# Creep Behavior of Rocks and Its Application to the Long-Term Stability of Deep Rock Tunnels
## 2 General Creep Background  
Under specific load influenced by time at constant temperature [26], the creep of rocks generally manifests in four traditional phases, namely instant elastic strain, primary creep, secondary creep, and tertiary creep [12; 26; 27; 28; 29; 30; 31; 32; 33]. The instant elastic strain is reversible and can takes place promptly when a constant load is applied. Primary creep is ephemeral and usually exhibits a decelerated strain rate. Secondary creep is the steady phase where the strain rate remains constant. Tertiary creep is the final phase which is generally characterized by an accelerated strain rate until the creep life is exhausted. Creep characteristics are observed in different types of rocks. The creep curves of the latter are basically similar despite their different strengths [34]. Figure 1 illustrates the creep behavior of rocks. Depending on the exposure conditions, exception can be made for certain rocks. In fact, at great depth, the rocks are generally subjected to high stresses. Under such stress levels, some hard rocks may display two-phase creep behavior and their failure can be brittle [11]. It should be noted, however, despite intact hard rocks generally deforming at low creep rates, their time-dependent behavior is considerable in many situations [35; 36]. Depending on the magnitude of the confining pressures, even some soft rocks can be deformed without exhibiting all phases of creep. For example, it was experimented by [PERSON] et al. [37] that only primary creep occurred during the deformation of shale rocks under high confining pressure. However, given the mechanical nature of creep, it is rare to observe soft rocks deforming without showing tertiary creep. In fact, one of the remarkable characteristics of soft rocks is that their creep deformation is significant [22].  
Generally, rocks show their creep behavior when their creep threshold is reached [14]. It is therefore important to precisely estimate such a threshold in terms of load or stress  
Figure 1: Sketch showing the creep behavior of rocks (Reprinted from [PERSON] et al. [25], Copyright ©2022, with permission from the publisher, License No. 5352440395617).  
for better control. The stress grade that generates the first cracks or fractures is usually considered as stress threshold grade [38]. More precisely, the stress threshold is regarded as the maximum load which engenders a non-severe creep deformation [39]. Depending on the rock type and conditions, rapid creep deformations may occur due to exceeding stress thresholds which may be different in the axial and lateral directions of the rocks [40]. Secondary and tertiary creep stages emerge to express plastic strain when the applied stress exceeds the threshold [14; 41; 42]. As an unstable creep stage, tertiary creep mainly appears when the secondary creep strain rate is greater than zero [43]. Ordinarily, as reported by [PERSON] et al. [44], the coupled effect of load and damage causes creep strain in the tertiary creep. Due to the unsteady behavior of tertiary creep that usually leads to failure in an accelerated manner, to ensure the long-term safety and stability of underground structures, the steady creep phase must be precisely controlled. The steady creep is viewed as the level of stress lower than the long-term resistance of rocks and which does not allow the triggering of tertiary creep [23]. Nevertheless, since tertiary creep is the nonlinear accelerated creep phase, the accurate prediction of its occurrence is extremely important to reveal the possible end of the long-term stability of underground openings.