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Accurately obtaining rock mass discontinuity information holds particular significance for slope stability analysis and rock mass classification. Currently, non-contact measurement methods have increasingly become a supplementary means to traditional techniques, especially in hazardous and inaccessible areas. This study introduces an innovative semi-automatic method to identify discontinuities from point clouds. A modified convolutional neural network, AlexNet, was established to identify discontinuity sets. The network consists of five convolutional layers and three fully connected layers, utilizing 1 × 3 normal vectors computed by K-nearest neighbor and principal component analysis as input and generating an output value “i” that represents the identified discontinuity set associated with the “i” category. Learning samples for network training were randomly selected from point clouds and automatically categorized using the improved fuzzy C-means (FCM) based on particle swarm optimization (PSO). The orientations of individual discontinuities, identified from the discontinuity set using hierarchical density–based spatial clustering of applications with noise, were calculated. Two outcrop cases were employed to validate the efficacy of the proposed method, and parameter analysis was conducted to determine optimal parameters. The results demonstrated the reliability of the method and highlighted improvements in automation and computational efficiency. [ABSTRACT FROM AUTHOR]

The geometry of rock blocks, including shape and size, is a crucial factor affecting the quarry's profitability. The block's dimension is limited by the fracture network properties, especially discontinuity's orientation, and spacing. Volumetric joint count (Jv), and weighted joint density (WJd) are two well-known indexes to determine the average block's volume. In this investigation the discontinuity properties of eight quarries are determined through the line and aerial mapping surveys. The investigation was performed along 2258 m scanline in 63 slope benches. Different indexes were used to compare the obtainable rock block's geometry. An empirical index was proposed considering different aspects of discontinuity network to increase the accuracy of measurements. The index was introduced based on the number of joints in each joint set, average spacing of joints in each joint set, and the total number of joints recorded during the investigation. The joint mean spacing index allows us to estimate the average volume of blocks and evaluate the quarry's profitability. By increasing the ratio of the joint mean spacing index, the obtainable rock block's volume and mine profitability increase. [ABSTRACT FROM AUTHOR]

Smartphones are usually packed with a large number of features. An increasing number of researchers are paying attention to the technological capabilities of smartphones, which is a new topic and research interest. This paper proposes a method using smartphones and digital photogrammetry to measure the discontinuity orientation of a rock mass. Smartphone photos satisfying a certain overlap rate provide an efficient method for generating point cloud models of rock outcrops based on image matching. Using the target and the generated point cloud model allows for determining actual geographic coordinates and the measurement of discontinuity orientations. The method proposed has been applied to two different study areas. The discontinuity orientations measured by the proposed method are compared with those measured by the manual method in two cases. The results show a good agreement, verifying the reliability and accuracy of the proposed method. The main contribution of this paper is to use knowledge of coordinate rotation to determine the actual geographic location of the model through a square target. The equipment used in this study is simple, and photogrammetric field surveys are easy to carry out.

Identification of rock discontinuities caused by orientation is an important basis for rock mechanics analysis and slope stability assessment. In order to obtain more objective and accurate clustering results, a modified K-means clustering algorithm based on genetic algorithm and simulated annealing algorithm is proposed, which overcomes the shortcomings of traditional K-means algorithm and realizes global optimization. A similarity measurement based on the negative sine-squared value of the acute angle between discontinuity unit normal vector was used to replace the original Euclidean distance measurement. In addition, the Xie-Beni validity index and the Davies-Bouldin validity index were introduced to determine the optimal clustering number. The validity of the method was analyzed on artificial and literature data where the data are synthetic and the clustering results can be clearly grasped; the results show that the maximum clustering error of the artificial data is 5.87% and the minimum is 0.24%. Meanwhile, the proposed method was used to clustering the discontinuities of rocky slopes on National Highway 317 in Sichuan Province, Southwest China. The results clearly demonstrate that the method achieved good and realistic clustering results with stronger robustness than other methods. [ABSTRACT FROM AUTHOR]

