# Creep Behavior of Rocks and Its Application to the Long-Term Stability of Deep Rock Tunnels
## 1 Introduction  
The creep behavior of rocks plays a fundamental role in tunnel engineering and related sciences. It usually occurs under the action of stresses exerted over a long period of time [1]. This is the case of underground structures which are generally planned to be operational for decades or even more than a hundred years. However, the deformations of these structures initiate rapidly once their surrounding rocks are excavated. Due to the complex loading-unloading process that the rocks undergo in the vicinity of the generated openings [2, 3], these are particularly softened and the extent of their deformation evolves as quickly as possible. As a result, there is formation of disturbed and damaged areas where the relevant properties of rocks are diminished. One of the most pronounced effects of rock excavations is that rock properties are lastingly altered in damaged zones. This is why one ordinarily observes considerable deformations and fractures around the tunnels [4]. In soft rocks particularly, large strain rates remain evident even after the installation of the initial supports of tunnels [5]. Nonetheless, depending on the relevant tunneling conditions and characteristics, any type of rock can present obvious deformations. In fact, with the evolution of time, the surrounding rocks always manifest their tendency to convergetowards the interior of the tunnels. Such tendency is usually associated with the spread of fractures and damage in excavated areas. This is mainly due to the fact that natural rocks contain pre-existing discontinuities and cracks which are generally increased by the effect of excavations. Indeed, the time-dependent deformation of rocks which is amply expressed by rock creep is therefore inevitable [6]. Rock creep is strongly related to the long-term stability of rocks [7; 8; 9; 10], and its effect on the long-term stability of structures is of great consequence [6; 11; 12]. Accordingly, its proper consideration is of paramount importance in assessing the long-term stability of tunnels [13]. Nevertheless, since rock creep is influenced by many factors that generally reduce its strength, the study of rock creep requires reasonable and thorough attention. Strong influencing factors include stress state, damage, water, and temperature. When these factors are not effectively considered in the assessment of rock creep parameters, the designed constitutive models may be ineffective in their actual applicability. For example, the accumulation of damage during creep can generally lead to rock failure [14; 15]. Effectively predicting the long-term stability of rock engineering therefore requires proper consideration of factors that strongly influence rock creep. Scholars and researchers have conducted numerous studies on creep behavior of rocks under different conditions. For instance, [PERSON] et al. [16] detailed creep failure of quasi-brittle materials such as rock and concrete subjected to high prolonged loads based on the development of a simple time-dependent continuous damage mechanics. [PERSON] et al. [17] studied the viscoelastic-plastic properties of amphibite to simulate the creep properties of these rock types via the method of loading and unloading staged by cyclic increment, under hydrous environment. They found that the rheological creep properties of amphibite are strongly affected by water and can be represented by the general shape of the Kelvin model. [PERSON] et al. [18] established the constitutive equations reflecting the time-dependent marble damage model based on experimental results. Their proposed mechanical model can describe the three stages of marble creep, which are essential to ensure the stability of underground structures both at the stage of their excavation and during their lifespan. From shear static test and shear creep test, [PERSON] et al. [19] revealed that the shear creep properties of limestone can be normally depicted by the Poyting-Thomson model.