## 3 Mechanical Characteristics of a THR Subject to Loading Under Different Parameters  
A roof's bending moment and limiting span directly affect the magnitude of energy accumulating within the strata. The greater the bending moment and the limiting span, the more significant the energy accumulation will be; hence, the stronger the SPBs in the coalface. To understand the macroscopic influence of different parameters on the bending moment and limit the span, we performed a case study using the UMC in the ZCM, where the extraction has been completed, and the mining conditions are similar to those discussed above. In this UMC, the roof thickness is \(h=8\) m, the angle of upward mining is \(\alpha=15^{\circ}\), the limiting span is \(l=21\) m, the elastic modulus is \(E=4.5\) GPa, [PERSON]'s ratio is \(v=0.25\), the tensile strength of the roof is \(\sigma_{t}=3.2\) MPa, the foundation coefficient is \(k=2000\) MPa/m, and the equivalent overburden load is \(q=1\) MPa for the THR. We analyzed the mechanical features of the THR subject to loading under different parameters (foundation coefficient, roof thickness, roof load, angle of upward mining, and overhang length).  
(1) Foundation coefficient (\(k\))  
The influence of the foundation coefficient on the bending moment and limiting span is shown in Figure 2. The roof bending moments are consistently negative values, indicating tensile stress. The larger the foundation coefficient, the more significant the variation in the roof bending moment due to mining activities and the faster the bending  
load (see Figure 3(a)). As the roof load increases, the roof limiting span decreases abruptly, and the frequency of weighting increases in the coalface (Figure 3(b)).  
(4) Angle of upward mining (\(\alpha\))  
The influence of the angle of upward mining on the bending moment and limiting span is characterized in Figure 5. The scope of influence on the bending moment does not vary with the angle of upward mining, and it extends about 10 m deep into the coal bodies ahead. The roof bending moment is affected in both the free overhang and coal-bearing zone, though to a lesser extent than other factors. The maximum bending moment occurs at about 2 m in front of the coal wall, the value being about \(-\)228 MN\(\cdot\)m (see Figure 4(a)). Moreover, the angle of upward mining affects the roof limiting span to a much lesser degree compared to other factors, and a non-linear increase is observed, as with all other factors (see Figure 4(b)).  
(5) Overhang length (\(l\))  
The influence of overhang length on the bending moment and limiting span is characterized in Figure 6. As the overhang length increases, the scope of influence on the bending moment expands continuously. The bending moment is affected in both the free overhang and coal-bearing zone, and the free overhang is more significantly influenced. The influence scope in the coal-bearing zone is consistently maintained at about 10 m in front of the coal wall. For every increase in the overhang length by 5 m, the maximum roof bending moment increases by about 40-90 MN\(\cdot\)m. A non-linear increase is observed, and the overhang length is a much more potent influencer than other factors. However, the increase in the overhang length does not affect the position where the maximum bending  
Figure 4: Influence of roof load on the bending moment and limiting span.  
Figure 5: Influence of angle of upward mining on the bending moment and limiting span.  
moment occurs. The maximum bending moment consistently occurs at about 2 m in front of the coal wall, and its magnitude is significantly influenced by the overhang length (Figure 6a). Additionally, as the roof limiting span increases, the fracture tensile strength of the roof increases continuously (see Figure 6b). Roofs with higher tensile strength generally have a longer overhang span.  
(6) Summary and comparison  
The mechanical characteristics of the THR subject to loading under different parameters are summarized in Table 1.