Highlights: An effective method for determining rock discontinuity sets based on the MWOA is proposed. The proposed method has a good clustering effect, convergence speed, and stability The proposed method can determine rock discontinuity sets with little user intervention [ABSTRACT FROM AUTHOR]

In the analysis of rock slope stability and rock mass hydraulics, the dominant partitioning of discontinuities of rock masses is a very important concept, and it is still a key for establishing the three-dimensional (3-D) network model of random discontinuities. The traditional graphical analysis method is inadequate and greatly influenced by subjective experience. A new method using density-based spatial clustering of applications with noise (DBSCAN) algorithm is proposed for the dominant partitioning of discontinuities of rock mass. In the proposed method, we do not need to determine the centers of every cluster before clustering, and the acnodes or outliers can be eliminated effectively after clustering. Firstly, the spatial coordinate transformation of the discontinuity occurrence is carried out and the objective function is established by using the sine value of the angle of the unit normal vector as the similarity measure standard. The DBSCAN algorithm is used to establish the optimal clustering centers by searching the global optimal solution of the objective function, and the fuzzy C-means clustering algorithm is optimized and the mathematical model of the advantage grouping of rock discontinuities is established. The new method and the fuzzy C-means method are compared and verified by using the artificially randomly generated discontinuity occurrence data. The proposed method is a better method than the fuzzy C-means method in general cases, and it can provide more accurate results by eliminating the acnodes or outliers. Finally, the proposed method is applied to discontinuity orientation partition data at Maji dam site, Nujiang River, and there is good agreement with the in situ measurement. [ABSTRACT FROM AUTHOR]

A methodology for determining overbreaks in hard rock tunnel construction using the drill-and-blast technique is presented in this paper. The methodology was developed for and applied to crystalline medium- to thick-bedded limestone, but it can be used in any jointed hard rock mass. Overbreaks are inevitable in hard rock tunnelling in a low-confinement environment (shallow tunnels up to several hundred meters deep) as a result of wedge failures along unfavourably oriented discontinuities caused by blasting. It is widely accepted in engineering practise that overbreaks will be inevitable even if smooth contour blasting is applied. If not controlled, overbreaks can result in extreme financial and time costs; and determining, predicting, and mitigating them is the key to successful tunnel construction in hard rock. Technological overbreaks, which are caused by the inappropriate use of drill-and-blast excavation, are not easily distinguished from the inevitable overbreaks dictated by the geological conditions with which they interfere and overlap. A methodology was developed with the aim of distinguishing the two causes of overbreaks, which can be applied in any phase of tunnel construction for evaluation or mitigation. The analysis of key inputs, including geological face mapping, shear strength tests along discontinuities of the rock mass, and their spatial orientation relative to tunnel advancement and survey overbreak measurements, is presented in this paper. Due to the stochastic and statistical nature of the problem, a probabilistic concept was also applied as part of the method so that the probability of failure around unprotected tunnel sections could be determined. The so-called stability criterion is introduced to distinguish between stable and unstable sections in terms of the probabilistic safety factor. The quantification of overbreaks, including the threshold value distinguishing technological from geological overbreaks, is proposed. The application of the methodology, demonstrated on an 8.1 km long section of a 12 km long pressure tunnel in hard rock, is presented in the paper. [ABSTRACT FROM AUTHOR]

In the analysis of rock slope stability and rock mass hydraulics, the dominant partitioning of discontinuities of rock masses is a very important concept, and it is still a key for establishing the three-dimensional (3-D) network model of random discontinuities. The traditional graphical analysis method is inadequate and greatly influenced by subjective experience. A new method using density-based spatial clustering of applications with noise (DBSCAN) algorithm is proposed for the dominant partitioning of discontinuities of rock mass. In the proposed method, we do not need to determine the centers of every cluster before clustering, and the acnodes or outliers can be eliminated effectively after clustering. Firstly, the spatial coordinate transformation of the discontinuity occurrence is carried out and the objective function is established by using the sine value of the angle of the unit normal vector as the similarity measure standard. The DBSCAN algorithm is used to establish the optimal clustering centers by searching the global optimal solution of the objective function, and the fuzzy C-means clustering algorithm is optimized and the mathematical model of the advantage grouping of rock discontinuities is established. The new method and the fuzzy C-means method are compared and verified by using the artificially randomly generated discontinuity occurrence data. The proposed method is a better method than the fuzzy C-means method in general cases, and it can provide more accurate results by eliminating the acnodes or outliers. Finally, the proposed method is applied to discontinuity orientation partition data at Maji dam site, Nujiang River, and there is good agreement with the in situ measurement.

