## 4 Analyses of Discontinuous Supporting in Gob-Side Entry Retention  
To explore the deformation law of the surrounding rock mass of gob-side entry retaining with large-diameter, concrete-filled steel tube roadside supports, a numerical model was established with the geologic parameters of the 91-101 working panel of Wang-Zhuang Coal Mine, as shown in Figure 8. The three-dimensional size was given by a length, width, and height of 205 m, 128 m, and 18 m, respectively. The diameter of the concrete-filled steel tube was 1.2 m. The model consisted of 961,280 units and 984,330 nodes. A uniform vertical stress of about 10 MPa was applied at the top of the model to represent the weight of overburden rock, the lateral pressure coefficient was set as 1.2, and the factors of the anchor bolts and cables support were not considered in this article. The model was set up with slip boundaries around the perimeter and fixed boundaries at the bottom. In addition, in order to clarify the impact of the concrete-filled steel tubes' future strength development on the deformation of the retained roadway surrounding rock, the model took into account the strength development characteristic of the concrete and servo-assigned the parameters of the concrete-filled steel tubes with the excavation. The constitutive model of rock stratum adopted the Mohr-Coulomb model, and the corresponding parameters of each rock stratum are shown in Table 1.  
Due to the fact that no built-in constitutive model of FLAC can accurately represent the mechanical properties of concrete-filled steel tubes, this study assumed the steel tube material as being in an elastic state and adopted an elastic constitutive model. Meanwhile, according to the literature, the strain-softening model is appropriate for concrete materials restrained by steel tubes, which reflects the diverse post-peak properties of concrete-filled steel tubes by setting the relationship between the cohesion and the internal friction angle \begin{table}
\begin{tabular}{c c c c c} \hline
**Lithology** & **Young’s** & **Poisson Ratio** & **Angle of Internal** & **Cohesion/MPa** & **Tensile** \\  & **Modulus/GPa** & & **Friction/\({}^{c}\)** & & **Strength/MPa** \\ \hline Fine sandstone & 12.3 & 0.27 & 35 & 6.0 & 4.0 \\ Mudstone & 8.75 & 0.26 & 30 & 4.9 & 3.8 \\
3\# Coal & 5.3 & 0.32 & 40 & 2.1 & 1.3 \\ Sandy mudstone & 12.3 & 0.27 & 35 & 6.0 & 4.0 \\ Fine mudstone & 15.0 & 0.26 & 34 & 6.5 & 4.3 \\ \hline \end{tabular}
\end{table} 
Table 1: Physical and mechanical parameters of numerical model stratum. Figure 8: Numerical model. and plastic shear strain. Tables 2 and 3 show the parameters corresponding to the elastic and plastic stages of the strain-softening model. The double yield model was adopted for the goat, and the stiffness of broken rock in the goat increased with the decrease in the volume of fractured rock, which is expressed as an increase in support to the overlying strata. The vertical displacements of the roof in the mining direction under different column spacings are shown in Figure 9. The cloud map shows that as the spacing of columns increased, the displacement of the roof and floor between the columns also increased. The area directly above the concrete-filled steel tubes was in a compression state, and the maximum tensile stress value of the roof and floor between the columns was sensitive to the change in column spacing. With the increase in column spacing, the maximum tensile value also increased. In order to make the arrangement of non-continuous supports achieve the effect of continuous wall roadside supports, the compressive stress field in the roof directly above the columns and the roof between the columns must form an \"intersection circle\" at the shallow part of the roadway roof and floor. The displacement of the roof in the section perpendicular to the mining direction under different column spacing was extracted for analysis, and the section plane was