# Estimating RQD for Rock Masses Based on a Comprehensive Approach
## 3 Case Study
### Geometric Information Acquisition of Rock Mass Discontinuities Based on Photogrammetry  
Traditional contact survey methods that use a compass and tape measure to collect discontinuity data are generally insufficient and inefficient. When measuring the joints of high-risk rock mass, surveyors are jeopardized. As a result, numerous scholars [36; 47; 48; 49]  
Figure 3: Geographical location of the study area. have begun to adopt non-contact measurement technologies such as 3D laser scanning and photogrammetry to collect rock discontinuity data and verify their accuracy in recent years. Close-range photogrammetry is applied to acquire rock discontinuity data from a fresh outcrop in the study area. The detailed photogrammetry principle can be found in the literature [50; 51], and Figure 4 depicts its specific field operation example. Digital close-range photogrammetry technology obtains multi-angle digital images of the target slope at close range using optical photography equipment such as digital cameras and then utilizes algorithms to detect the same feature points in different photographs (that is, in Figure 4, \(\mathrm{P_{L}}\) and \(\mathrm{P_{R}}\)) to generate a 3D model of the target slope. In addition, a target disc and a range pole must also be positioned on the slope. The distance between the center of the top and lower disc of the range pole is 2.35 m, and a compass is required to measure the azimuth angle between the target disc and the lower disc, providing a true direction and size reference for the 3D model. It is worth noting that it is necessary to select an appropriate distance between two shots, that is, the baseline distance, according to the distance to the measurement target to improve the success rate of calculating the 3D model. A three-dimensional model of the research slope surface can be created using the procedures described above. Assuming that the discontinuity is a spatial plane, the mathematical expression of the plane where the discontinuity is located can be obtained by fitting the plane with the least squares method according to the coordinates of the feature points on the discontinuity. Therefore, the orientation of the discontinuity can be calculated according to the normal vector of this plane. This allows the geometric parameters of the outcrop, such as orientation distribution, trace length, and liner density, to be further statistically calculated. Figure 5 depicts the measurement results and distribution of the study area discontinuities. Figure 4: An example showing the general method of discontinuity observation using photogrammetry. Figure 5: Schematic diagram of discontinuity measurements and results. (**a**) Attitude data partition; (**b**) Pole diagram of orientation of discontinuities. According to the discontinuity grouping, as shown in Figure 5, the sample size of each group can be obtained, and if the Fisher distribution is assumed, the orientation concentration parameter \(\kappa\)[52] is given by  
\[\kappa=\frac{n-2}{n-\sqrt{\left(\sum_{i=1}^{n}\cos\alpha_{i}\sin\beta_{i} \right)^{2}+\ \left(\sum_{i=1}^{n}\sin\alpha_{i}\sin\beta_{i}\right)^{2}+\ \left(\sum_{i=1}^{n}\cos\beta_{i}\right)^{2}}} \tag{19}\]  
where \(n\) is the sample size of a given discontinuity group; \(\alpha_{i}\), and \(\beta_{i}\) are the dip direction and dip angle, respectively, of the \(i\)th fracture; \(i\) = 1, \(\ldots\), \(n\); cos is the cosine operator; and sin is the sine operator. \(\kappa\) is generally representative of fracture-to-fracture parallelism and ranges from 0 to infinity, with larger values indicating greater parallelism [53]. A difficulty with fracture network modeling lies in estimating the probability distribution of the fracture disc diameter from the probability distribution of the trace length.