# Photogrammetry-Based 3D Textured Point Cloud Models Building and Rock Structure Estimation
## 5 The Rock Structure Analysis for the Rock Slope
Because the dimension of the studied slope is greater in the horizontal direction, several topographic sampling windows were placed at different locations of the slope (shown as Figure 9), and the average results were used. The area density (\(\rho_{\rm A}\)) and the mean trace length of joints (\(l_{\rm t}\)) in a sampling window were inferred with Equations (18) and (19) [30]. \[\rho_{\rm A}=\frac{m}{0.5\pi{d_{\rm c}}^{2}} \tag{18}\]  
\[l_{\rm t}=\frac{\pi{d_{\rm c}}n}{4m} \tag{19}\]  
where \(m\) is the number of joint endpoints inside a circular sampling window; \(n\) is the number of joint intersections with the circular scanline; \(d_{\rm c}\) is the diameter of the circular sampling window. The mean diameter of joint disks was estimated with Equation (20) [31]. \[{\rm E}({d_{\rm i}}^{2})=1.5{\rm E}(l_{\rm t}^{2}) \tag{20}\]  
where \(d_{\rm i}\) is the diameter of a joint disk. The volume density of joints (\(\rho_{\rm A}\)) was inferred with Equation (21) [32]. \[\rho_{\rm v}=\frac{\rho_{\rm A}}{{\rm E}(d_{\rm i})\cdot\sin(\gamma)} \tag{21}\]  
where \(\gamma\) is the angle between a topographic sampling window and the mean joint plane. The number of joint disks in each of the joint sets can be determined according to the volume density. The orientation and diameter distributions of the joint disks are shown in Figure 10. The parameters of the joint disk model built for the rock slope are listed in Table 4. The space distribution of the joint disks in each joint set and the final joint disk model are shown in Figure 11.  
The rock quality designation (RQD), which is defined as the percentage of the lengths of intact rock core pieces that are not shorter than 0.1 m, of the rock slope was calculated according to the joint disk model. A total of 300 equally spaced boreholes were drilled in the joint disk model, with 100 boreholes distributed on each of the planes of _xy_, _yz_, and _zx_. Figure 12 displays the layout of the boreholes in the model. The lengths of core pieces between two adjacent joints on the borehole lines were measured to calculate the value of RQD. Figure 13 shows the distribution of the lengths of intact rock core pieces. The average value of RQD is equal to 97.05%. According to Figures 12 and 13 and Table 4, the following points can be concluded. (1) The joints in set 1 are generally subhorizontal, with the mean dip value of 14.7\({}^{\circ}\), while the joints in sets 2 and 3 are nearly vertical, with the mean dip values of 76.6\({}^{\circ}\) and 81.5\({}^{\circ}\), respectively. (2) The sizes of the joints in set 1 are the largest in all 3 joint sets, with a mean length of 0.67 m. (3) The rock structure of slope is good, according to the value of RQD. (4) The method of photogrammetry-based rock structure analysis proposed in this study is applicable in real rock engineering. Figure 7:0 Parameters of the three joint sets used in the joint disk model. (**a**) Poles diagram of the joint disk orientations used in the joint disk model. (**b**) Diameter distributions of the three joint sets used in the joint disk model. (**b**) Diameter distributions of the three joint sets used in the joint disk model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Orientation**} & \multicolumn{3}{c}{**Diameter**} \\
**Joint Set Series** & **Volume Density (m\({}^{-3}\))** & \multicolumn{3}{c}{**(Fisher Distribution)**} & \multicolumn{3}{c}{**(Lognormal Distribution)**} \\ \cline{3-6}  & & **Dip Direction (\({}^{\circ}\))** & **Dip (\({}^{\circ}\))** & **\(K_{\mathbf{F}}\)** & **Mean Value (m)** & **Variance (m\({}^{2}\))** \\ \hline
1 & 3.02 & 335.6 & 14.7 & 12.0 & 0.67 & 1.28 \\
2 & 7.86 & 179.4 & 76.6 & 7.1 & 0.38 & 0.22 \\
3 & 3.99 & 90.1 & 81.5 & 8.1 & 0.31 & 0.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters used in the joint disk model of the rock slope. Figure 11: Joint disk models of the rock slope. Figure 12: Layout of the boreholes in the joint disk model.