Identification of rock discontinuity sets is essential for each studied jointed rock slope, and is also an initial step in many existing methods for rock slope stability analysis. This paper presents a new hierarchical agglomerative clustering method using modified agglomerative nesting (MAGNES) algorithm for automatically partitioning discontinuity sets. It is an orientation-based clustering method, and different linkage criteria (single, complete, and average) are incorporated for merging two closest clusters. The performance of MAGNES is tested using a complicate artificial data set, Shanley and Mahtab’s data set, and a real data set from unmanned aerial vehicle (UAV) survey. In addition, the clustering results of four other well-recognized clustering methods are also chosen as comparisons. It shows that the single linkage criterion is inapposite for partitioning orientations and the complete linkage criterion is not robust. Only MAGNES using average linkage criterion (MAGNES_AVG) shows good performance for detecting discontinuity sets. Generally, the main discrepancies among the clustering results lie mainly in the poles at the boundary of two adjacent joint sets. Considering the real data sets are characterized by “ground truth,” the artificial data set with known classification labels is used to further test which method performs better. The number of misclassification points is adopted as an evaluation index, and MAGNES_AVG performs best in partitioning the poles at the boundary of adjacent joint sets. Another advantage of the proposed algorithm is that it is independent of initial parameters, which is user-friendly. [ABSTRACT FROM AUTHOR]

This study wants to give a contribution to the semi-automatic evaluation of rock mass discontinuities, orientation and spacing, as important parameters used in Engineering. In complex and inaccessible study areas, a traditional geological survey is hard to conduct, therefore, remote sensing techniques have proven to be a very useful tool for discontinuity analysis. However, critical expert judgment is necessary to make reliable analyses. For this reason, the open-source Python tool named DCS (Discontinuities Classification and Spacing) was developed to manage point cloud data. The tool is written in Python and is based on semi-supervised clustering. By this approach the users can: (a) estimate the number of discontinuity sets (here referred to as "clusters") using the Error Sum of Squares (SSE) method and the K-means algorithm; (b) evaluate step by step the quality of the classification visualizing the stereonet and the scatterplot of dip vs. dip direction from the clustering; (c) supervise the clustering procedure through a manual initialization of centroids; (d) calculate the normal spacing. In contrast to other algorithms available in the literature, the DCS method does not require complex parameters as inputs for the classification and permits the users to supervise the procedure at each step. The DCS approach was tested on the steep coastal cliff of Ancona town (Italy), called the Cardeto–Passetto cliff, which is characterized by a complex fracturing and is largely affected by rockfall phenomena. The results of discontinuity orientation were validated with the field survey and compared with the ones of the FACETS plug-in of CloudCompare. In addition, the algorithm was tested and validated on regular surfaces of an anthropic wall located at the bottom of the cliff. Eventually, a kinematic analysis of rock slope stability was performed, discussing the advantages and limitations of the methods considered and making fundamental considerations on their use. [ABSTRACT FROM AUTHOR]

