Predictive Model for Drilling Specific Energy at Carmen De Andacollo, Chile Submitted by Cristián David Jeraldo Garrido To

Predictive Model for Drilling Specific Energy at

Carmen de Andacollo, Chile

Submitted by Cristián David Jeraldo Garrido to the University of Exeter as a dissertation towards the degree of Master of Science by advanced study in Mining Geology, August 2017.

I certify that all material in this dissertation which is not my own work has been identified and that no material is included for which a degree has previously been conferred on me.

...... (signature)

Abstract Drilling Specific Energy (DSE) is defined as the energy applied per a unit volume of material removed during rotational drilling. The advantages of using DSE technology include low cost, a large amount of data generated and robustness. Carmen de Andacollo (CDA) is an open pit situated in the north-central part of Chile. From 2012, the CDA three drill rigs have incorporated the system Thunderbird®, which allows the determination of DSE for every blast hole. This research assessed the precision of DSE data comparing different both drill rigs and operators. The research found that the geological attributes at CDA exercise a strong control over DSE values. This is used to define DSE domains through exploratory data analysis and additionally, demonstrates the coherence of the CDA geological model. The CDA grade control block model contains the DSE values estimated via inverse distance. Nonetheless, because blast hole is only available for grade control, DSE values for the 5-year-plan are currently estimated at CDA as an average by geological domain. In this research, three regression models were generated using data included in the grade control block model with the purpose of improving the predictability of DSE values for 5-year-plan. The data was divided into a train group to build the model and a test group for statistical validation. The results of the validation show that two of the models, the regression tree and the multiple linear regression, display a similar or worse performance than the current average by domain model. However, the results of the artificial neural networks model developed here exceed the average by domain model results. Therefore, the former is used to predict the DSE for the 5- year-plan block model. CDA operative difficulties include low grades and the proximity to Andacollo town. Using the artificial neural networks model might allow better mine planning, thus improving CDA operations. In operative terms, the model could permit a better determination of the power factor and tool consumption. Additionally, but no less important, it would allow reducing dust emissions (PM10) from blasting and, consequently, would improve the CDA relationship with the community and local and national authorities. This is key since Andacollo town was declared PM10 saturated zone in 2009. The results of the research presented here demonstrate the potential of using DSE in the light of the financial and environmental complexities of the current and future mining industry.

Acknowledgements

I am grateful to my family: my wife Fabiola and my lovely daughters, Francisca y Colomba, who have provided me all the possible support. I am also grateful to my all family members and friends, who have supported me for the success of this wonderful adventure of studying at the University of Exeter. I would like to say thank you all, especially to my sister Priscila, my mother Miriam and my grandmother Olga that always have believed on me; for their prayers and good wishes.

This project could not have been possible without the precious support of Becas Chile. To my dear colleagues of Teck, With a special mention to my boss and friend Víctor Araya, as well as Ricardo Schmidt, Héctor Berríos, Luis Godoy, Juan Carlos Olivares, Martin Lapointe, Claire Chamberlain, Jelena Puzic and Óscar Gutiérrez. Thank you, colleagues and friends, for your wholehearted support.

Very special people for getting in here were my “boss” Verónica Escobar and the generous lecturers from Universidad Católica del Norte, M. Soledad Benbow and Hans Wilke, who selflessly helped me with the application for university and scholarship. For all my friends in Chile: Javier Cruz, Christian Ibarra, Marcelo Tapia, Alejandro Macci; Syndy Barraza, Julio Escárate, Claudio y Sergio Barrientos. My new friends of Chile-in-England, Oliver y Carolina. Also for my friends from the entire world: Thank you, Ginny Gay. For my smart and gentle classmates, particularly Elena Sikdar, Fred Van der Berg, Harry Upfield, Septami Setiawati and Margarita Sakali. A very special gratitude goes out to Gamze Ersoy, Mustafa Çelebi, Ryan (Abdul) Riyansiah and Oliver Hamann. Oh, my dear friends, what could have done without you all? I am also grateful to the university staff, especially for Hylke Glass, Luke Palmer and Paul Wheeler (you rock Paul!) and the unique Language Team, particularly Isabel Noon, Hannah Johns and Richard Little (you make the exceptional happen).

Finally, to everyone in Camborne School of Mines. You all are remarkable part of our beloved university.

Thanks for all your encouragement!

III

To Fabiola, Francisca and Colomba To my parents

“Somewhere, something incredible is waiting to be known” Carl Sagan

“Ignorance is the curse of God; knowledge is the wing wherewith we fly to heaven” William Shakespeare

“It is not the strongest of the species that survives, nor the most intelligent, but the one most responsive to change” Charles Darwin

CONTENTS

1. Introduction ...... 1 1.1 Location ...... 1 1.2 Climate ...... 2 1.3 Framework and Methodology for the research ...... 3 2 Geology ...... 5 2.1 Tectonic Framework ...... 5 2.2 Regional Geology ...... 6 2.3 Geology of the Carmen de Andacollo deposit ...... 8 2.3.1 Structures ...... 8 2.3.2 Lithology ...... 11 2.3.3 Alteration and Mineralization ...... 13 3 Mining and Processing ...... 20 3.1 Drilling Operation ...... 22 3.1.1 DSE Definition ...... 22 3.1.2 Drilling at CDA ...... 23 4 Integrity of DSE data ...... 24 4.1 Drill Rig validation ...... 24 4.2 Operators validation ...... 26 5 DSE Exploratory Data Analysis...... 28 5.1 DSE for Lithology ...... 34 5.2 DSE for Minzone in Lithology ...... 35 5.2.1 DSE for Minzone in Breccia ...... 35 5.2.2 DSE for Minzone in Andesite ...... 36 5.2.3 DSE for Minzone in Pormin ...... 37 5.2.4 DSE for Minzone in Porpost ...... 38 5.2.5 DSE for Minzone in Tuff ...... 39 5.3 DSE for Alteration in Lithological-Minzone Combination ...... 41 5.3.1 DSE for Alteration in Breccia (A1) ...... 41 5.3.2. DSE for Alteration in Andesite in Supergene (A2) ...... 42 5.3.3 DSE for Alteration in Andesite in Primary (A3) ...... 43 5.3.4 DSE for Alteration in Pormin (A4) ...... 44 5.3.5 DSE for Alteration in Porpost (A5) ...... 45 5.3.6 DSE for Alteration in Tuff in Supergene (A6) ...... 46 5.3.7 DSE for Alteration in Tuff in Primary (A7) ...... 47 5.4 DSE for Argillic in Lithological-Minzone- Alteration Combination ...... 48 5.4.1 DSE for Argillic Intensity in Breccia (B1) ...... 48 5.4.2 DSE for Argillic Intensity in Andesite in Supergene (B2) ...... 49 5.4.3 DSE for Argillic Intensity in Andesite in Primary with Biotite, quartz-sericite, Argillic or Propylitic (B3) ...... 50 5.4.4 DSE for Argillic Intensity in Andesite in Primary with Albite or Potassic (B4) ...... 51

