# In-Situ Block Characterization of Jointed Rock Exposures Based on a 3D Point Cloud Model

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Sites

#### 2.1. Site 1: A Road Cut Slope in Catalonia, Spain

#### 2.2. Site 2: Yinshan Open-pit Copper Mine in Dexing, China

#### 2.3. A Synthetic Test Model: The Dataset of Cardboard Boxes

## 3. Methodology

#### 3.1. Treatment of Data Source

#### 3.2. Identification of Discontinuities from PCM

#### 3.3. PCM-DDN: Global Searching of Block Candidates

#### 3.4. PCM-DDN: Polyhedral Modeling

#### 3.5. PCM-DDN: Block Characterization

_{D}representation. The 25%, 50%, and 75% quantiles of IBSD

_{D}(D

_{25}, D

_{50}, and D

_{75}) and the mean volume were also calculated. As the PCM was surveyed in a geodetic coordinate system, all extracted discontinuities and blocks were also georeferenced. The exact position of every block was obtained, and the EBSD

_{D}with a volume indicator was analyzed to precisely reconstruct on-site spatial states.

_{D}integrated with $\alpha $ and $\beta $ was established as shown in Figure 8. Six zones that encompass basic shapes were classified to completely demonstrate the block shape, including C (cubic), E (elongated), P (platy), and three transitional shapes (CE, EP, and PC).

_{D}of extracted blocks can be determined using the stereographic projection method.

#### 3.6. PCM-SDS: Deriving Fundamental Discontinuity Parameters

#### 3.7. PCM-SDS: 3D Stochastic DFN Simulation

^{gen}[68]. The 3DEC was used here due to availability. The geometrical characteristics of discontinuities were adopted as the input properties; a series of discrete, planar, and disc-shaped discontinuities of finite size were created; and then, the cubic-shaped rock mass model was developed for block system generation [2,19,27,69,70].

#### 3.8. PCM-SDS: Block Extraction and Characterization

_{S}, BSD

_{S}, and BOD

_{S}were also acquired following the description in Section 3.5.

## 4. Results

#### 4.1. Results of the Synthetic Box Model

#### 4.2. Comparison of the Results of Site 1 Using Two Procedures

_{D}and IBSD

_{S}) of Site 1 are shown in Figure 12 and Table 3. Model ID 75 from PCM-SDS was selected for comparative analysis. It is apparent that the cumulative distribution curve of IBSD

_{D}basically falls in the stripe formed by IBSD

_{S}in all simulations. This similarity of the results relies on the well-exposed outcrop in the study area, which verifies the feasibility and validity of the PCM-SDS method. As seen from Table 3, the values of D

_{50}and D

_{75}and the mean block size from IBSD

_{D}are less than the values from IBSD

_{S}. This discrepancy could be attributed to the limited surveying area where the large blocks are poorly exposed and maintained. The EBSD

_{D}of 97 rock blocks extracted from PCM-DDN and their exact locations are presented in Figure 13.

_{D}and BSD

_{S}of model ID 75 are shown in Figure 14c,d. It can be observed that the BSD

_{D}and BSD

_{S}present similar trends, that is, the main distribution zones are the C, CE, E, and PC sections, which match the field observations well. The BSD

_{S}from simulations certainly illustrates an abundant shape presentation, while the smallest blocks range between all block shapes. The difference is that the BSD

_{D}is mostly dominated by C and CE shapes (Figure 14a), and the BSD

_{S}is mainly composed of E (≤D

_{75}, small blocks) and CE (>D

_{75}, large blocks) shapes (Figure 14b).

_{D}and BOD

_{S}of model ID 75) are shown in Figure 14e,f, and Table 3. The dominant block orientations (115°/26° from PCM-DDN and 124°/17° from PCM-SDS) are roughly consistent. The major dip directions of blocks are clearly distributed within the range of dip directions of Set 1 (127°/56°) and Set 2 (291°/45°).

## 5. Discussion

#### 5.1. Practical Application of the Proposed Method

- (1)
- (2)
- Blasting design, e.g., explosive consumption and fragmentation energy optimization for mining or tunneling [73]. Taking a quarry project as an example, the IBSD curve and the block shape distribution are important for blasting design and quarry yield prediction. The blasting can be considered as a transformation from IBSD to fragmented size distribution (or blasted block size distribution, BBSD) and the main framework of the energy-block- transition (E-B-T) model can be established [74] (Figure 15c).
- (3)
- (4)
- Stability evaluation and support design of slopes or excavations in jointed rock masses [8].
- (5)

#### 5.1.1. Practical Applicability of PCM-DDN

^{3}, and the maximum volume is 5.99 m

^{3}(Figure 16b). The blocks are mainly presented in CE shapes (Figure 16c).

