# Creep Behavior of Rocks and Its Application to the Long-Term Stability of Deep Rock Tunnels
## 3 Mechanism of Rock Creep  
It is well known that rocks are heterogeneous materials that naturally have micro-voids or microcracks and discontinuities. Under load, micro-voids and microcracks spread, multiply, and become larger and larger. These defects facilitate the evolution of rock creep over time. The creep mechanism of rocks can be seen at both microscopic and macroscopic scales. In microscopic scale, the creep deformation is mainly governed by the propagation of initial cracks and dislocation networks, as well as by the deformation provoked between the internal constituents of rocks [45]. For instance, the displacement of a large number of dislocations leads generally to plastic deformations. According to [PERSON] and [PERSON] [46], mechanisms of rock creep from a microscopic point of view can be cataclastic creep (retarded weakening of microstructure) and granular creep (friction-induced grain repositioning). Macroscopically, creep is a continuous anelastic deformation under constant loading [47]. In fact, the macroscopic creep deformation widely depends on the evolution of microcracks. Habitually, these build up gradually even under low loads, and can become increasingly important over time. As expressed by [PERSON] et al. [48], macroscopic creep deformations are caused by the inevitable time-dependent propagation of microcracks, even under low loads. Under high loads, microcracks can grow faster to produce microscopic creep strains. Macroscopic deformation and microcracks evolution can be correlated as follows [49]:  
\[\varepsilon=\beta(-\ln\left[1-\left(l+a\mu\right)^{3}\!D_{0}/\left(a\alpha \right)^{3}\right])^{1/m} \tag{1}\]  
where \(\varepsilon\) is axial strain; \(\beta\); \(m\): constants related to the material; \(D_{0}\) is initial damage; \(a\): radius of initial penny-shaped microcracks; \(l\): wing crack length; \(\mu\): cosine of the angle of crack concerned. Two types of evolution mechanism can be distinguished for macro-cracks. The first one is that macro-cracks can accumulate rapidly and generate fracture surfaces reflecting the creep fracture mechanism which is generally transient. The second one can be the long-term development of macro-cracks describing the steady state of the rock creep mechanism. It should be noted that the creep failure mechanism depends on the ductility and brittleness of rocks. In fact, such rock features evolve under the influence of embedding depth of the structures and geo-stress [50]. The spreading and coalescence of microcracks could be responsible for the failure triggered during brittle creep, while the ductile failure may be caused by dislocation-slip coupling where the exponential increase in steady creep rate is sudden [50]. In fact, brittle rocks involve quasi-linear axial deformation and non-linear lateral deformation [51], and they generally show no evident deformation at failure [52]. There is local stress concentration and relative crack concentration in the affected areas in brittle creep rupture [50]. However, it should be noted that such rocks are characterized by their ubiquitous dilatancy when compressed to failure [53]. According to [PERSON] et al. [54], brittle failure, triggered by the growth of mode I subcritical cracks, can be time-dependent. In the case of coalescence of many microcracks, the propagation of the cracks is described as unstable, indicating that the rocks can no longer bear increased loads [51]. However, there is no failure if the current long-term strength of the rocks is not attacked [55]. The main mechanism of the time-dependent steady-state behavior of rock creep is subcritical crack extension due to stress corrosion, while that of tertiary creep is crack interaction [56]. At great depths, due to moisture and groundwater pressure, stress corrosion cracking is common and is responsible for the continued propagation of fractures and spalling of brittle rocks [57].