5.4.5 DSE for Argillic Intensity in Pormin (B5) ...... 52 5.4.6 DSE for Argillic Intensity in Porpost (B6) ...... 53 5.4.7 DSE for Argillic Intensity in Tuff in Supergene (B7) ...... 54 5.4.8 DSE for Argillic Intensity in Tuff in Primary with Biotite or Argillic (B8) ...... 55 5.4.9 DSE for Argillic Intensity in Tuff in Primary with Quartz-sericite, propylitic, Albite or Potassic (B9) ...... 56 6 Regression Models for DSE ...... 59 6.1 Regression Model for DSE based on Multiple Linear Regression ...... 63 6.1.1 DSE Validation for Multiple Linear Regression ...... 66 6.2 Regression Model for DSE based on Regression Tree ...... 67 6.2.1 DSE Validation for Regression Tree ...... 69 6.3 Regression Model for DSE based on Artificial Neural Networks ...... 70 6.3.1 DSE Validation for Artificial Neural Network Regression ...... 72 6.4 Regression Models for DSE: Results Comparison ...... 73 7 DSE Prediction for 5YP ...... 74 7.1 Spatial Comparison for DSE Block Models ...... 75 8. Discussion ...... 80 9. Conclusions ...... 82 10. Recommendations ...... 84

VII

Figures

Figure 1.1. Location of Carmen de Andacollo mine...... 2 Figure 1.2. Chilean Coastal Range near Carmen de Andacollo...... 2 Figure 1.3. Conceptualization for the research...... 4 Figure 2.1. Regional geology of the Carmen de Andacollo area...... 7 Figure 2.2. Major faults in the Carmen de Andacollo deposit...... 8 Figure 2.3. Crosscutting of the Andacollo fault by El Churque fault ...... 9 Figure 2.4. Twila fault in eastern slope at CDA open pit...... 9 Figure 2.5. El Toro Fault showing dextral offsetting. Tuff and andesite in contact...... 10 Figure 2.6. Extensional faulting array in Carmen de Andacollo deposit ...... 10 Figure 2.7. Lithological units in Carmen de Andacollo deposit...... 11 Figure 2.8. Lithological types at Carmen de Andacollo deposit...... 12 Figure 2.9. Lithological units and major faults in Carmen de Andacollo deposit ...... 12 Figure 2.10. Alteration units in Carmen de Andacollo deposit...... 13 Figure 2.11. (1) Veinlet of quartz-biotite (2) Microphotography of the same veinlet ..... 14 Figure 2.12. (1) Microphotography of chalcopyrite and magnetite and albite ...... 14 Figure 2.13. Quartz-chlorite-carbonate veinlet ...... 14 Figure 2.14. Microphotography displaying molybdenite and chalcopyrite ...... 15 Figure 2.15. (1) Quartz-sericite veinlet. (2) Sulphide association...... 16 Figure 2.16. Quartz-sericite intensity units in Carmen de Andacollo deposit ...... 16 Figure 2.17. Minzone units in Carmen de Andacollo deposit ...... 17 Figure 2.18. Secondary chalcocite ...... 17 Figure 2.19. Argillic intensity units in Carmen de Andacollo deposit ...... 18 Figure 2.20. Crosscutting relationships ...... 19 Figure 2.21. Alteration and mineralization paragenesis at Carmen de Andacollo ...... 19 Figure 3.1. Panoramic view of CDA mine ...... 20 Figure 3.2. Heap leaching simplified layout in Carmen de Andacollo mine...... 21 Figure 3.3. Simplified comminution circuit layout in CDA mine...... 21 Figure 3.4. Configuration for drilling and blasting at CDA mine...... 23 Figure 4.1. Statistical distribution of DSE values for five lithological domains...... 25 Figure 4.2. Statistical distribution of DSE values for six main operators ...... 27 Figure 5.1. Plan view displaying the spatial distribution of DSE values...... 28 Figure 5.2. Plan view showing the spatial distribution of DSE values by lithology...... 29 Figure 5.3. Plan view illustrating the spatial distribution of DSE values by minzone. ... 30 Figure 5.4. Plan view illustrating the spatial distribution of DSE values by alteration ... 31 Figure 5.5. Plan view displaying the spatial distribution of DSE values by argillics ...... 32 Figure 5.6. Plan view presenting the spatial distribution of DSE values by QS...... 33 Figure 5.7. Importance Plot for geological attributes and dependent variable DSE ..... 34 Figure 5.8. Probability Plot for DSE by lithology...... 35 Figure 5.9. Probability Plot for DSE by minzone in breccia...... 36 Figure 5.10. Probability Plot for DSE by minzone in andesite...... 37 Figure 5.11. Probability Plot for DSE by minzone in pormin...... 38 Figure 5.12. Probability Plot for DSE by minzone in porpost...... 39 Figure 5.13. Probability Plot for DSE by minzone in tuff...... 40 Figure 5.14. Probability Plot for DSE by alteration in breccia...... 41 Figure 5.15. Probability Plot for DSE by alteration in andesite in supergene...... 42 Figure 5.16. Probability Plot for DSE by alteration in andesite in primary...... 43 Figure 5.17. Probability Plot for DSE by alteration in pormin...... 44 Figure 5.18. Probability Plot for DSE by alteration in porpost...... 45 Figure 5.19. Probability Plot for DSE by alteration in tuff in supergene...... 46

