## 1 Introduction  
As the construction of mountain tunnels continues to increase, the safety of construction in weak surrounding rock has caused significant concerns in the tunnel engineering community [1, 2, 3, 4]. Among these concerns are large deformation problems resulting from the large amounts of ground stress in soft rock tunnels. This problem has become prominent because the increase in deformation caused by the nonlinear rheological behavior of the surrounding squeezing rock results in a reduced amount of space for running trains, delayed construction, and increased construction materials' consumption and cost. In some cases, it also seriously affects the long-term safe operation and maintenance of the tunnel [5, 6, 7, 8, 9]. These safety issues have been observed in various tunnel projects, e.g., the Muzhailing Tunnel of the Gannan Weiwu Expressway and the Dali West Water Conveyance Tunnel of the Central Yunnan Water Diversion Project. Site monitoring results have suggested that deformation can be as large as 1500 mm when it was converged [10]. Therefore, it is necessary to investigate possible engineering remediation measures to control squeezing rock deformation. To this end, the rheological behavior of the squeezing rock must be considered in the design activities to create tunnel supports. Rheological models are integral for describing rock deformation during tunnel excavation. Most of the models combine the basic elements of other models to describe the viscoelastic properties of squeezing rock [11; 12; 13]. They consider both the transient and the steady-state regimes of rock rheology. However, many engineering practices and laboratory test studies have shown that soft rocks exhibit nonlinear rheology under certain stress levels [14; 15; 16; 17; 18; 19; 20]. In other words, there is a third regime, i.e., accelerated rock rheology regimes. Therefore, a complete nonlinear rheological model should consider the transient, the steady-state, and the accelerated regimes of rock rheology [21; 22]. The constitutive model [23] for viscoplastic elements in the acceleration stage of nonlinear rheology considers the two-fold criteria (such as the Mohr-Coulomb criterion) as the threshold of the acceleration regime. However, experimental and theoretical studies have shown that the intermediate principal stress significantly influences the strength of rock mass [24; 25; 26; 27; 28]. This provides the motivation for the present study, in which a non-linear rheological model is combined with the Drucker-Prager yield criterion. The latter allows for the consideration of the effect of the intermediate principal stress on the strength of rock mass. The aim of the present paper is to determine the length of the rock bolts for tunnels by considering the nonlinear rheological behavior of squeezing rock. It is well known that rock bolts represent a popular permanent support measure to increase the strength of surrounding soft rock. Thus, they are helpful to control the large deformation of the surrounding rock and to improve the stability of the excavated surface during the excavation of tunnels [29; 30]. However, the effects of the rock bolts on the long-term stability of the surrounding rock is a new topic. A few scholars have attempted to investigate the mechanical behavior of rock mass containing bolts [31; 32]. However, it was still challenging to determine the length of the rock bolts because the constitutive models that were developed excluded accelerated rock rheology regimes. Safety accidents often occur due to the wrong choice of bolt length. In this context, a nonlinear visco-elastic-plastic constitutive model for rock, referred to as the Komamura-Huang-Bingham model, combined with the Drucker-Prager (DP) yield criterion is proposed in the present paper. Numerical simulations adopting the proposed rheological model are performed and there is a focus on sensitivity analysis with respect to the length of the bolts and the ground stress.