## 3 Results and Analysis
### Theoretical Analysis  
#### 3.3.1 Calculation of Overlying Load of CPB Roof  
The overlying load on the CPB roof is the vertical load acting on the CPB roof after mining the stope. There are many theoretical formulas for determining the overlying load  
Figure 4: Results of stress–strain measurements: (**a**,**c**) are the strains and stresses in 48# stope, (**b**,**d**) are the strains and stresses in 40# stope, respectively.  
of CPB roofs, but the different factors (the size of the stope, the physical and mechanical properties of the CPB and the overlying load on the CPB roof) considered in each formula lead to large differences in the calculated results [35; 36; 37; 38; 39]. This study investigates the theory of optimal CPB roof overburden calculation based on the field measurements and the engineering characteristics of the downward mining method [40; 41; 42; 43; 44].  
The more commonly used calculation theories are Platts theory of ground pressure, the Biebermann pressure theory, the Classical Janssen pressure theory and the Terzaghi bearing capacity theory, whose calculation models are shown in Equations (2)-(5) [45; 46; 47]. The Biebermann pressure theory, Classical Janssen pressure theory and Terzaghi bearing capacity theory take into account the size of the stope, the physical and mechanical properties of the filling body and the effect of the height of the overburdened filling body on the load, and their calculation methods are more reasonable. Although the Platts theory of ground pressure takes into account the size of the approach stope and the physical and mechanical properties of the filling body, it does not consider the key factor of the height of the overburdened filling body, so its calculation results are somewhat one-sided.  
(1) [PERSON] theory of ground pressure:  
\[q=\frac{\gamma\left[a+h\tan\left(45^{\circ}-\frac{\varphi}{2}\right)\right]}{f} \tag{2}\]  
In Equation (2), \(q\) is the load on the CPB roof, \(h\) is the height of the stope, \(a\) is the span of the stope, \(\gamma\) is the capacity of the filling body, \(\varphi\) is the friction angle in the filling body and \(f\) is the solidity factor.  
(2) [PERSON] pressure theory:  
\[\left.\begin{array}{l}q=\gamma H\left[1-\frac{H}{a_{1}}K_{1}-\frac{2c}{a_{1 }\gamma}(1-2K_{2})\right]\\ a_{1}=a+2h\tan\left(45^{\circ}-\frac{\varphi}{2}\right)\\ K_{1}=\tan\varphi\tan^{2}\left(45^{\circ}-\frac{\varphi}{2}\right)\\ K_{2}=\tan\varphi\tan\left(45^{\circ}-\frac{\varphi}{2}\right)\end{array}\right\} \tag{3}\]  
In Equation (3), \(H\) is the buried depth, \(c\) is the cohesion of the filling body and \(a\) is the span of the stope.  
(3) Classical Janssen pressure theory:  
\[q=\frac{\gamma S}{k\tan\varphi p}\left[1-\exp\left(-\frac{kpH\tan\varphi}{S} \right)\right] \tag{4}\]  
In Equation (4), \(S\) is the horizontal section area of the stope (\(s=a\times b\)), \(b\) is the length of the stope, \(p\) is the perimeter of the horizontal section of the stope and \(k\) is the lateral pressure coefficient.  
(4) Terzaghi bearing capacity theory:  
\[q=\frac{\gamma a_{1}-c}{k\tan\varphi}\left[1-\exp\left(-\frac{kH\tan\varphi}{ a_{1}}\right)\right] \tag{5}\]