VIII

Figure 5.20. Probability Plot for DSE by alteration in tuff in primary...... 47 Figure 5.21. Probability Plot for DSE by argillic intensity in breccia...... 49 Figure 5.22. Probability Plot for DSE by argillic intensity in andesite in supergene...... 50 Figure 5.23. Probability Plot for DSE by argillic intensity in andesite in primary I...... 51 Figure 5.24. Probability Plot for DSE by argillic intensity in andesite in primary II...... 52 Figure 5.25. Probability Plot for DSE by argillic intensity in pormin...... 53 Figure 5.26. Probability Plot for DSE by argillic intensity in porpost...... 54 Figure 5.27. Probability Plot for DSE by argillic intensity in tuff in supergene...... 55 Figure 5.28. Probability Plot for DSE by argillic intensity in tuff primary I...... 56 Figure 5.29. Probability Plot for DSE by argillic intensity in tuff primary II ...... 57 Figure 5.30. Plan view showing the distribution of domains for 33,842 DSE data...... 58 Figure 6.1. Spatial distribution for both grade control and 5YP block models...... 60 Figure 6.2. Distribution of domains ...... 60 Figure 6.3. Concept of model considered in this research...... 61 Figure 6.4. Distribution of samples (blocks) for train and test groups...... 62 Figure 6.5. Simple linear regression. Modified from Weisberg, 2005...... 64 Figure 6.6. A linear regression when p=2 (Weisberg, 2005)...... 65 Figure 6.7. Scatterplot for DSE in the test group ...... 66 Figure 6.8: An example of regression tree...... 67 Figure 6.9. First eleven nodes of the regression tree generated ...... 68 Figure 6.10. Scatterplot for DSE in the test group ...... 69 Figure 6.11. Diagram of biological neurons. From Hagan et al., 2014...... 70 Figure 6.12. Layout of an artificial neural network ...... 71 Figure 6.13. Layout of an artificial neural network with weighting ...... 72 Figure 6.14. DSE in the test group using the artificial neural networks model ...... 72 Figure 7.1. Comparison of DSE mean by domain ...... 74 Figure 7.2. Distribution of DSE data (actual) for the grade control block model...... 75 Figure 7.3. Plan view for distribution of DSE data ...... 76 Figure 7.4. Distribution of DSE data for the 5YP block model ...... 77 Figure 7.5. Plan view for distribution of DSE data for the 5YP block model ...... 77 Figure 7.6. Distribution of DSE data for the 5YP block model ...... 79 Figure 7.7. Plan view of DSE data for the 5YP block model ...... 79

Tables

Table 4.1. DSE data for lithology, minzone and drill rigs...... 24 Table 4.2. Basic DSE statistics for the three drill rigs...... 25 Table 4.3. Number of DSE data by drill rig operator...... 26 Table 4.4. Basic DSE statistics for six main operators...... 26 Table 5.1. DSE basic statistics by lithology...... 34 Table 5.2. DSE basic statistics by minzone in breccia...... 35 Table 5.3. DSE basic statistics by minzone in andesite...... 37 Table 5.4. DSE basic statistics by minzone in pormin...... 38 Table 5.5. DSE basic statistics by minzone in porpost...... 39 Table 5.6. DSE basic statistics by minzone in tuff...... 40 Table 5.7. DSE basic statistics by the seven lithology-minzone combinations...... 40 Table 5.8. DSE basic statistics by alteration in breccia...... 41 Table 5.9. DSE basic statistics by alteration in andesite in supergene...... 42 Table 5.10. DSE basic statistics by alteration in andesite in primary...... 43 Table 5.11. DSE basic statistics by alteration in pormin...... 44 Table 5.12. DSE basic statistics by alteration in porpost...... 45 Table 5.13. DSE basic statistics by alteration in tuff in supergene...... 46 Table 5.14. DSE basic statistics by alteration in tuff in primary...... 47 Table 5.15. DSE basic statistics by nine lithology-minzone-alteration combinations. .. 48 Table 5.16. DSE basic statistics by argillic intensity in breccia...... 48 Table 5.17. DSE basic statistics by argillic intensity in andesite in supergene...... 49 Table 5.18. DSE basic statistics by argillic intensity in andesite in primary I...... 51 Table 5.19. DSE basic statistics by argillic intensity in andesite in primary II ...... 52 Table 5.20. DSE basic statistics by argillic intensity in pormin...... 53 Table 5.21. DSE basic statistics by argillic intensity in porpost...... 54 Table 5.22. DSE basic statistics by argillic intensity in tuff in supergene...... 55 Table 5.23. DSE basic statistics by argillic intensity in tuff in primary I...... 56 Table 5.24. DSE basic statistics by argillic intensity in tuff in primary II ...... 57 Table 5.25. Basic statistics of DSE by the twelve combinations...... 58 Table 6.1. Variables from the grade control block model...... 61 Table 6.2. Linear correlations between DSE and predictors ...... 66 Table 6.3. Results for the actual data and the multiple linear regression model...... 67 Table 6.4. Results for the actual data and the regression tree model...... 69 Table 6.5. Results for the actual data and the artificial neural networks model...... 73 Table 6.6. Statistics results in the test group for generated models...... 74

1. INTRODUCTION

This document presents the results of a predictive model for Drilling Specific Energy at Carmen de Andacollo deposit, Chile.

The general purpose of this research is:

• Develop a predictive model for Drilling Specific Energy based on the data contained in the blocks of the grade control model; applying this to predicts Drilling Specific Energy for the blocks of five-year mining plan (5YP).

The specific purposes of this investigation are:

• Determine the relationships among Drilling Specific Energy and different variables enclosed in the Carmen de Andacollo block model. • Elaborate a predictive model for Drilling Specific Energy based on statistical approach. • Assess the confidence of the estimated values using statistical tools. • Predict the DSE values for the 5YP block model.

1.1 LOCATION

Carmen de Andacollo, from now on “CDA”, is an open pit mine located in the north-central part of Chile, South America, in the vicinity of Andacollo town (Figure 1.1) This operation is situated 55 km to the southeast of the La Serena city and 350 km to the north of Santiago, the capital of the country. Carmen de Andacollo is located approximately at 1,000 metres above sea level.

Figure 1.1. Location of Carmen de Andacollo mine.

1.2 CLIMATE

CDA is an open pit mine situated in the Cordillera de la Costa (Chilean Coastal Range), in the southernmost section of the Atacama Desert, which determines the cool semi-arid desert climate of this part of Chile (Figure 1.2). The average yearly temperature is 18,8°C, including extremes varying from -5°C in winter to 32°C during summer. Most rain falls from May to August with an average of 100 mm/year.

Figure 1.2. Chilean Coastal Range near Carmen de Andacollo.

1.3 FRAMEWORK AND METHODOLOGY FOR THE RESEARCH

Drilling Specific Energy (DSE) is generated from drill rig operations. In CDA, three drill rigs are sending information about operational parameters (torque, the velocity of penetration among others) which allows the calculation of this variable in real time and automatically. Also, the relationships between DSE and geological features has been studied (Araya et al., 2015), such as faults (low DSE areas) or lithological and alteration domains (i.e. tuff with albitic alteration, showing high DSE values).

