## 4 Physical Similarity Models
### The Results of the Physical Similarity Model  
The results of the physical similarity simulation experiment for 1# piece are shown in Figure 11. The fracture formed by hydraulic fracturing is delineated by the yellow dashed lines in the figure. It can be observed that the fracture initiated from the bare-eye section within the borehole and extended downwards, successfully crossing the immediate roof-pseudo roof interface (sandy mudstone-mudstone). The hydraulic fractures changed direction at the cementation interface between the mudstone and coal rock, continuing to penetrate into the coal seam. Eventually, the fractures penetrated through the coal rock, resulting in an overall staircase-like pattern. The interpretation of acoustic emission monitoring is presented in Figure 12, showing the formation of smaller elliptical fracture within the roof and a clear separation of the coal seam directly below the borehole, indicating significant interlayer fracturing.  
The results of the physical similarity simulation experiment for 2# piece are shown in Figure 13, and the interpretation of the acoustic emission monitoring is presented in Figure 14. The fracture in Test Specim 2 initiated from the bare-eye section within the borehole and formed a larger elliptical fracture within the roof. The downward extension of the fracture did not penetrate the interbedded mudstone layer. The hydraulic fractures propagated along the interface between the mudstone layer and the sandstone layer of the roof, eventually penetrating through the specimen. As a result, the hydraulic fractures did not affect the coal seam, and the overall fracture pattern appeared as a T-shaped fracture.  
Figure 11: Physical simulation results of hydraulic fracturing for 1# piece.  
From the experimental process, it can be concluded that when horizontal boreholes were arranged within the sandy mudstone of the fractured coal seam roof, were under conditions of reasonable vertical distance and high-volume fracturing fluid injection, and if the coal seam had a thin pseudo roof of mudstone (pseudo roof thickness not exceeding 4 cm), the fracture can propagate through the immediate roof-pseudo roof interface (sandy mudstone-mudstone interface) and the pseudo roof-coal seam interface (mudstone-coal seam interface), extending into the underlying coal seam. The fracture formed a curved and irregular vertical fracture, indicating that hydraulic fracturing can achieve the goal of the simulation.  
Figure 14: Schematic diagram of fracture interpretation for acoustic emission monitoring of 2#.  
Figure 12: Schematic diagram of fracture interpretation for acoustic emission monitoring of 1# piece.  
Figure 13: Physical simulation results of hydraulic fracturing for 2# piece.  
enhancing production and transforming soft and hard coal seams. However, when the coal seam had a thick mudstone pseudo roof (mudstone pseudo roof thickness of 6 cm or more), the mudstone presented strong resistance to hydraulic fracturing, making it difficult for the fracture to propagate into the underlying coal seam. Thus, the mudstone pseudo roof acted as a disadvantageous factor for hydraulic fracturing and production enhancement in the coal seam.