## 3 Results
### Values of the Inclinations Observed on the Land Surface  
The inclination values of the land surface determined using the geodetic measurements were calculated for the middles of the sections located between neighboring points. The value of the inclination (\(T\)) for the \(i,i+1\) section was calculated with Formula (9) as a quotient of the change in the altitude differences (\(\Delta h\)) of the \(i,i+1\) neighboring ground points between the final (\(f\)) (\(\Delta h_{(i+1)}\))--17 August 2019), and the initial (\(s\)) (\(\Delta h_{(i,i+1)s}\)--4 March 2019) measuring cycles, as well as the length (\(l\)) between the \(i,i+1\) points measured in the final cycle (\(f\)) (\(l_{(i,i+1)f}\)), as follows:  
\[T_{(i,i+1)}=\frac{\Delta h_{(i,i+1)f}-\Delta h_{(i,i+1)s}}{l_{(i,i+1)f}}\Big{[} \frac{\text{mm}}{\text{m}}\Big{]}, \tag{9}\]  
where the following holds:  
* \(f\)--The final measuring cycle;
* \(i\)--The number of measuring points;
* \(l\)--The length of the section [m];
* \(s\)--The initial measuring cycle;
* \(T_{(i,i+1)}\)--The measured value of the inclination [\(\frac{\text{mm}}{\text{m}}\)]. Table 4 presents the values of the altitude differences (\(\Delta h\)) measured at the \(i,i+1\) sections in the initial (\(s\)) and the final (\(f\)) measuring cycles, the lengths (\(l\)) of the sections measured in the final (\(f\)) cycle, the inclinations (\(T\)) measured after the end operations in the 1/II longwall of the \(405/1\) hard coal seam, the \(S\) biased and \(\vartheta\) unbiased estimators of the standard deviation, calculated according to Formulas (10) and (11), as follows:  
\[S=\sqrt{\frac{\sum_{i=1}^{N_{T}}\left(T_{i}-\overline{T}\right)^{2}}{N_{T}-1 }}\Big{[}\frac{\text{mm}}{\text{m}}\Big{]}, \tag{10}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & \(\mathbf{a}\) & \(\mathbf{tan}\beta\) & \(\mathbf{A_{1}}\) & \(\mathbf{R_{B}}\) \\ \hline Value & \(0.976\pm 0.0032\) & \(2.167\pm 0.0072\) & \(0.117\pm 0.0004\) & \(0.9967\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameter values for [PERSON]’s model (source: own study). \[\vartheta=\frac{S}{c_{33}}=\frac{S}{0.99222}\Big{[}\frac{\text{mm}}{\text{m}}\Big{]}. \tag{11}\]  
The results of the geodetic surveys carried out on the ground points indicate that the maximum values of the inclinations of the land surface occurred along the z51d-z52d section (\(T_{z51d-z52d}=18.6\)\(\frac{\text{mm}}{\text{m}}\), north from the B8 building), the z10d-z11d section (\(T_{z10d-z11d}=-14.2\)\(\frac{\text{mm}}{\text{m}}\), northeast from the B3 building), and the z07g-z08g section (\(T_{z07g-z08g}=-13.8\)\(\frac{\text{mm}}{\text{m}}\), northeast from the B2 building). It should be emphasized that to the north of the B2 and B3 buildings, ground steps occurred with heights of 15 cm and 20 cm, respectively, so they may be the cause of the increase in the inclination values in this area. The \(\vartheta\) unbiased estimator of the standard deviation was equal \(5.17\)\(\frac{\text{mm}}{\text{m}}\). Taking into account the categories of the mining area for the values of the inclinations presented in Table 5, the investigated mining area can be appropriately categorized. Each observed value of the \(T_{i,i+1}\) inclination was assigned an appropriate mining area category (Table 4), and then quantitative descriptions of the determined categories were made, as shown in Table 6.  
From the data presented in Table 6, the results show that the high values for the observed inclinations (4 th and the 5 th categories of mining area) represent 9.1% of all observed values for the inclinations. The largest share of all observed values had the inclinations of a terrain, which classifies it in the 1 st category of mining area (39.4%).