A methodology for determining overbreaks in hard rock tunnel construction using the drill-and-blast technique is presented in this paper. The methodology was developed for and applied to crystalline medium- to thick-bedded limestone, but it can be used in any jointed hard rock mass. Overbreaks are inevitable in hard rock tunnelling in a low-confinement environment (shallow tunnels up to several hundred meters deep) as a result of wedge failures along unfavourably oriented discontinuities caused by blasting. It is widely accepted in engineering practise that overbreaks will be inevitable even if smooth contour blasting is applied. If not controlled, overbreaks can result in extreme financial and time costs; and determining, predicting, and mitigating them is the key to successful tunnel construction in hard rock. Technological overbreaks, which are caused by the inappropriate use of drill-and-blast excavation, are not easily distinguished from the inevitable overbreaks dictated by the geological conditions with which they interfere and overlap. A methodology was developed with the aim of distinguishing the two causes of overbreaks, which can be applied in any phase of tunnel construction for evaluation or mitigation. The analysis of key inputs, including geological face mapping, shear strength tests along discontinuities of the rock mass, and their spatial orientation relative to tunnel advancement and survey overbreak measurements, is presented in this paper. Due to the stochastic and statistical nature of the problem, a probabilistic concept was also applied as part of the method so that the probability of failure around unprotected tunnel sections could be determined. The so-called stability criterion is introduced to distinguish between stable and unstable sections in terms of the probabilistic safety factor. The quantification of overbreaks, including the threshold value distinguishing technological from geological overbreaks, is proposed. The application of the methodology, demonstrated on an 8.1 km long section of a 12 km long pressure tunnel in hard rock, is presented in the paper.

This study wants to give a contribution to the semi-automatic evaluation of rock mass discontinuities, orientation and spacing, as important parameters used in Engineering. In complex and inaccessible study areas, a traditional geological survey is hard to conduct, therefore, remote sensing techniques have proven to be a very useful tool for discontinuity analysis. However, critical expert judgment is necessary to make reliable analyses. For this reason, the open-source Python tool named DCS (Discontinuities Classification and Spacing) was developed to manage point cloud data. The tool is written in Python and is based on semi-supervised clustering. By this approach the users can: (a) estimate the number of discontinuity sets (here referred to as “clusters”) using the Error Sum of Squares (SSE) method and the K-means algorithm; (b) evaluate step by step the quality of the classification visualizing the stereonet and the scatterplot of dip vs. dip direction from the clustering; (c) supervise the clustering procedure through a manual initialization of centroids; (d) calculate the normal spacing. In contrast to other algorithms available in the literature, the DCS method does not require complex parameters as inputs for the classification and permits the users to supervise the procedure at each step. The DCS approach was tested on the steep coastal cliff of Ancona town (Italy), called the Cardeto–Passetto cliff, which is characterized by a complex fracturing and is largely affected by rockfall phenomena. The results of discontinuity orientation were validated with the field survey and compared with the ones of the FACETS plug-in of CloudCompare. In addition, the algorithm was tested and validated on regular surfaces of an anthropic wall located at the bottom of the cliff. Eventually, a kinematic analysis of rock slope stability was performed, discussing the advantages and limitations of the methods considered and making fundamental considerations on their use.

This study compared the reliability of discontinuity orientation data collected in 2016 using unmanned aerial systems (UAS) with traditional transit compass data as a control, to evaluate UAS-generated results for rock slope stability analysis. The 2016 UAS operations were primitive by 2020 standards. Lessons learned are reviewed and related to UAS procedures common today. Two sites in Virginia were selected: a cut slope along State Route 629 (Site 1) and an abandoned shale quarry below Cove Mountain (Site 2). For logistical reasons, a different UAS was used at each of the two sites. Overlapping images from UAS flights were used to create point clouds from which discontinuity orientation data were extracted. Discontinuity data from both UAS and transit compass methods were imported into Dips 7.0, Roc-Plane 3.0, and Swedge 6.0 software for stereonet, statistical, and kinematic analyses. Statistical evaluation of the data sets suggested better overall reliability of UAS results for Site 2 than for Site 1. Compared to transit compass data, Site 1 UAS results are reliable for plane failure analysis only, whereas Site 2 UAS results are reliable for analyzing all types of failure. Possible reasons for this include different drone systems used at the two sites with different navigation and camera characteristics, interference from high-voltage electrical transmission lines at Site 1, and biases in human versus artificial interpretations. Compensating for some identified factors is now simpler by adding surveyed ground-control points to the model. Representative compass data should always be acquired for quality assurance. [ABSTRACT FROM AUTHOR]

