## 2 Establishment of a Nonlinear Discrete Creep Model  
### Engineering Background and Structural Characteristics of the Surrounding Rock  
The dip angle of the No. 2-1 coal seam in Quandian Coal Mine is approximately 27\({}^{\circ}\), with a coal thickness of 4.5 m and a coal strength index (\(f\)) less than 0.5. The coal is characterized as soft, small, loose, and granular, and it exhibits extrusion rheology tendencies. The transportation roadway associated with the 11,050 working faces is a measured roadway that is located at a buried depth of approximately 550 m. The excavation of the roadway is carried out along the roof. The section of roadway is designed as a straight wall arch, with dimensions of 5.2 m in width and 4 m in height. The net section area of the roadway measures 17.9 m\({}^{2}\). The immediate roof of the coal seam is primarily composed of sandy mudstone and siltstone, with a thickness ranging from 1.5 to 5 m. The immediate floor consists mainly of sandy mudstone and siltstone, with a typical thickness ranging from 2.5 to 5 m.  
In the shed-cable combined support system, the transportation roadway of working face 11,050 experienced significant deformation. The maximum approach amounts for the roadway roof, floor, and the two ribs were 1045 mm and 1233 mm, respectively. Additionally, the local floor heave of the roadway ranged from 600 mm to 800 mm. The 36U sheds were severely deformed, with some even broken. The maximum deformation amount reached 500 mm, significantly impacting the normal production and operation of the mine. This deformation scenario is illustrated in Figure 1b. Promptly after completing excavation, a monitoring section was established. Figure 1b shows the response of the original support to peripheral rock deformation over time during the excavation period. Under the original support, the roadway deformation exhibited clear creep characteristics. During the decay-state creep stage from 0 to 20 d, the deformations of the two ribs, which were 396 mm and 245 mm, respectively, were smaller than those of the roof and floor. The steady-state creep stage was relatively brief. In the accelerated-state creep stage, not only were the deformations of the two ribs larger than those of the roof and floor, but the maximum deformation rates for the two ribs, at 19.2 mm/d and 9.6 mm/d, respectively, were also greater.  
The YTJ-20 rock detection recorder (Xuzhou Zhongkuang Huatai Technology Development Co., Ltd., Xuzhou, China) is utilized for the observation and analysis of the internal structure of the surrounding rock on the ribs. Representative graphics, depicted in Figure 2, are selected for analysis. Borehole peeping results indicate a noticeable granularity in the soft coal on both ribs. The argillaceous sandstone, after a depth of 1.9 m on the left rib, exhibits severe fracturing. Within the range of 0-0.5 m on the right rib, the surrounding rock shows slight fragmentation, while the coal appears coarse. In this state, the failure of the shed's cable support structure is evident.  
Due to the prominent creep characteristics observed in the deformation of the transportation roadway in the 11,050 working faces of Quandian Coal Mine, along with the compromised integrity of the surrounding rock within the roadway, extensive crack development occurs. Consequently, this paper focuses on the selection of a suitable creep model and utilizes numerical simulation to investigate the creep characteristics specific to soft coal.  
Figure 1: The 11,050 working-face roadway situations: (**a**) The original shed cable support of the roadway; (**b**) Deformation characteristics of the roadway.