## 4 Key Parameters of the PCO-Goaf Treatment Scheme
### Safe Thickness of the Overlying Rock in PCO-Goafs  
To ensure normal production and safe operation, the overlying strata of the open-pit mine must maintain a certain thickness when there are goafs underneath the OP-slope. Different methods are selected to calculate the safe thickness of the overlying strata [36], and the safe thickness of the PCO-goaf and roof is shown in Figure 5.  
M1--Thick-span ratio method: it is based on engineering experience.  
\[h=0.5K\cdot L \tag{6}\]  
Here, \(h\) is the thickness of overlying strata in the goaf, m; \(L\) is the span of goaf, m; and \(K\) is the safety factor, which is 1.3.  
M2--Intersection method of load transfer lines: it is based on engineering experience.  
\[h=\frac{L}{2\tan\beta} \tag{7}\]  
Here, \(\beta\) is the load transfer, and the diffusion angle is generally 35\({}^{\circ}\).  
M3--Pratt arch theory estimation method: under the action of gravity and load, the roof stress will form a natural arch, and the safe thickness of the roof should be two times that of the arch height.  
\[h=2\frac{0.5L+h_{K}\tan(45-\theta/2)}{f} \tag{8}\]  
Here, \(h_{K}\) is the height of the goaf, m; \(\theta\) is the rock internal friction angle, \({}^{\circ}\); and \(f\) is the Platts coefficient of the rock.  
M4--Beam theory calculation method in structural mechanics: according to the integrity of the goaf roof and surrounding rock, it can be divided into simple supported beam theory and cantilever beam theory.  
\[h=0.25L\frac{\gamma\cdot L+\sqrt{\left(\gamma\cdot L\right)^{2}+8 lq\sigma_{t }}}{l\cdot\sigma_{t}} \tag{9}\]  
Here, \(\gamma\) is the bulk density of the goaf roof rock, kN/m\({}^{3}\); \(l\) is the calculated width of the roof unit, =1 m; \(q\) is the additional load of the open pit, kPa; \(\sigma_{t}\) is the allowable tensile stress, kPa, and uniaxial tensile strength is the allowable tensile stress.  
M5--[PERSON]. [PERSON] theoretical calculation method: On the one hand, the theory considers the internal factors that affect the safety thickness of overlying strata in the goaf and also considers the influence of the working equipment on the upper step of the goaf.  
Figure 5: Relation between span of goaf and safety thickness of overlying rock.  
\[h=K\frac{0.25\gamma\cdot L^{2}/g+\sqrt{\left(\gamma\cdot L/g\right)^{2}+0.8q\sigma_{ B}}}{98\sigma_{B}} \tag{10}\]  
\[\sigma_{B}=\frac{\sigma_{n3}}{k_{3}k_{0}} \tag{11}\]  
Here, \(\sigma_{B}\) is the ceiling strength limit, MPa; \(k_{3}\) is the strength safety factor, \(k_{3}\) = 4-10; \(k_{0}\) is the structural weakening coefficient, \(k_{0}\) = 2-3; \(\sigma_{n3}\) is the ultimate strength of rock, taken as 7-10% of the \(\sigma_{c}\), MPa; and \(\sigma_{c}\) is the uniaxial ultimate compressive strength of the rock, MPa.  
M6--Theoretical calculation method of slab beam: The theory of plate beam mainly takes into account the mechanical properties of rock and assumes that the goaf is a plate beam with fixed ends, neglecting the influence of roof span and external load.  
\[h=K\frac{\gamma\cdot L^{2}}{2\sigma_{t}} \tag{12}\]  
The letters in the formula are the same as above.  
Due to the difference in the above six theoretical considerations, the calculated thickness of overlying strata is different to some extent. For safety, the maximum value is taken as the theoretical safe thickness. For example, the span of the 1365 m goaf is 54 m, which corresponds with 41 m for the thickness of the overlying rock.  
Based on the goaf data and the layout of detection holes, the primary blast hole spacing is 6 m with a row spacing of 4 m. The pre-split hole spacing is set at 1.5 m, while the main blast hole rows are staggered in a triangular arrangement. When positioning the main blast holes above void areas, a hanging-hole method is employed with a charge depth of 0.5 m from the top of the void area and a stemming length of 5 m. Uncoupled charges are used for pre-split holes with an ultra-deep setting of 0.5 m to ensure complete roof collapse in void areas, allowing for appropriate encryption of hole spacings.