# Photogrammetric Prediction of Rock Fracture Properties and Validation with Metric Shear Tests

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}) method produces an estimate with −7% (medium) and + 12% (large) errors. The photogrammetry-based Z′

_{2}is an objective method that consistently produces usable estimates for the JRC and peak friction angle.

## 1. Introduction

## 2. Methodology

#### 2.1. Overview of the Research Methods Used

#### 2.2. Manufacturing of the Slab Pairs

#### 2.3. Surface Roughness Measurements

#### 2.3.1. Roughness Measurements Using the Profilometer

#### 2.3.2. Roughness Measurements Using Photogrammetry

#### 2.4. Photogrammetric Joint Roughness Coefficient (JRC) Calculation from a 2D Line

_{2}),

_{2}represents the RMS (Equation (3)):

#### 2.5. Push-Shear Test Setup

#### 2.6. Estimation of Peak Friction Angle

## 3. Results and Discussions

#### 3.1. Characterization of Damaged Areas of the Fracture Surface

#### 3.1.1. JRC Estimated by the Profilometer

#### 3.1.2. Photogrammetric JRC Values

_{2}, Z

_{2}methods shown in Table 5 reveals that the modified RMS (Z′

_{2}) resulted in significantly lower JRC values for the large sample from approximately 10 to approximately 7 (Figure 9a, Figure 10a and Figure 11a). There is no remarkable difference between the JRC from the profilometer (9.3) and Z′

_{2}(8.9) methods for the medium sample. However, the JRC values obtained from Z

_{2}(10.9), or the medium sample, are greater by almost 2 JRC units or 17% of the JRC value.

#### 3.2. Shear Test Diagrams

^{2}for the peak strength is 0.95 and for the residual strength 0.98 (Figure 14).

_{5}and S

_{6}in Figure 5b) registered readings 0.7–1.0 mm higher than the rear sensors (S

_{3}and S

_{4}in Figure 5b). For the large sample, the elevation difference was 14.9 mm uphill over 2000 mm or 0.43°, and for the medium sample the elevation difference was 2.3 mm uphill over 500 mm or 0.26°. Considering that almost every single natural joint set encloses certain inclination degrees of its shearing plane (joint surfaces) regarding the shearing direction [69], a correction of the dilation data for the large test was performed to account for the influence of the slope effect. The same correction was applied in evaluating the dilation results of the medium sample, which also sheared uphill. Figure 16 and Figure 17 present the adjusted curves of dilation phenomena for the large and medium slabs, respectively, once the uphill effect had been corrected.

_{7}, S

_{8}, S

_{9}, S

_{10}. At the beginning of the shearing, and consistently for stages 1 to 4, but most noticeably in stages 1 and 2, the dilation recorded for the top slab went up quickly with a sudden drop and fast axial displacement, corresponding to the moment when the peak shear strength was overcome. After this point, the dilation continued with an increasing trend as in the large case. While the dilation decreased with increasing normal stress and shearing stage in the large test, this statement did not become a tendency for the medium sample. Figure 17 shows there was no correlation between the normal stress applied and the dilation. With increasing normal stress and shearing stages, the bigger asperities on the fracture surface should be crushed, reducing their height and the displacement-opposing surface area. This is consistent with the quasi-identical curves of stages 2 and 4, where the results are similar to the large case.

#### 3.3. Method Comparison for Peak Friction Angles

_{2}method underestimates the JRC by −19%, and the Z′

_{2}method by −7%. The peak friction angles estimated with Equation (8) were close to the results of the shear test between 75° to 78°, except the peak friction angle predicted by Z

_{2}, that results in 70°.

_{2}method gives a result similar to the scaled JRC with −9% underestimation. The modified RMS (Z′

_{2}) produces a result (6.95, +13%) comparable with the experimental result (6.17). The estimated JRC value by the modified RMS (Z′

_{2}) method and the JRC from the shear test are similar (6.95 and 6.17), and the estimated peak friction angle and the experimental peak friction angles are 66.22° (+6% error) and 62.51°, respectively.

