## 5 Field Measurement of Overburden Damage Height
### Three-Band Height Formula Correction Analysis  
Since the physical simulation and numerical simulation are already simplifying the relevant geological conditions, there are deviations between their obtained data and the actual data in the field. Therefore, in order to obtain more accurate research data, based on the above comprehensive analysis, four groups of data from similar physical simulation experiments, numerical simulation experiments, empirical formula analysis and field actual measurements are compared with the measured maximum value: the height of the collapse zone is 47.76 m, and the height of the water-conducting fracture zone development is 170.76 m. We refer to the empirical formula derived from a study by [PERSON] [38]:  
\[H_{m}=\frac{100\Sigma M}{0.49\Sigma M+19.12}\pm 4.17 \tag{1}\]  
\[H_{li}=\frac{100\Sigma M}{0.23\Sigma M+6.10}\pm 10.42 \tag{2}\]  
where: \(H_{m}\) is the height of collapse zone, \(H_{li}\) is the height of hydraulic fracture zone, and \(M\) is the thickness of coal seam mining, take 9 m.  
According to the formula of the height of the hydraulic fracture zone, the height of the overlying rock collapse zone in the mining area is 34.07-42.42 m, respectively; and the height of the fracture zone development is 99.74-120.57 m. In the process of using downhole quantitative detection, the amount of water injection leakage within this height should be focused on observation. The experimental observations and the values calculated by the empirical formula are now compared and analyzed as shown in Table 2.  
As shown in Table 2, the height of the hydraulic fracture zone calculated by empirical formula has a large error of \(-\)29.39% with the field measurement results. According to the calculation results in Table 2, because the field observation results of the development height of hydraulic fissure zone of mining overburden differ greatly from the calculation results of the empirical formula, and the development height of the hydraulic fissure zone of the mining working face is not clear, for the sake of safety, the maximum field observation \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method Classification**} & \multicolumn{2}{c}{**Overburden Damage Height/m**} & \multicolumn{2}{c}{**Error/\%**} \\ \cline{2-5}  & **Collapse Zone** & **Water-Conducting Fissure Zone** & **Collapse Zone** & **Water-Conducting Fissure Zone** \\ \hline Physical Simulation & 52.4 & 162 & +9.72 & \(-\)5.13 \\ Numerical Simulation & 48.11 & 164 & +0.73 & \(-\)3.96 \\ Empirical formulas & 42.42 & 120.57 & \(-\)11.18 & \(-\)29.39 \\ Field measurements & 47.76 & 170.76 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of two-band heights under different methods. data, taken as the height of hydraulic fissure zone under the conditions of this mine, the height of the collapse zone and the height of the hydraulic fracture zone of the traditional \"three under mining\" (abbreviation for coal mining under water bodies, under buildings and under railroads.) specification empirical formula are both expected to be significantly lower than the measured values. There will be certain safety risks if the relevant safety regulations are formulated in this way, while the prediction model of similar simulation experiments, numerical simulation and the actual measured values in the field are in good agreement, with an error of less than 5%. Therefore, the traditional empirical formula of the \"three under mining\" specification is optimized by using the variance coefficient to meet the actual needs of production mines. The standard deviation theory is applied to analyze the height of the hydraulic fracture zone and the height of the collapse zone, namely:  
\[\sigma=\sqrt{\frac{\sum\limits_{i=1}^{n}(x_{i}-\overline{x})^{2}}{n}} \tag{3}\]  
where: \(\overline{x}\) is the average of the data. The root mean square error of the collapse zone and the hydraulic fracture zone of the Wangwa coal mine No.