## 4 Numerical Simulation of Repeated Supportability of Roadway Roof
#### 4.1.2 Numerical Simulation Results When the Direct Roof Is Sandy Mudstone  
The fragmentation range and displacement distribution of the roof strata, when composed of sandy mudstone, are presented in Figures 18-20. These figures illustrate the various thicknesses of the roof strata, namely 0.8, 1.6, and 3.2. Additionally, Figure 21 displays the displacement changes and relative displacement results along the monitoring lines of both the baseline and the roof strata.  
Figure 16: The results of roof crushing and displacement change when the direct roof thickness is 2.4 m. (**a**) Schematic diagram of roof crushing, (**b**) Changes in roof displacement.  
Figure 17: Basic roof and direct roof monitoring line displacement and relative displacement change results. (**a**) Direct roof thickness 0.8 m, (**b**) Direct roof thickness 1.6 m, (**c**) Direct roof thickness 2.4 m.  
Figure 15: The results of roof crushing and displacement change when the direct roof thickness is 1.6 m. (**a**) Schematic diagram of roof crushing, (**b**) Changes in roof displacement.  
Based on Figure 18, for the original rock stress and repeated support conditions, when the direct roof consists of sandy mudstone with a 0.8 m thickness, the maximum displacement of the direct roof surface reaches 28 mm. Although the roof plate has not exhibited any topping phenomenon yet, the crushing range of the roof plate has already reached the interface between the direct roof and the basic roof. Further in Figure 21a, the maximum relative displacement between the two displacement monitoring lines at the interface of the direct roof and the basic roof is recorded at 6 mm, indicating the onset of roof delamination.  
Figure 19: The results of roof crushing and displacement change when the direct roof thickness is 1.6 m. (**a**) Schematic diagram of roof crushing, (**b**) Changes in roof displacement.  
Figure 20: The results of roof crushing and displacement change when the direct roof thickness is 2.4 m. (**a**) Schematic diagram of roof crushing, (**b**) Changes in roof displacement.  
Figure 18: The results of roof crushing and displacement change when the direct roof thickness is 0.8 m. (**a**) Schematic diagram of roof crushing, (**b**) Changes in roof displacement.  
Based on Figures 19 and 20, it is observed that for direct roofs with thicknesses of 1.6 m and 2.4 m, the maximum extent of crushing spans a range of 0.8-1 m. The respective maximum displacements on the surface of the direct roof amount to 32 mm and 35 mm. When temporary support and permanent support work in conjunction, as depicted in Figure 21b,c, the maximum relative displacement along the two displacement monitoring lines at the interface between the direct roof and the basic roof remains below 2 mm. This observation falls within the acceptable range for the direct roof to remain stable and securely attached to the layer.  
Thus, in cases where the roof is composed of sandy mudstone and the thickness of the direct roof is less than approximately 1 m, the crushing range of the roof extends to the layering interface, leading to a certain level of detachment and presenting a safety risk to the permanent support structure. Consequently, when the roof thickness is less than 1 m, it is not suitable for repeated support of the roadway, and immediate provision of permanent support after excavation is required. On the other hand, when the roof thickness exceeds 1 m, it fulfills the criteria for repeatable support, meeting the conditions for employing stepping temporary support.