## 1 Introduction  
Deep-buried tunnels often suffer large deformations that can persist for a long period of time. Indeed, the host rocks of these tunnels usually tend to undergo appreciable time-dependent deformations, and their stability is increasingly affected. The rock mass properties, the rigidity, and the installation time of the support structure are among the major factors governing the displacements in the surrounding rocks of deep tunnels [1, 2]. In fact, in deep rocky environments where there are generally durable actions of high stress, abundant groundwater, and fluctuating temperatures, the time-dependent deformation and long-term stability of the host rocks of deep underground tunnels are of increasing concern. This is due to the fact that gradual deformation of the surrounding rocks is inevitable, once deeply buried tunnels are drilled. Owing to the unavoidable creep behavior of loaded rock materials [3, 4], the development of microcracks around underground tunnels is imperative [5]. Creep is the time-dependent strength and deformations of rocks [6], and it is linked to the long-term stability of deep rock engineering. The time-dependent behavior of deep soft rock engineering is generally viewed as important, and poses serious stability problems. In the field of tunnel engineering, considerable progress and fruitful results have already been achieved. In spite of that, it is still difficult to guarantee the long-term stability of deep soft rock tunnels, which typically suffer from extreme rheology, and are characterized by significant creep deformations. According to [PERSON] et al. [7], the consequences of dilatancy-induced high in situ stress and the deformation caused by inadequate support are responsible for the enormous deformation of such tunnels. The time-dependent behavior and long-term stability of deep rock soft tunnels based on rock creep have been investigated by many scholars and researchers. For example, by studying the key risks related to underground engineering, [PERSON] et al. [8] revealed that inordinate creep is the predominant cause of failure of deep underground storage structures. They explained that a better description and application of creep properties are of utmost importance to avoid failure of the mentioned structures, particularly when they are located in low-strength soft rock environments. On their sides, and by associating volumetric creep and deviatoric behavior, [PERSON] et al. [9] established a creep constitutive model for porous sandstone. However, their model cannot fully depict the behavior of surrounding rocks of deep tunnels constructed in bedded porous sandstones affected by the presence of water. Based on an improvement of the Burgers model and the empirical-theoretical method, a visco-elastic-plastic creep constitutive model was conceived by [PERSON] et al. [10] to reflect the time-dependent behavior and stability of deep soft rock tunnels mainly built in soft schist media. [PERSON] et al. [11] studied the creep behavior of deep sandstones, and employed fractional derivatives to design two nonlinear creep models that take into account viscoelasticity and time-dependent damage. However, the engineering applications of these models are not detailed. To combat the large deformation, and ensure the stability of deep tunnels located in broken soft rock layers, [PERSON] et al. [12] designed a creep model by taking the Burger Constitutive Viscoplastic (Burger model jointed to the Mohr-Coulomb body) model as a basis. They then analysed the possibility of optimizing the support scheme for these tunnels. A viscoelastic-plastic creep model was developed by [PERSON] [13] to forecast time-dependent deformations of deep soft rock roadways mainly lodged in mudstone. For their part, [PERSON] et al. [14] studied the long-term stability of deep tunnels using both the creep constitutive model of the surrounding rocks and that of the support, and emphasizing the long-lasting impact of creep on the support structure.