Abstract
This paper offers a new method for the definition of geotechnical sectors in open pit mines based on multivariate cluster analysis. A geological-geotechnical data set of a manganese open pit mine was used to demonstrate the methodology. The data set consists of a survey of geological and geotechnical parameters of the rock mass, measured directly in several points of the mine, structured initially in twenty-eight variables. After the preprocessing of the data set, the clustering technique was applied using the k-Prototype algorithm. The squared Euclidean distance was used to quantify the proximity between numerical variables, and the Jaccard's coefficient of similarity was used to quantify the proximity between the nominal variables. The different cluster results obtained were validated by the multivariate analysis of variance. The identification of cluster structures was achieved by plotting them on the mine map for spatial visualization and definition of geotechnical sectors. These sectors are spatially contiguous and relatively homogeneous regarding their geological–geotechnical properties, indicated by a high density of points of the same group. It was possible to observe a great adherence of the proposed sectors to the mine geology, demonstrating the practical representativeness of the clustering results and the proposed sectors.
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Source: Adapted from a map provided by the mine company
Source: Adaptead from a map provided by the mine company
Source: Adapted from a map provided by the mine
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Acknowledgements
The authors wish to thank the mine company for contributing to the accomplishment of this work, providing the data set and other materials necessary for its completion. Also, the authors thank Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001 and CNPq (Conselho Nacional de Desenvolvimento Científico) for supporting this work.
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Appendices
Appendix 1 Extract of Some Observations from the Original Data Set
As presented in Table 4.
Point | Bench | Sector | Litho | Family | Type | X | Y | Z | Direction | Dip Direction | Dip | R | W | Frat/m | GF | # Families | JN | JV | RQD | Spacing |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
386 | 950S | 4B | IGT | FOL/CONT1 | Foliation/Contact | 628,137.66 | 7,717,858.56 | 949.92 | 115.00 | 205 | 88 | 5 | 2 | 2 | F3 | 2.5 | 6 | 5 | 98 | 0.5 |
386 | 950S | 4B | IGT | FOL/CONT2 | Foliation/Contact | 628,137.66 | 7,717,858.56 | 949.92 | 160.00 | 250 | 86 | 5 | 2 | 2 | F3 | 2.5 | 6 | 5 | 98 | 0.5 |
386 | 950S | 4B | IGT | FRAT1 | Fracture | 628,137.66 | 7,717,858.56 | 949.92 | 260.00 | 350 | 82 | 5 | 2 | 2 | F3 | 2.5 | 6 | 5 | 98 | 0.5 |
386 | 950S | 4B | IGT | FRAT2 | Fracture | 628,137.66 | 7,717,858.56 | 949.92 | 60.00 | 150 | 78 | 5 | 2 | 2 | F3 | 2.5 | 6 | 5 | 98 | 1.5 |
Point | Length | Separation | Roughness | Infilling | Weathering | JR | JA | JW |
|---|---|---|---|---|---|---|---|---|
386 | > 20 m | > 5 mm | Rough | Hard; < 5 mm | Slightly weathered | Slickensided/Undulating | 1 | Dry |
386 | > 20 m | > 5 mm | Rough | Hard; < 5 mm | Slightly weathered | Slickensided/Undulating | 1 | Dry |
386 | 3 a 10 m | > 5 mm | Rough | Soft; < 5 mm/Hard; > 5 mm | Slightly weathered | Slickensided/Undulating | 1 | Dry |
386 | 3 a 10 m | > 5 mm | Rough | Soft; < 5 mm/Hard; > 5 mm | Slightly weathered | Slickensided/Undulating | 2 | Dry |
Appendix 2 Extraction of Some Observations from the Final Data Set
As presented in Table 5.
Point | Litho._1 | Litho._2 | Litho._3 | Litho._4 | Litho._5 | Litho._6 | Litho._7 | Litho._8 | Litho._9 | Litho._10 | Litho._11 | Litho._12 | Litho._13 | Litho._14 | Litho._15 | Litho._16 | Litho._17 | Litho._18 | Litho._19 | Litho._20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
386 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Point | Type_1 | Type_2 | Type_3 | Type_4 | Family_1 | Family _2 | Family _3 | Family _4 | Family _5 | Family _6 | Family _7 | Family _8 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
386 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
Point | X | Y | Z | R | W | Spacing | Length | Separation | Roughness | Infilling | Weathering | JW |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
386 | 628,137.7 | 7,717,858.6 | 949.918 | 6 | 4 | 3 | 1 | 1 | 4 | 2 | 4 | 2 |
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Nazareth, A.F.D.V., Lana, M.S. A Methodology for the Definition of Geotechnical Mine Sectors Based on Multivariate Cluster Analysis. Geotech Geol Eng 39, 4405–4426 (2021). https://doi.org/10.1007/s10706-021-01771-6
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DOI: https://doi.org/10.1007/s10706-021-01771-6