The present article exposes the procedure to achieve the three-dimensional geometric model of a rock mass from a pair of photographic shots made with a current camera, use of free/open software such as Octave and other free libraries, construction of equipment and simple tools and the appropriation of important knowledge in artificial vision. It is described taking as an example the three-dimensional model of a blast cut of the rock mass of the Santa Rita Quarry, located southwest of the city of Medellín (Colombia). Finally, it is shown by a validation, based on field measurements, that the procedure described here is promising so that it can be established as a tool for the geometric characterization of discontinuities of rock mass. [ABSTRACT FROM AUTHOR]

This paper presents a new method for extracting blocks and calculating block size automatically from rock surface 3D point clouds. Block size is an important rock mass characteristic and forms the basis for several rock mass classification schemes. The proposed method consists of four steps: 1) the automatic extraction of discontinuities using an improved Ransac Shape Detection method, 2) the calculation of discontinuity intersections based on plane geometry, 3) the extraction of block candidates based on three discontinuities intersecting one another to form corners, and 4) the identification of “true” blocks using an improved Floodfill algorithm. The calculated block sizes were compared with manual measurements in two case studies, one with fabricated cardboard blocks and the other from an actual rock mass outcrop. The results demonstrate that the proposed method is accurate and overcomes the inaccuracies, safety hazards, and biases of traditional techniques. [ABSTRACT FROM AUTHOR]

Use of the scanline mapping technique in geometric surveys of rock discontinuities can often lead to a bias, in that discontinuities are not always observed when they are at small angles to the scanline. Terzaghi introduced the concept of a blind zone to explain this bias, and developed a widely used procedure to correct for it. Unfortunately, little is known about errors that may occur when the Terzaghi procedure is used outside the blind zone. This paper presents a detailed derivation to show that such errors arise with this application of the Terzaghi procedure. This error was evaluated using simulated orientation data and a case study of the 2008 Wenchuan earthquake (Sichuan, China). The results of these tests yield the optimal values of grid size and sample density for reducing the error. [ABSTRACT FROM AUTHOR]

This paper presents a new method for extracting discontinuity orientation automatically from rock mass surface 3D point cloud. The proposed method consists of four steps: (1) automatic grouping of discontinuity sets using an improved K-means clustering method, (2) discontinuity segmentation and optimization, (3) discontinuity plane fitting using Random Sample Consensus (RANSAC) method, and (4) coordinate transformation of discontinuity plane. The method is first validated by the point cloud of a small piece of a rock slope acquired by photogrammetry. The extracted discontinuity orientations are compared with measured ones in the field. Then it is applied to a publicly available LiDAR data of a road cut rock slope at Rockbench repository. The extracted discontinuity orientations are compared with the method proposed by Riquelme et al. (2014). The results show that the presented method is reliable and of high accuracy, and can meet the engineering needs. [ABSTRACT FROM AUTHOR]

The mechanical and hydraulic behavior of rock masses vary from one domain to another because of the presence of discontinuities. Hence, structural domain boundaries should be determined according to the properties of these discontinuities. In this work, a new method for identifying structural domain boundaries based on discontinuity orientation and trace length is proposed. The new method is performed in three steps. First, Schmidt plots are divided into equal-area patches on the hemisphere. Second, the discontinuities occurring in each patch are ranked according to their trace lengths. Third, the Wald-Wolfowitz runs test is used to analyze the sequence of discontinuities. The results obtained by applying the new method to four simulated discontinuity data sets were more rigorous than Miller's method in that Miller's method only considers discontinuity orientation whereas the new method considers both orientation and trace length. Both the proposed method and Miller's method gave the same, reliable, results when they were applied to discontinuity data collected from four adjacent adits at the Songta dam site. Only PD232 and PD252 corresponded to the same structural domain according to the two methods, because the discontinuity data collected from PD232 and PD252 had not only similar orientation distributions but also similar trace length distributions. The other advantage of the new method is that it can be used to evaluate the homogeneity of structural populations with small sample sizes. [ABSTRACT FROM AUTHOR]

The article focuses on the identification of rock discontinuity sets through K-means algorithm based on particle swarm optimization (PSO) (KPSO) where K stands for the number of clusters. Topics discussed include the representation of the directional data planar structure and spatial orientation, the steps in KPSO method, and the application of the algorithm on the real discontinuity data sets collected at the dam site of hydropower station in Songta, China.