As an important limitation, DSE is only available for grade control planning, because drill rigs develop blast holes of only one or two benches depth. It solely permits to develop DSE inverse distance estimation to only three months in advance and DSE values for blocks into the 5-year plan (5YP) are only calculated through an average by geological domain. To overcome this limitation, through this research three predictive model for DSE will be created using a statistical approach. The goal is to obtain a better performance for any of the regression models than the current average by domain model for DSE. If this is achieved, the blocks of the 5YP will be populated with DSE values estimated from the regression (Figure 1.3).

The principal steps for this research are framed as follows:

1. Definition of DSE domains using the historical DSE data (Figure 1.3), based on a combination of geological attributes: lithology, minzone, alteration and the intensity of argillic and quartz-sericite alterations.

2. Construct three regression models for DSE (Equation 1), using as predictors the information contained in the grade control block model (assays, geological, geotechnical and geo-metallurgical).

(Equation 1) 퐷푆퐸=푓(푥1, 푥2,…,푥푛) 푤ℎ푒푟푒 푥𝑖=푣푎푟𝑖푎푏푙푒푠 푓푟표푚 푏푙표푐푘 푚표푑푒푙

Figure 1.3. Conceptualization for the research.

3. To construct the model, a train group is used, which corresponds to the information contained in approximately 90% of grade control blocks. Modelling will be carried out using statistical approaches. Algorithms to be used are multiple linear regression (MLR), regression trees and artificial neural networks. Advantages for MLR are simplicity and opportunity to incorporate it easily into the block model, for instance via scripts in Vulcan®. One MLR disadvantage is that is only applicable for quantitative variables. Advantages for regression tree and artificial neural networks are their usually better predictive performance and use of both qualitative and quantitative variables.

4. For a statistical validation, a test group is used, which corresponds to about 10% of grade control blocks. The test group comprises fresh data that has never been “seen” by the model. Using the test group, a complete statistical evaluation will be conducted comparing the performance of each regression model.

5. The best regression model regarding statistical results on the test group, will be compared to the results of the average by domain model, currently used in CDA. If the results of this regression model are better than the results average by domain model on the test group, then the regression model will be used to predict the 5YP block model.

6. Areas with geological combinations still not reached for the drill rig operation, particularly, primary with gypsum/anhydrite veinlets, will not be considered in the analysis and as a consequence, DSE values will be not predicted (N/A zone, Figure 1.3).

2 GEOLOGY

2.1 TECTONIC FRAMEWORK

The geological evolution of Chile has mainly been occasioned by the subduction of the Pacific Ocean floor below South America. The main feature generated by this long process is the Andes chain of mountains (Pankhurst and Hervé, 2007).

Subduction has been active from Early Jurassic (approximately 200 Ma) and has experienced not only different subduction directions but also changing convergence rate (Allmendinger and González, 2010; Pardo-Casas and Molnar, 1987; Kay et al., 1999). Rapid convergence rates (> 100 mm/year) has been associated with a high tectonic activity, whereas low convergence rates (<50 mm/year) has been related to diminished tectonic periods but intense magmatic activity (Pardo-Casas and Molnar, 1987). During orogenic evolution, several oceanic ridges were subducted. Their location has determined the orogen segmentation as well as the different subduction angles where the Juan Fernández and the Chile ridges intersect the continental margin (Pardo et al., 2002, Charrier et al., 2007).

2.2 REGIONAL GEOLOGY

The presence of plutonic, sedimentary and volcanic units determine the regional geology of the studied area (Figure 2.1). The Arqueros Formation and the Quebrada Marquesa Formation represent the Early Cretaceous volcanic arc in the studied area (Aguirre and Egert, 1965). These formations comprise thick volcaniclastic deposits and lavas with marine calcareous intercalations (Aguirre & Egert, 1965; Thomas, 1967). The close relationship between limestones and lavas indicates that this arc was topographically depressed (Charrier et al., 2007). The Arqueros Formation is Neocomian age, based upon fossiliferous content and 40Ar/39Ar radiometric dating on amphibole. The Quebrada Marquesa Formation conformably overlies the Arqueros Formation (Aguirre & Egert, 1965), and comprises a 1900-m-thick succession of continental coarse and fine sedimentary deposits, volcaniclastic deposits, and lavas, with an intercalation of fossiliferous limestone at the base. These fossils and radiometric dating signpost a Hauterivian to Middle Albian age for this unit (Aguirre & Egert, 1962; Thomas, 1967; Pineda and Emparán, 2006; Charrier et al., 2007).

Plutonic activity was developed contemporaneously with trans-tensional tectonic associated with the Romeral Fault, syn-magmatic east-dipping structure, characterized for mylonite and cataclasite facies (Charrier et al., 2007). Regionally, intrusives belong to the Complejo Intrusivo Tablalalume (Tablalalume Intrusive Complex), which comprises diorite, granodiorite, and tonalite (Thomas, 1967).

Figure 2.1. Regional geology of the Carmen de Andacollo area (Emparán and Pineda, 2006).

2.3 GEOLOGY OF THE CARMEN DE ANDACOLLO DEPOSIT

The CDA deposit is constrained by a fault-bounded north-south depression filled with gravels of Tertiary age. Beneath the gravels, the Quebrada Marquesa Formation contains volcanic and volcaniclastic sequences, affected by a non- deformational burial metamorphism which varies from zeolite to greenschist facies (Oyarzún et at., 1996). Dioritic to tonalitic stocks and dykes (98 ± 2, 104 ± 3 Ma whole rock K/Ar ages, Reyes, 1991) intrude the Quebrada Marquesa Formation.

2.3.1 STRUCTURES

Both faults and joints are recognized in CDA. The major faults of the deposit are shown in Figure 2.2.

Figure 2.2. Photogrammetric image displaying major faults in the Carmen de Andacollo deposit. The image is facing to the north.

All the structures in the deposit belong to one of the following three systems:

Andacollo-Central-Hermosa Fault System. North-south strike and dipping 70° to 80°W, displaying from 1 m width (Hermosa Fault) up to more than 10 m (Andacollo Fault, Figure 2.3). The Andacollo Fault shows dilatational displacement of about 100 m and corresponds to the eastern limit for mineralization. Also, the Hermosa Fault controls the emplacement of porphyry and hydrothermal fluids in the deposit (Araya et al., 2012).

Figure 2.3. Crosscutting of the Andacollo fault by El Churque fault at the eastern slope of Carmen de Andacollo open pit.

