for proper application in deep rock engineering.