The article presents a study which examines the rock slope instability using spatially distributed structural orientation data in Darjeeling, India. It discusses a geographic information system (GIS)-based methodology for rock slope instability assessment based on geometrical relationships between rock's topographic slopes and structural discontinuities. It reports that the stress-induced rock slope instability tends to increase with increasing level of water saturation in unstabled rock slopes.

Orientation data of discontinuities are of paramount importance for rock slope stability studies because they control the possibility of unstable conditions or excessive deformation. Most orientation data are collected using linear sampling techniques, such as borehole fracture mapping and the detailed scanline method (outcrop mapping). However, data acquired by such linear sampling techniques are subject to bias, owing to the orientation of the sampling line. Even if a weighting factor is applied to orientation data to reduce this problem, the bias will not be significantly reduced when certain sampling orientations are involved. If the linear sampling orientation nearly parallels the discontinuity orientation, most of these parallel discontinuities will be excluded from the survey results. This phenomenon can cause serious misinterpretation of discontinuity orientation data because critical information is omitted.In the case study, orientation data collected using the borehole fracture mapping method (vertical) were compared to those based on orientation data from the detailed scanline method (horizontal scanline). Differences in results for the two procedures revealed a concern that a representative orientation of discontinuities was not accomplished. Equal area, polar stereo nets were used to determine the distribution of dip angles and to compare the data distribution for the borehole method with that for the outcrop scanline. [Copyright &y& Elsevier]

This study presents experimental results from assessing fault orientation using triangulation and a combinatorial algorithm. We constructed two geological surfaces with vertical and inclined faults. These surfaces were documented by boreholes and represented by triangulated surfaces. We first calculated orientations for a small sample of triangles genetically related to faults that were also members of the Delaunay triangulation. To reduce the epistemic uncertainty regarding the true fault strike, we applied a combinatorial algorithm that allowed us to investigate the orientation distribution of all planes genetically related to the fault. The experiment revealed three unintuitive effects that require further studies: 1) greater concentration of observations about the true dip direction; 2) the same dip direction for different triangles; and 3) triangles that dip in the opposite direction to the fault. To conduct spatial clustering within surfaces, we suggest considering a broader interval of orientations related to faults. This broader interval serves to honor the observation that orientations can be genetically related to faults, even if they indicate a relatively high directional within-dissimilarity. We suggest statistical methods for circular data to investigate the resulting distributions. The computer code associated with this study is open source and freely available. • Assessing uncertainty on fault orientation using a three point approach. • Combinatorial algorithm was used to constrain the fault strike. • Counterintuitive behavior of the triangles' orientation was demonstrated. • Implications for conducting spatial clustering were given. [Display omitted] [ABSTRACT FROM AUTHOR]

Realistic discontinuity network modelling of rocks requires the accurate input of the three-dimensional discontinuity orientation distribution (3DDOD), but in practice, access to such three-dimensional information is limited. Fouché recently developed a method for estimating the 3DDOD from one-dimensional scanline-mapping observations. However, little is known about the error in such 3DDOD estimates. This study focuses on (1) the error and its possible contributors, (2) error prediction, and (3) error mitigation. An error investigation based on synthetic discontinuity geometry data reveals that the 3DDOD estimates are not always accurate. The error is significantly impacted by three factors: the Fisher constant (к), the angle between the major discontinuity plane and the mapping scanline (θ), and the discontinuity sample size (n), with larger к , θ , or n values contributing to lower errors. This к -, θ -, and n- dependent error appears to be inherently related to the sample density, which is defined as the pole number per unit cell (1° × 1°) in the Fouché method. Additionally, a predictor of the error based on an error-and-factors empirical relationship is developed to provide precise error prediction and optimize the scanline sampling for error mitigation. The weakness of the developed predictor is also disclosed. [ABSTRACT FROM AUTHOR]