Carmen-Stan-Twila Fault System. Striking N60°W and dipping 70° to 85°S, displaying from 1 m width (Stan Fault) up to more than 10 m (Twila Fault, Figure 2.4).

Figure 2.4. Twila fault in eastern slope at CDA open pit. The activity of this structure has generated the brownish shade fractured zone in the image.

El Churque-El Toro Fault System. Striking N30° to 40°E and dipping 70° to 85°N, metric width. Corresponds to the later deformational stage, offsetting through a dextral-extensional movement all the other systems (Figure 2.5).

Tuff

PorfMin

Andesite

Tuff

Figure 2.5. El Toro Fault showing dextral offsetting. Tuff and andesite in contact.

To sum up, the structural framework is particularly important in Carmen de Andacollo deposit, not only controlling the mineralization processes but also offsetting the lithological and minzone units (Figure 2.6). Additionally, the faults control the supergene alteration process, bringing about the reduction of rock quality and accordingly impacting on Drilling Specific Energy.

Figure 2.6. Extensional faulting array in Carmen de Andacollo deposit, offsetting blanket of secondary enrichment.

2.3.2 LITHOLOGY

The Quebrada Marquesa Formation corresponds to the main lithological framework in the Carmen de Andacollo deposit. In the studied area, this formation consists of andesitic breccia and lava underlying dacitic tuff (Figure 2.7).

Figure 2.7. Lithological units in Carmen de Andacollo deposit with original topography (before mining). The Quebrada Marquesa Formation correspond to andesites (green) and tuff (yellow).

Lithological units display several textural varieties (Figure 2.8). Andesitic sequences locally denominated Lower Volcanic Unit, comprise interlayer of porphyritic and micro porphyric andesite, andesitic breccia and aphanitic andesite. Underlying this unit, Upper Volcanic Unit consists of vitreous, crystalline and lithic tuff and trachytic lava. Intrusive rocks cut both the Lower Volcanic Unit and the Upper Volcanic Unit. Early intrusions comprise north-western dyke-like dacitic porphyry, locally denominated PorMin. PorPost corresponds to rhyolitic to andesitic porphyry dyke-like striking north-south or irregular stock. Finally, associated with the western part (hanging wall) of Hermosa Fault, the Hermosa Breccia comprises a strongly tectonically deformed hydrothermal breccia (Araya et al., 2012).

Upper Volcanic Unit Volcanic Upper

Coarse porphyritic andesite Fine porphyritic andesite Vitreous tuff Volcanoclastic rock

VolcanicUnit Lower

Microporphyritic andesite aphanitic andesite Crystalline tuff Traquitic lava Hermosa Breccia Hermosa

Andesitic breccia Medium porphyritic andesite Lithic tuff

PorPost PorMin

Dacitic porphyry Rhyolitic porphyry Andesitic porphyry Figure 2.8. Lithological types at Carmen de Andacollo deposit. As indicated above, major faults have offset and put in contact different lithological units in the deposit. In this context, the Hermosa Fault displays the most remarkable offset in Carmen de Andacollo. For this structure, hanging wall contains tuff (western portion), whereas footwall (eastern portion), corresponds to andesite (Figure 2.9).

Figure 2.9. Photogrammetric image displaying lithological units and major faults in Carmen de Andacollo deposit. The image is facing to the north.

2.3.3 ALTERATION AND MINERALIZATION

Alterations and mineralization identified in CDA deposit are typical of porphyry type deposits, including late magmatic, transitional, hydrothermal and supergene stages (Araya et al., 2012).

Late magmatic stage comprises a potassic-sodic alteration central zone surrounded by propylitic alteration (Figure 2.10).

Figure 2.10. Alteration units in Carmen de Andacollo deposit with original topography (before mining).

Porphyry, particularly porfmin, are spatially associated with potassic-sodic alteration. Characteristically for andesite, alteration corresponds with fine-grained secondary biotite and minor K-feldspar and anhydrite (Figure 2.11), typically expressed as veinlets of EB or A type, considering the definition from Gustafson and Hunt (1975). Sodic alteration, distinctive of tuff, comprises albite and minor K-feldspar, chlorite, and quartz (Figure 2.12). Sodic alteration brings about a white colour on the tuff. Mineralization associated with potassic-sodic alteration corresponds to pyrite, chalcopyrite, magnetite and minor bornite and molybdenite. For propylitic alteration, distinctive minerals are chlorite, calcite, epidote, ankerite, and actinolite (Figure 2.13). Mineralization of this zone corresponds to magnetite, pyrite and minor chalcopyrite.

Figure 2.11. (1) Veinlet of quartz-biotite. Scale in cm (2) Microphotography of the same veinlet showing quartz central suture and biotite, K-feldspar and anhydrite halo. Cross polarized. Magnification 40X.

Figure 2.12. (1) Microphotography of disseminated chalcopyrite and magnetite in a tuff matrix. Cross polarized reflected light. 100X. (2) Microphotography of matrix tuff replaced by albite. Parallel polarized light. Magnification 40X.

Figure 2.13. Quartz-chlorite-carbonate veinlet. Parallel polarized light (1) and cross polarized light (2). Magnification 40X.

Transitional stage comprises continuous planar quartz molybdenite veinlet (Figure 2.14), usually expressing internal banding and up to 5 cm in width. Frequently these veins display coarse prismatic crystals of quartz, orthogonal to the wall and locally containing chalcopyrite. These veins are classified as type B, using the definition from Gustafson and Hunt (1975).

Figure 2.14. Microphotography displaying molybdenite and chalcopyrite in quartz veinlet. Cross polarized reflected light. Magnification 100X.

Hydrothermal stage: this is showing both structural and lithological control. Structurally, the Hermosa fault acts as the main control for hydrothermal alteration, whereas tuff is the main lithological control. Hydrothermal stage contains phyllic and intermediate argillic sub-stages. A fined-grained aggregate of quartz and sericite and minor clays (Figure 2.15), analogous to the D vein defined by Gustafson and Hunt (1975) at El Salvador characterises the phyllic sub-stages. Mineralization contains a large amount of pyrite and minor chalcopyrite and traces of sulphosalt. Intermediate argillic sub-stage comprises kaolin, smectite, siderite, and baritine. Mineralization includes sphalerite, galena, and cinnabar. Also, a categorical model for high, mid and low phyllic (quartz- sericite) alteration intensity is presented in Figure 2.16.