#### 5.1.2. Practical Applicability of PCM-SDS

_{S}, as well as BSD

_{S}and BOD

_{S}of model ID 61, are shown in Figure 17 and Table 5. The investigated rock mass is dominated by E, EP and P shape types. The large blocks (>D

_{50}) possess more EP shapes, and the small blocks (≤D

_{50}) possess more E shapes. As the main block orientation (306°/33°) has a consistent directivity of Set 1 (305°/81°), Set 1 plays a controlling role in the major block shape and orientation of this case.

#### 5.2. Comparison with an Representative Analytical Approach

#### 5.2.1. The Persistence Factor Estimation

#### 5.2.2. Comparison with ${V}_{b}$ Calculation

_{25}, D

_{50}, D

_{75}and mean value) from the PCM-SDS of Site 3 were compared with ${V}_{b}$. Applying the product of three persistence values (${P}_{1}{P}_{2}{P}_{3}$) as the independent variable, the ${V}_{b}~{P}_{1}{P}_{2}{P}_{3}$ curve was derived. In Figure 18, the D

_{25}, D

_{50}, D

_{75}, and mean value from PCM-SDS with the corresponding shading zone of standard deviation are illustrated. The ${V}_{b}$ from the analytical equation is slightly greater than the D

_{75}and mean value from PCM-SDS, and the curve segment is situated at the upper part of the standard deviation zones of D

_{75}and mean value. The difference between ${V}_{b}$ and the mean value from PCM-SDS is in the range of 0.015–0.045 m

^{3}. This shows a slight overestimation of block size with the equation for this case. The result indicates this empirical equation may not fully reflect the actual influence of the persistence on block size calculation, even the persistence values of all sets are set to 1.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The surveyed rock exposure of Site 1 [43]. A partial magnification of two blocks is demonstrated, and some interrelated discontinuities are marked. The two white boards are 60 by 60 cm in dimension, and act as supplementary scale and orientation reference markers during the analysis of the laser scanned point cloud data. View direction is towards the East.

**Figure 2.**(

**a**) Site map of Yinshan open-pit copper mine extracted from Google Earth. (

**b**) Orthophoto of the eastern slope generated from UAV photogrammetry. (

**c**) Orthophoto of the southern slope generated from UAV photogrammetry.

**Figure 5.**Scheme of normal vector estimation based on Nesti-Net algorithm updated from Ben-Shabat et al. [53]. The multi-scale point statistics for each point from a given PCM is computed. Then, the optimal scale is determined by a scale manager network. The normal vectors are calculated by mixture-of-experts CNN, and mapped by a HSV-rendering technique (Liu and Kaufmann [55]).

**Figure 6.**(

**a**) Discontinuity set assignment to each point of Site 1 using different colors. (

**b**) Each individual discontinuity of Set 1 is separated and delineated using different colors. (

**c**) One example of parameters calculated for discontinuity A: orientation, trace length, and fitting plane equation. (

**d**) Digital trace mapping of Set 1.

**Figure 7.**The discontinuity collections of Blocks 1 (

**a**) and 2 (

**d**), the polyhedral modeling based on extension of existing discontinuity planes of Blocks 1 (

**b**) and 2 (

**e**), and the final block model and calculated parameters for Blocks 1 (

**c**) and 2 (

**f**).

**Figure 9.**The orientation results for Site 1 in the stereographic projection (i.e., equal angle net on the lower hemisphere).

**Figure 10.**Three-dimensional (3D) rock block model based on the stochastic DFN simulation before and after excluding the boundary blocks.

**Figure 11.**(

**a**) The stereographic projection of three sets of planes (i.e., equal angle net on the lower hemisphere). (

**b**) The extraction of blocks of the synthetic box model with all blocks labeled.

**Figure 12.**The block volume distribution of IBSD

_{D}and IBSD

_{S}. All color curves represent IBSD

_{S}from PCM-SDS of all simulated models.

**Figure 14.**The shape distribution and block volume ranges obtained from PCM-DDN (

**a**) and PCM-SDS (

**b**) for Site 1. The block shape distribution from PCM-DDN (

**c**) and PCM-SDS (

**d**) for Site 1. The block orientation distribution from PCM-DDN (

**e**) and PCM-SDS (

**f**) for Site 1.

**Figure 15.**(

**a**) The main inherent rock mass parameters in the RMi according to [75]. (

**b**) A schematic view of the RFFM. The change in block volume distribution by fragmentation. The IBSD results in an increase of the number of blocks by fragmentation (RBSD) modified from Ruiz-Carulla and Corominas [79]. (

**c**) Schematic view of the energy-block-transition model modified from Salmi and Sellers [74].

**Figure 16.**(

**a**) The EBSD

_{D}of rock blocks extracted from PCM-DDN. (

**b**) The block volume distribution of extracted rock blocks. (

**c**) The block shape distribution from PCM-DDN.

**Figure 17.**(

**a**) The block volume distribution of IBSD

_{S}from PCM-SDS of all simulated models. (

**b**) The block shape distribution from PCM-SDS. (

**c**) The corresponding shape distribution with block volume ranges. (

**d**) The block orientation distribution from PCM-SDS.

**Figure 18.**The relation between${V}_{b}$ and ${P}_{1}{P}_{2}{P}_{3}$ from the analytical approach by Cai et al. [26]. The D

_{25}, D

_{50}, D

_{75}, and mean value from PCM-SDS with the corresponding shading zone of the standard deviation are also illustrated.