## 4. Conclusions

_{2}estimate resulted in an error of −7%. For the large sample, the scale-corrected profilometer-based method leads to an underestimation of both the JRC and peak friction angle, with a −9% error. Here, the photogrammetry-based method Z′

_{2}produces an estimate with +12% overestimation. In conclusion, the photogrammetry-based method Z′

_{2}is an objective method that consistently produces usable estimates for the JRC and peak friction angle.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Experimental

**Figure A2.**(

**a**) Top view of the experimental setup. (

**b**) Close-up of contact mechanism between the hydraulic cylinders and the rock slab. Dimensions in centimeters [cm]. 1—Hydraulic cylinders; 2—Actuators; 3—Steel beams—frame; 4—Steel beams—lateral restriction; 5—Steel beam—H-beam (force transfer); 6—Bolts; 7—Barrier; 8—Ball plates; 9—Wooden pallet; 10—Floor anchors; 11—Steel clamps; 12—Steel plates; 13—Wooden blocks—force transfer; 14—Wooden plate—centralizer; 15—Steel support—HSS profile.

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**Figure 1.**The measurement lines for acquiring the joint roughness coefficient (JRC) value for the fracture surfaces of the large (

**a**,

**b**) and medium (

**c**,

**d**) rock blocks. The viewing direction is toward the fracture surface, either bottom (B) or top (T) of the slab.

**Figure 2.**The photogrammetry setup with (

**a**) camera positioning in the back-and-forth photographing direction, (

**b**) the slider track setup.

**Figure 3.**Diagram illustrates the camera movement to photograph the horizontal slab. (

**a**) along corners and edges (

**b**) opposite direction along the edges and the corners (

**c**) shooting along the positive and negative X-axis and (

**d**) along the positive and negative Y-axis.

**Figure 4.**Push shear test setup for the large sample: large sample 2000 mm × 1000 mm (

**a**), and medium sample 500 mm × 250 mm (

**b**).

**Figure 5.**Layout of the locations of the displacement sensors: (

**a**) large, and (

**b**) medium. The positions of the linear variable differential transformers (LVDTs) are shown by the symbol S.

**Figure 6.**Damage mapping after four shearing stages on the bottom surface of the sample mapped by a ruler: (

**a**) large sample and (

**b**) medium sample. The colored dots show damaged areas in the different stages of the shear tests.

**Figure 7.**Photogrammetry data of the large sample (2000 mm × 1000 mm), (

**a**) initial topography, (

**b**) sheared topography and (

**c**) damaged areas based on the comparison between pre-shearing and post-shearing stages.

**Figure 8.**Photogrammetry data of the medium sample (500 mm × 250 mm), (

**a**) initial topography, (

**b**) sheared topography and (

**c**) damaged areas based on the comparison between pre-shearing and post-shearing stages.

**Figure 9.**The JRC profilometer results of the slabs; pre-shearing of the large sample (

**a**), pre-shearing of the medium sample (

**b**).

**Figure 10.**The photogrammetry method and Z

_{2}to define the JRC roughness profiles of the slabs before shearing of the large sample (

**a**), before shearing of the medium sample (

**b**).

**Figure 11.**The photogrammetry method and Z′2 to define the JRC roughness of the slabs (

**a**) pre-shearing of the large sample (2000 mm × 1000 mm), (

**b**) pre-shearing of the medium sample (500 mm × 250 mm).

**Figure 12.**Shear test results for the large sample (2000 mm × 1000 mm) as a function of normal stress and shear displacement: (

**a**) 50 mm displacement, (

**b**) 1.5 mm displacement.

**Figure 13.**Shear test results for the medium sample (500 mm × 250 mm) as a function of normal stress and shear displacement: (

**a**) 50 mm displacement, (

**b**) 1.5 mm displacement.

**Figure 18.**Transition from negative to positive values of dilation during the different stages of the large push shear test.

Phase | Description | Normal Stress (kPa) |
---|---|---|

Pre-test | Photogrammetry | |

First stage: | Pushing without extra normal stress | 3.6 |

Damage mapping 1 | Visual assessment of damage locations and resetting | |

Second stage: | Pushing with extra normal weight | 6.0 |

Damage mapping 2 | Visual assessment of damage locations and resetting | |

Third stage: | Pushing with extra normal weight | 8.5 |

Damage mapping 3 | Visual assessment of damage locations and resetting | |

Fourth stage: | Pushing without extra normal stress | 3.6 |

Damage mapping 4 | Photogrammetry | |

Fifth stage: Unmatched residual | Pushing without extra normal stress, top sample rotated through 180° | 3.4 |