Figure 2.15. (1) Quartz-sericite veinlet (Type D) with pyrite-(chalcopyrite) suture and quarz-sericite halo in andesite. (2) Microphotography showing pyrite-chalcopyrite- molybdenite association. Cross polarized reflected light. Magnification 100X.

Figure 2.16. Quartz-sericite intensity units in Carmen de Andacollo deposit with original topography (before mining).

Supergene stage represents the last and the most superficial alteration and mineralization stage. Irregular layers characterise the supergene stage (Figure 2.17).

Figure 2.17. Minzone units in Carmen de Andacollo deposit with original topography (before mining).

From top to bottom the layers are the following:

• Leached: a profusion of iron oxides and sulphide traces.

• Esec1: Strong secondary enrichment zone. Presence of chalcocite and traces of covellite. Only vestiges of chalcopyrite (Figure 2.18).

Figure 2.18. (1) Secondary chalcocite partially replaced by copper oxides. (2) Pyrite and chalcopyrite replaced by secondary chalcocite. Cross polarized reflected light. Magnification 100X.

• Esec2: Weak secondary enrichment zone. Esec2 encompasses chalcocite and covellite and a significant amount of chalcopyrite.

• Primc: Primary with cavities. The supergene acid solution has dissolved the sulphates (anhydrite/gypsum).

• Prims: Primary without cavities. The supergene acid solution has not dissolved the sulphates (anhydrite/gypsum). Hence, this zone has very low amount of open fractures.

The clays halloysite, nontronite, montmorillonite, and kaolin are characteristic for the supergene process. The intensity of argillic alteration decreases with depth. Also, a categorical model for high, mid and low for argillic (clays) alteration intensity is presented in Figure 2.19. Finally, it is also important to emphasize that DSE is contained in all the layers, with the important exception of prims, because blast hole drilling still has not reached this zone of the deposit.

Figure 2.19. Argillic intensity units in Carmen de Andacollo deposit with original topography (before mining).

The relationships between the different alteration-mineralization stages has been established at CDA (Araya et al., 2012). Figure 2.20 displays some crosscutting relationships distinctive of CDA. Additionally, the paragenesis for alteration- mineralization mineral species at CDA deposit is presented in Figure 2.21.

Figure 2.20. Crosscutting relationships, showing different stages in the evolution of Carmen de Andacollo deposit. From oldest to later: EB-type, early biotite-quartz; A-type veinlet, quartz-K-feldspar; B-type, quartz-molybdenite banded veinlet.

Figure 2.21. Alteration and mineralization paragenesis at Carmen de Andacollo deposit. Modified from Araya et al. (2012).

3 MINING AND PROCESSING

CDA is an open pit mine with heap leaching and concentrator plant operations (Figure 3.1).

Figure 3.1. Panoramic view of CDA mine. The photograph is looking to the northwest.

The CDA project started its operations as a heap leaching operation in 1996 and will terminate its activities in 2021. Originally, the project was based on reserves of 34 million tonnes with 0.73% soluble copper. This operation has developed to date 18 mining phases considering 5 m height bench and 90 tonnes mining trucks. Mineralogically, the ore is characterized by the presence of chalcocite and minor covellite. Copper oxides are present only as traces. The simplified layout for the mineral processing is displayed in Figure 3.2. It comprises crushing, agglomeration, heap leaching (static leach pad), solvent extraction and electrowinning. The output of the process is cathodes, with an annual copper production in the region of 4,500 tonnes.

Figure 3.2. Heap leaching simplified layout in Carmen de Andacollo mine. From 2010, a 55,000 tonnes/day concentrator plant has been operating in CDA. The mining operation is scheduled in 9 phases up to the year 2035 and considers 10 m height bench and ten mining trucks of 185 tonnes capacity, one backhoe and one face shovel excavator of 27 m3 bucket capacity and smaller support machinery. Initial reserves for concentrator plant were 400 million tonnes of primary sulphides, with 0.4% total copper and 0.14 ppm gold. Mineralogically, the ore corresponds to chalcopyrite (>95% of total sulphides) and minor bornite, sulfosalts, sphalerite, galena, and cinnabar. Figure 3.3 illustrates the simplified layout of CDA comminution circuit, which comprises pre-crushed, SAG mill, pebbles crusher, and two ball mills. The result of the process is copper concentrates, with an annual production in the order of 280,000 tonnes of concentrate, containing around 72,000 tonnes of copper and 52,000 gold ounces.

Figure 3.3. Simplified comminution circuit layout in CDA mine.

3.1 DRILLING OPERATION

3.1.1 DSE DEFINITION

Drilling Specific Energy or DSE (Teale, 1965) is defined as the energy applied per a unit volume of material removed during rotational drilling (Equation 2).

푡표푡푎푙 푒푛푒푟𝑔푦 Equation 2 퐷푆퐸 = 푣표푙푢푚푒푛 푟푒푚표푣푒푑

Volume removed by drilling corresponds to the area of the cross section multiplied by the depth of penetration. Total energy is equivalent to the Force multiplied by distance. During drilling, there are two forces working on the drill bit: the weight on bit, corresponding to the axial force and torque, related to the rotational force. These parameters are additive for DSE (Hamrick, 2011). These two components can be expressed as shown in Equation 3.

푣푒푟푡푖푐푎푙 푒푛푒푟𝑔푦 푖푛푝푢푡 푟표푡푎푡푖표푛푎푙 푒푛푒푟𝑔푦 푖푛푝푢푡 Equation 3 퐷푆퐸 = + 푣표푙푢푚푒푛 푟푒푚표푣푒푑 푣표푙푢푚푒푛 푟푒푚표푣푒푑 푊푂퐵∗훥ℎ 푡표푟푞푢푒∗2휋 퐷푆퐸 = + 푎푟푒푎∗훥ℎ 푎푟푒푎∗훥ℎ

In Equation 3, WOB = weight on bit (lb), whereas Δh is equivalent to the distance covered by the bit and can be expressed as indicated in Equation 4. In Equation 4, RPM = rotations per minute, whereas ROP = rate of penetration (in/hr). Finally, DSE can be termed as indicated in Equation 5.

푅푂푃 Equation 4 훥ℎ = 푅푃푀

푊푂퐵 푡표푟푞푢푒∗2휋∗푅푃푀 Equation 5 퐷푆퐸 = + 푎푟푒푎 푎푟푒푎∗푅푂푃

3.1.2 DRILLING AT CDA

A polygon is the area of a bench in which a specific configuration for drilling and blasting is defined (powder factor, burden, spacing, the length of stemming and amount and disposition for detonators). Both production and contouring polygons are used at CDA. Production polygons (Figure 3.4, zone A) include areas not in contact with final phase or pit slope. Contouring polygons (Figure 3.4, zone B) include limits for the pit or a phase. For this reason, in contouring polygons pre- cut and buffer drilling and blasting are carried out.