Set | Orientation (°) | Trace Length (m) | Normal Set Spacing (m) | ||||
---|---|---|---|---|---|---|---|

Fisher Distribution | Log Normal Distribution | Log Normal Distribution | |||||

Dip Dir | Dip | $\mathbf{Fisher}\mathit{\kappa}$ | Mean | Standard Deviation | Mean | Standard Deviation | |

Set 1 | 127 | 56 | 15.17 | 0.27 | 0.135 | 0.34 | 0.016 |

Set 2 | 291 | 45 | 35.09 | 0.55 | 0.304 | 0.15 | 0.067 |

Set 3 | 227 | 83 | 34.89 | 0.45 | 0.386 | 0.25 | 0.061 |

Set 4 | 279 | 81 | 37.96 | 0.44 | 0.107 | 0.18 | 0.119 |

Block ID | Manually Measured Size (m^{3}) | Extracted Size (m^{3}) | Percent Deviation |
---|---|---|---|

1 | 0.2160 | 0.2111 | 2.27% |

2 | 0.4320 | 0.4307 | 0.30% |

3 | 0.0689 | 0.0701 | 1.74% |

4 | 0.3645 | 0.3780 | 3.70% |

5 | 0.0506 | 0.0531 | 4.94% |

6 | 0.0540 | 0.0561 | 3.89% |

7 | 0.0630 | 0.0642 | 1.90% |

8 | 0.0180 | 0.0187 | 3.89% |

9 | 0.0270 | 0.0284 | 5.19% |

Method | Block Size (m^{3}) | Block Orientation (Dip Dir/Dip, °) | |||
---|---|---|---|---|---|

D_{25} | D_{50} | D_{75} | Mean | ||

PCM-DDN | 0.005 | 0.014 | 0.038 | 0.041 | 115/26 |

PCM-SDS: Model ID 75 | 0.006 | 0.035 | 0.120 | 0.101 | 124/17 |

PCM-SDS: All models ^{1} | M: 0.005 | M: 0.027 | M: 0.092 | M: 0.084 | -- |

SD: 0.003 | SD: 0.014 | SD: 0.044 | SD: 0.060 |

^{1}M: mean value; SD, standard deviation.

Set | Orientation (°) | Trace Length (m) | Normal Set Spacing (m) | Persistence Factor | ||||
---|---|---|---|---|---|---|---|---|

Fisher Distribution | Log Normal Distribution | Log Normal Distribution | -- | |||||

Dip Dir | Dip | $\mathbf{Fisher}\mathit{\kappa}$ | Mean | Standard Deviation | Mean | Standard Deviation | Value Range | |

Set 1 | 305 | 81 | 93.76 | 1.14 | 0.601 | 0.25 | 0.069 | 85–100% |

Set 2 | 6 | 76 | 99.60 | 1.52 | 0.862 | 0.61 | 0.240 | 85–100% |

Set 3 | 108 | 42 | 273.68 | 1.52 | 1.183 | 0.745 | 0.387 | 90–100% |

**Table 5.**Summary of block characterization results of Site 2 acquired from PCM-SDS of the southern slope.

Method | Block Size (m^{3}) | Block Orientation (Dip dir/Dip, °) | |||
---|---|---|---|---|---|

D_{25} | D_{50} | D_{75} | Mean | ||

PCM-SDS: Model ID 61 | 0.009 | 0.053 | 0.212 | 0.192 | 306/33 |

PCM-SDS: All models ^{1} | M: 0.008 | M: 0.051 | M: 0.196 | M: 0.179 | -- |

SD: 0.004 | SD: 0.025 | SD: 0.092 | SD: 0.079 |

^{1}M: mean value; SD, standard deviation.

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## Share and Cite

**MDPI and ACS Style**

Kong, D.; Wu, F.; Saroglou, C.; Sha, P.; Li, B.
In-Situ Block Characterization of Jointed Rock Exposures Based on a 3D Point Cloud Model. *Remote Sens.* **2021**, *13*, 2540.
https://doi.org/10.3390/rs13132540

**AMA Style**

Kong D, Wu F, Saroglou C, Sha P, Li B.
In-Situ Block Characterization of Jointed Rock Exposures Based on a 3D Point Cloud Model. *Remote Sensing*. 2021; 13(13):2540.
https://doi.org/10.3390/rs13132540

**Chicago/Turabian Style**

Kong, Deheng, Faquan Wu, Charalampos Saroglou, Peng Sha, and Bo Li.
2021. "In-Situ Block Characterization of Jointed Rock Exposures Based on a 3D Point Cloud Model" *Remote Sensing* 13, no. 13: 2540.
https://doi.org/10.3390/rs13132540