# Creep Behavior of Rocks and Its Application to the Long-Term Stability of Deep Rock Tunnels
## 5 Potential Factors Influencing Rock Creep
### Damage and Time-to-Failure  
Damage can be an internal factor that has an extreme influence on rock creep. Similarly, the time-to-failure of rocks, which is particularly associated with the scope of damage, affects the process of rock creep. Owing to the stress perturbations that impose stress redistributions around the rocks surrounding the excavated areas, rock damage is inevitable. Excavation-damaged zones (EDZ) and excavation-disturbed zones (EdZ) are therefore evident consequences of stress redistributions. Generally, there is lasting damage to pertinent rock properties in the EDZ [104,105]. It should be pointed out that most of the rocks contain pre-existing damage which is increased by that generated by the tunneling. Then, their extent increases with time due to the time-dependent behavior of natural rocks. According to [PERSON] et al. [106], it is even indispensable to determine the damage generated by different deformations of rocks. Due to the random distribution of microcracks in rocks [107], the evolution of damage mainly results in nonlinear deformations [108]. Indeed, tertiary creep and rock failure can be caused by the time-dependent damage of rocks [109]. More specifically, as related by [PERSON] et al. [85], critical damage triggers the appearance of the tertiary creep. Typically, damage accumulates in the secondary creep phase and then reaches the tertiary creep until it leads to rock failure [8,110]. Under the effect of damage, the spectacular reduction in the mechanical properties of rock usually corresponds to the failure [111]. Therefore, a correct description of rock creep cannot be made without adequate consideration of the damage factor. The accuracy of constitutive rock creep models is questionable when they do not take into account the actual rock damage. The damage variable (\(D\)) can be expressed as follows [8,14]:  
\[D=1-\left(1-\frac{t}{t_{c}}\right)^{\frac{1}{1+\delta}} \tag{8}\]  
where \(t\) is the time initial; \(t_{c}\) is the moment of the total damage of rocks; \(\delta\) is a constant related to the rock material. Quantitatively, the damage factor can vary from 0 (intact rock) to 1 (rock totally damaged) during creep [8,14,21,32,101,112,113]. The damage effect on the overall creep process is considerable. It not only affects the rocks surrounding the tunnels, but also the linings. When these are not properly designed to resist rock creep deformation, they can be severely damaged over time [114]. As such, the damage severity to tunnel linings varies with the strength of the rocks. For tunnels located in weak rocks, the deformation of the linings can be uncontrollable and their failure may occur more quickly than expected. Even tunnels in high strength rocks can have their supports with a high extent of damage over time [115]. In this respect, selecting and developing rock constitutive creep models without evaluating and integrating the rock damage variable may be unrealistic. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Study (Year)** & **Rock Type** & **Specimen Conditions** & **Testing Type** & **Duration of Tests** & **Effect of Temperature on Rock Creep** \\ \hline [PERSON] et al., (2017) [64] & \multirow{4}{*}{Shale} & Contained a water & \multirow{4}{*}{C creep tests} & \multirow{4}{*}{2-7} & The increase in temperature leads to the increase of the primary creep strain as well as the decrease of the creep resistance. \\ [PERSON] et al., (2017) [64] & & & & & \\ [PERSON] et al., (2017) [64] & & & & & \\ [PERSON] et al., (2017) [64] & & & & & \\ [PERSON] et al., (2017) [64] & & & & & \\ [PERSON] et al., (2017) & & & & & \\ [PERSON] et al. The time-to-failure of rocks is the time taken for rocks to be fractured during creep until failure. It varies with the type of rocks and the applied stress. Specifically, with the increase of the latter and of the secondary creep rate, the time-to-failure reduces [31]. Under the effect of loads, fractures which generally result from the evolution and coalescence of pre-existing cracks cause the rock to break [116].