Figure 3.4. Configuration for drilling and blasting at CDA mine.

4 INTEGRITY OF DSE DATA

To assure the integrity of DSE data, validation has been conducted based upon a comparison of different drill rigs and operators.

For validation, a 44,192 DSE data base has been used, which includes the identification of drilling rigs and the operators of this machinery. This data is distributed between 1,040 and 880 benches.

4.1 DRILL RIG VALIDATION

Table 4.1 displays the results of the crossing of minzone and lithology attributes for DSE data, with regards to drill rigs D003, D005, and D006. Because more than 90% of data belong to prim (40,204 out of 44,192 DSE data), only this mineral zone will be used, regarding all others mineral zones as not containing enough data to carry out an appropriate validation.

Table 4.1. DSE data for lithology, minzone and drill rigs. minzone lithology Drill Rig esec1 esec2 leached prim Grand Total D003 197.3 187.7 216.9 197.0 196.8 andesite D005 200.5 185.6 186.2 D006 153.3 186.4 234.0 197.8 197.6 total andesite 185.5 191.5 218.0 195.1 195.1 D003 167.9 182.6 182.6 182.3 breccia D005 199.0 169.2 182.2 D006 166.0 184.5 183.2 183.2 total breccia 167.2 186.2 181.8 182.6 D003 149.2 190.9 139.3 203.3 202.6 pormin D005 188.6 189.9 188.3 188.5 D006 155.2 193.5 182.1 198.5 197.2 total pormin 171.2 191.3 177.3 198.7 197.7 D003 152.6 200.1 204.6 204.6 porpost D005 220.4 209.5 198.1 198.3 D006 217.3 206.7 206.8 total porpost 186.5 208.8 204.5 204.5 D003 199.2 204.7 217.8 215.4 tuff D005 199.8 194.8 204.8 203.5 D006 180.2 199.2 161.7 215.1 212.4 total breccia 195.5 200.1 161.7 213.2 211.0 Grand Total 193.7 198.0 195.3 203.9 203.3

Table 4.2 shows the basic statistics of DSE for each drill rig, considering as stated above, only mineral zone prim.

Table 4.2. Basic DSE statistics for the three drill rigs.

Drill Rig mean N stdev Q25 median Q75 D003 206.2 16,161 37.2 176.9 204.0 233.9 D005 197.0 9,237 35.4 169.4 192.4 220.3 D006 205.7 14,806 36.5 177.7 203.1 232.3 Total 203.9 40,204 36.7 175.4 200.9 230.4

Drill rigs D003 and D006 display a similar mean, Q25, median and Q75. However, the mean for D005 is 4.5 and 4.3% lower than the means of D003 and D006, respectively. Furthermore, for D005 lower values for Q25, median and Q75 are recognized. Figure 4.1 presents the distribution of DSE values for each lithology, using Q25, median, and Q75. For the five lithological domains, interquartile range

(IQR, interval Q25-Q75) for D005 is significantly lower than IQR for D003 and D006. Moreover, IQR for D003 and D006 exhibit comparable distribution. Consequently, DSE data for D005 is removed from the analysis and henceforth, only data from D003 and D006 drill rigs will be considered.

Figure 4.1. Statistical distribution of DSE values for five lithological domains.

4.2 OPERATORS VALIDATION

Table 4.3 lists the count of DSE data by the operator of drill rig machinery. To simplify the validation process only the operators with more than 2,500 blast holes drilled will be studied. These six operators are highlighted in bold in Table 4.3.

Table 4.3. Number of DSE data by drill rig operator.

Operator Total CARLOS_TIRADO 4,340 AQUILES_YÁÑEZ 3,837 JUAN_GONZÁLEZ 3,676 PATRICIO_ARÉVALO 3,074 CARLOS_HONORES 2,802 WILSON_VÉLIZ 2,594 HÉCTOR_BUGUEÑO 1,599 JUAN C._MORALES 1,516 GUILLERMO_NÚÑEZ 1,511 HÉCTOR_DÍAZ 1,473 LUIS_PASTÉN M 1,445 PEDRO_ROMERO 1,242 CLAUDIO_UGARTE 911 ROBINSON_ARAYA 872 JUAN_NÚÑEZ 698 MARIO_CASTILLO 681 DIEGO_CUELLO 618 MATEO_ACUÑA 308 NELSON_ROMERO 262 CARLOS_FERNÁNDEZ 154 MIGUEL_MUÑOZ 89 LUIS_PASTÉN C 81 NO OP_DEFAULT 58 PERCY_PÉREZ 1 Total 33,842

Table 4.4 exhibits the basic statistics of DSE for the six operators considered. As indicated previously, Table 4.4 solely includes data from drill rigs D003 and D006 and minzone prim.

Table 4.4. Basic DSE statistics for six main operators.

Operator mean N stdev Q25 median Q75 Aquiles Yánez 205.5 3,495 34.6 179.8 203.3 230.3 Wilson Véliz 201.1 2,334 35.5 173.4 197.3 225.5 Carlos Honores 207.0 2,635 38.0 176.3 204.4 236.1 Juan González 206.4 3,323 37.0 177.5 204.1 233.6 Carlos Tirado 212.5 4,036 36.3 185.0 211.1 239.7 Patricio Arévalo 205.7 2,686 38.7 174.2 203.7 235.3 Total 206.9 18,509 36.8 178.2 204.5 234.0

Figure 4.2 shows the DSE values for the six operators, using Q25, median, and

Q75. In consideration of 4 different lithological domains, no operator systematically displays the highest or the lowest of Q25, median, and Q75 for DSE. Therefore, this result allows validating the DSE data, which is not dependant on the operators.

Figure 4.2. Statistical distribution of DSE values for six main operators, divided by four principal lithological domains.

In short, revision of DSE data considering the three drill rigs and six operators in a context of lithological domains in mineral zone “Prim”, has permitted on the one hand to recognize that D005 expresses DSE values significantly lower than D003 and D006. Thus, data from D005 will be removed from the analysis. On the other hand, the review has revealed that there is no distinct difference for the DSE data among the six operators evaluated.

For the stated above, from the original data base of 44,192 DSE data, 10,350 data from drill rig D005 has been removed. Consequently, the final data base for carrying out this research comprises of 33,842 DSE data.

