The ultimate pit may affect other aspects in the life of a mine such as economical, technical, environmental, and social aspects. What makes it even more complex is that most often there are many pits which are economically minable. This calls for a heuristic approach to determine which of these pits is the ultimate pit. This study presents a means of selecting an ultimate pit during design operations of the Hebei Limestone mine. During optimization processes of the mine, many pit shells were created using Whittle Software. Normally, Whittle Software optimizes these processes and assigns a revenue factor of 1 for the ultimate pit. Unfortunately, the pit shells created did not satisfy the criteria with a revenue factor of 1 based on the parameters. As a result of this, statistical analysis was implemented to further understand the relationship, variability, and correlation of the pit shells created (data). Correlation Analysis, K-means++ Analysis, Principal Component Analysis, and Generalized Linear models were used in the analysis of the pit shells created. The results portray a salient relationship of the optimization variables. In addition, the proposed method was tested on Whittle Sample projects which satisfy the selection of ultimate pit selection with a revenue factor of 1. The results show that the proposed model produced almost the same results as the Whittle model with a revenue factor of 1 and was also able to determine the ultimate pit in cases which did not satisfy the Whittle selection criteria.
References
[1]
Ebrahimi, A. (2019) Ultimate Pit Size Selection, Where Is the Optimum Point? SRK Consulting Inc., Canada.
https://docs.srk.co.za/sites/default/files/file/AEbrahimi_UltimatePitSizeSelection_2019_1.pdf
[2]
Caccetta, L. and Giannini, L.M. (1987) An Application of Discrete Mathematics Design of an Open Pit Mine. Discrete Applied Mathematics, 21, 1-19.
https://doi.org/10.1016/0166-218X(88)90030-3
[3]
Turpin, R.A. (1980) A Technique for Assessing Ultimate Open-Pit Mine Limits in a Changing Economic Environment.
https://preserve.lehigh.edu/cgi/viewcontent.cgi?article=3291&context=etd
[4]
Godoy, M. (2009) Mineral Reserve Estimation in the Real World: A Review of Best Practices and Pitfalls. Golder Associates, Los Andeles.
[5]
Michaud, D. (2018) Mining Engineering and Mineral Exploration Economics.
https://www.911metallurgist.com/blog/mining-engineering
[6]
Gemcom (2013) Geostatistics. Gemcom Software International Inc. (Gemcom), Vancouver.
[7]
Noumea, (2013) Resource Estimation and Surpac Noumea. Mining Associates. Spring Hill.
[8]
Jalloh, A.B. and Sasaki, K. (2014) Geo-Statistical Simulation for Open Pit Design Optimization and Mine Economic Analysis in Decision-Making. In: Drebenstedt, C. and Singhal, R., Eds., Mine Planning and Equipment Selection, Springer, Cham, 93-101. https://doi.org/10.1007/978-3-319-02678-7_10
[9]
Gemcom (2013) Block Modelling. Gemcom Software International Inc. (Gemcom), Vancouver.
[10]
Khademi, A. (2016) Applied Univariate, Bivariate, and Multivariate Statistics. Journal of Statistical Software, 72, 1-4. http://dx.doi.org/10.18637/jss.v072.b02
[11]
Uraibi, S.H. and Midi, H. (2019) On Robust Bivariate and Multivariate Correlation Coefficient. Economic Computation and Economic Cybernetics Studies and Research, 53, 221-239. https://doi.org/10.24818/18423264/53.2.19.13
[12]
Garbade, M.J. (2018) Understanding K-Means Clustering in Machine Learning.
https://towardsdatascience.com/understanding-k-means-clustering-in-machine-learning-6a6e67336aa1
[13]
Efendiyev, G.M., Mammadov, P.Z., Piriverdiyev, I.A. and Mammadov, V.N. (2016) Clustering of Geological Objects Using FCM-Algorithm and Evaluation of the Rate of Lost Circulation. Procedia Computer Science, 102, 159-162.
Pernet, C.R., Wilcox, R. and Rousselet, G.A. (2013) Robust Correlation Analyses: False Positive and Power Validation Using a New Open Source Matlab Toolbox. Frontiers in Psychology, 3, Article No. 606.
https://doi.org/10.3389/fpsyg.2012.00606
[16]
Thobaven, D. and Willoughby, J. (2012) Strategic Mine Planning in Whittle. Gemcom Software International Inc., Vancouver.
[17]
Drezner, Z. (1995) Multirelation—A Correlation among More than Two Variables. Computational Statistics & Data Analysis, 19, 283-292.
https://doi.org/10.1016/0167-9473(93)E0046-7
[18]
Data Science (2019) Pearson vs Spearman vs Kendall.
https://datascience.stackexchange.com/questions/64260/pearson-vs-spearman-vs-kendall
Jolliffe, I.T. and Cadima, J. (2016) Principal Component Analysis: A Review and Recent Developments. Philosophical Transactions A, 374, Article: 20150202.
https://doi.org/10.1098/rsta.2015.0202
[21]
Jaadi, Z. (2020) A Step by Step Explanation of Principal Component Analysis.
https://builtin.com/data-science/step-step-explanation-principal-component-analysis
[22]
Maklin, C. (2018) K-Means Clustering Python Example.
https://towardsdatascience.com/machine-learning-algorithms-part-9-k-means-example-in-python-f2ad05ed5203
[23]
Shillito, M.L. and Marle, D.J.D. (1992) Value: Its Measurement, Design, and Management. Wiley & Sons, Inc., New York, 368 p.
[24]
McCullagh, P. and Nelder, F.J. (1989) Generalized Linear Models. Chapman and Hall, Chicago.
[25]
Haq, Z., Hanna, T., Michal, K., Kraljevic, T. and Stubbs, M. (2018) Generalized Linear Model (GLM).
https://docs.h2o.ai/h2o/latest-stable/h2o-docs/data-science/glm.html
[26]
Müller, M. (2004) Generalized Linear Models. Fraunhofer Institute for Industrial Mathematics, Kaiserslautern.
[27]
Nykodym, T., Kraljevic, T., Wang, A. and Wong, W. (2017) Generalized Linear Modeling with H2O. H2O.ai, Inc., CA.
http://docs.h2o.ai/h2o/latest-stable/h2o-docs/booklets/GLMBooklet.pdf
[28]
Gniazdowski, Z. (2017) New Interpretation of Principal Components Analysis. Zeszyty Naukowe WWSI, 11, 43-65.
[29]
Grekousis, G. (2020) Spatial Analysis Theory and Practice: Describe-Explore-Explain through GIS. Cambridge University Press, New York.
https://doi.org/10.1017/9781108614528
[30]
Burnham, K.P. and Anderson, D.R. (2004) Multimodel Inference: Understanding AIC and BIC in Model Selection. Sociological Methods & Research, 33, 261-304.
https://doi.org/10.1177/0049124104268644
[31]
Dziak, J.J., Coffman, D.L., Lanza, S.T. and Li, R. (2012) Sensitivity and Specificity of Information Criteria. The Methodology Center, Pennsylvania.