Phase of Shearing Test | Weight (kg) | Normal Stress (kPa) | ||||||
---|---|---|---|---|---|---|---|---|

Large Sample Test | Medium Sample Test | |||||||

Slab | Frame | Additional | Total | Slab | Additional | Total | ||

First stage | 697.60 | 34.5 | 0 | 732.10 | 17.11 | 28.65 | 45.76 | 3.6 |

Second stage | 697.60 | 34.5 | 500.23 | 1232.33 | 17.11 | 59.91 | 77.02 | 6.0 |

Third stage | 697.60 | 34.5 | 1000.20 | 1732.30 | 17.11 | 91.16 | 108.27 | 8.5 |

Fourth stage | 697.60 | 34.5 | 0 | 732.10 | 17.11 | 28.65 | 45.76 | 3.6 |

Fifth stage | 697.60 | 0 | 0 | 697.60 | 17.11 | 26.49 | 43.60 | 3.4 |

**Table 3.**Shear test results for both the large (2000 mm × 1000 mm) and medium (500 mm × 250 mm) samples.

PHASE | Normal Stress | Large Size Sample 2000 mm × 1000 mm | Medium Size Sample 500 mm × 250 mm | ||||
---|---|---|---|---|---|---|---|

Peak Shear Strength | Residual Shear Strength | Shear Displacement at Peak | Peak Shear Strength | Residual Shear Strength | Shear Displacement at Peak | ||

(kPa) | (kPa) | (kPa) | (mm) | (kPa) | (kPa) | (mm) | |

First stage | 3.6 | 6.9 | 3.7 | 0.52 | 17.8 | 3.9 | 0.08 |

Second stage | 6.0 | 9.5 | 5.4 | 0.73 | 21.1 | 5.4 | 0.11 |

Third stage | 8.5 | 12.0 | 7.9 | 0.68 | 28.6 | 8.0 | 0.07 |

Fourth stage | 3.6 | 5.2 | 3.2 | 0.50 | 10.4 | 2.8 | 0.10 |

Fifth stage | 3.4 | N/A | 2.05 | 60.0 | N/A | 2.5 | 1.18 |

**Table 4.**Cohesion and friction angle according to Mohr–Coulomb failure criteria from the shear test.

Sample | Peak Friction Angle (°) | Peak Cohesion (kPa) | Residual Friction Angle (°) | Residual Cohesion (kPa) |
---|---|---|---|---|

Large sample (2000 mm × 1000 mm) | 53.34 | 1.27 | 41.9 | 0.217 |

Medium sample (500 mm × 250 mm) | 71.19 | 3.51 | 42.72 | 0.028 |

Item (Using Barton–Bandis’s Criterion) | Large | Medium | ||||
---|---|---|---|---|---|---|

JRC | Peak Friction Angle (°) | JRC | Peak Friction Angle (°) | |||

Direct shear test | 6.17 | 62.51 | 9.54 | 78.6 | ||

Profilometer | L_{0} | 10.5 | 81 | 9.3 | 77 | |

L_{scaled} | 5.6 | 59.8 | 6.9 | 66 | ||

Photogrammetry | Z_{2} | L_{0} | 10.11 | 77.53 | 10.88 | 85 |

L_{scaled} | 5.5 | 59.3 | 7.7 | 69.8 | ||

Z′_{2} | 6.95 | 66.22 | 8.91 | 75.58 |

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**MDPI and ACS Style**

Uotinen, L.; Torkan, M.; Baghbanan, A.; Hernández, E.C.; Rinne, M. Photogrammetric Prediction of Rock Fracture Properties and Validation with Metric Shear Tests. *Geosciences* **2021**, *11*, 293.
https://doi.org/10.3390/geosciences11070293

**AMA Style**

Uotinen L, Torkan M, Baghbanan A, Hernández EC, Rinne M. Photogrammetric Prediction of Rock Fracture Properties and Validation with Metric Shear Tests. *Geosciences*. 2021; 11(7):293.
https://doi.org/10.3390/geosciences11070293

**Chicago/Turabian Style**

Uotinen, Lauri, Masoud Torkan, Alireza Baghbanan, Enrique Caballero Hernández, and Mikael Rinne. 2021. "Photogrammetric Prediction of Rock Fracture Properties and Validation with Metric Shear Tests" *Geosciences* 11, no. 7: 293.
https://doi.org/10.3390/geosciences11070293