5 DSE EXPLORATORY DATA ANALYSIS

The use of geological attributes of a deposit and the understanding of their relationships, allows the definition of domains through Exploratory Data Analysis (EDA). This process can take a substantial amount of time, especially if the total combinations of geological attributes is considered (Rossi and Deutsch, 2014). Nonetheless, carrying out EDA is key for any estimation process, because the quality of estimation is improved using these geological domains (Rossi and Deutsch, 2014; Sinclair and Blackwell, 2002).

For this research, EDA is carried out using the 33,842 DSE valid data. Spatial distribution of these is displayed in Figure 5.1.

Figure 5.1. Plan view displaying the spatial distribution of DSE values.

The aim of EDA is to determine appropriate domains for DSE regarding statistical behaviour. To reach this goal, the statistical distribution of DSE for different geological attributes included in the CDA block model are compared. DSE data is grouped in domains if the statistical distribution is similar. The specific geological attributes considered in this research are: a) lithology; b) minzone; c) alteration types; d) argillic intensity; e) quartz-sericite intensity.

a) Lithology includes five types: andesite, tuff, porfpost, porfmin and hydrothermal breccia. The distribution of 33,842 DSE values by each lithology is shown in Figure 5.2.

Figure 5.2. Plan view showing the spatial distribution of DSE values by lithology.

29 b) Minzone comprises four types: leached, esec1, esec 2 and primc. the distribution of 33,842 DSE values by each minzone is presented in Figure 5.3.

Figure 5.3. Plan view illustrating the spatial distribution of DSE values by minzone.

c) Alteration is composed of six types: albitic, biotitic, propylitic, argillic, quartz-sericite and potassic. The distribution of 33,842 DSE values by each alteration is displayed in Figure 5.4.

Figure 5.4. Plan view illustrating the spatial distribution of DSE values by alteration type.

d) Argillic includes three intensities: low, medium and high. The distribution of 33,842 DSE values by the three argillic intensities is exhibited in Figure 5.5.

Figure 5.5. Plan view displaying the spatial distribution of DSE values by argillic intensities. e) Quartz-sericite consists of three intensities: low, medium and high. The distribution of 33,842 DSE values by these three quartz-sericite intensities is exhibited in Figure 5.6.

Figure 5.6. Plan view presenting the spatial distribution of DSE values by quartz- sericite intensities.

The relationships between DSE and the five geological attributes are evaluated using an Importance Plot graphic (Figure 5.7). This graphic is based on a 2

Fisher independence test, regarding null hypothesis (H0): “DSE is not dependent on the geological attributes”. The greater the value of 2 (bar length), the more valid is that H0 is incorrect. Considering the graphic, the attributes that best explain or are more dependent on DSE are lithology, alteration, argillic intensity (“Arg”) and minzone. Quartz-sericite intensity (“QS”) is not related to the statistical behaviour of DSE, and it is not taken into account for EDA. Nonetheless, in attribute alteration, the quartz-sericite intensity is indirectly considered in the category “quartz-sericite”.

Figure 5.7. Importance Plot for geological attributes and dependent (response) variable DSE.

5.1 DSE FOR LITHOLOGY

Table 5.1 displays the DSE basic statistics by lithology, whereas the probability plot (Figure 5.8) shows the statistical distribution of these data. Based on these results, each lithology corresponds to the individual group for the following analysis.

Table 5.1. DSE basic statistics by lithology.

Standard Lithology Means N Q Median Q deviation 25 75 Andesite 197.3 13,441 33.0 172.8 193.8 218.6 PorMin 199.5 1,930 35.1 172.8 196.2 223.3 Tuff 213.9 15,069 38.7 183.8 214.9 244.8 PorPost 205.9 2,801 38.0 175.9 202.7 234.1 Breccia 182.6 601 36.1 155.1 174.5 203.6 All Grps 205.3 33,842 37.2 176.1 202.7 232.7

Figure 5.8. Probability Plot for DSE by lithology.

5.2 DSE FOR MINZONE IN LITHOLOGY

5.2.1 DSE FOR MINZONE IN BRECCIA

Table 5.2 exhibits the basic statistics of DSE for minzones in breccia, while the probability plot (Figure 5.9) displays the statistical distribution of these data. Considering the low number of samples (N=601) and the correspondence of statistics and distribution of these groups, all the minzones in breccia are grouped in only one unit.

Table 5.2. DSE basic statistics by minzone in breccia.

Standard Minzone Means N Q Median Q deviation 25 75 Prim 182.8 469 36.4 154.9 174.5 203.6 Esec1 181.8 24 43.8 146.1 165.7 200.0 Esec2 182.0 108 33.3 157.2 175.1 204.2 All Grps 182.6 601 36.1 155.1 174.5 203.6

Figure 5.9. Probability Plot for DSE by minzone in breccia.

5.2.2 DSE FOR MINZONE IN ANDESITE

Table 5.3 shows the basic statistics of DSE for minzones in andesite, whereas the probability plot (Figure 5.10) displays the statistical distribution of these data. Minzones are assembled into two groups considering the number of samples and the differences in statistics and distribution of these groups between primary and supergene minzones, with higher and lower DSE values, respectively. Despite the high DSE values for leached minzone, it is necessary to group it with esec1 and esec 2, because these three minzones together comprise the supergene zone. As previously indicated (Chapter 2), leached corresponds to the upper part of this zone. Also, it is not appropriate to separate leached minzone as an individual unit due to its low number of samples (N=17).

Table 5.3. DSE basic statistics by minzone in andesite.

Standard Minzone Means N Q Median Q deviation 25 75 Prim 197.5 13,141 32.9 173.1 193.9 218.8 Esec1 180.5 21 37.7 145.3 182.2 197.6 Esec2 187.5 262 34.7 160.5 180.0 203.6 Leached 219.5 17 40.1 204.1 234.0 239.5 All Grps 197.3 13,441 33.0 172.8 193.8 218.6

Figure 5.10. Probability Plot for DSE by minzone in andesite.

5.2.3 DSE FOR MINZONE IN PORMIN

Table 5.4 demonstrates the basic statistics of DSE for minzones in pormin, while the probability plot (Figure 5.11) exhibits the statistical distribution of these data. Vis-à-vis the low number of samples for supergene minzones (esec1, esec2 and leached) compared with primary, all the minzones in pormin are assembled as a unique unit.

Table 5.4. DSE basic statistics by minzone in pormin.

Standard Minzone Means N Q Median Q deviation 25 75 Prim 200.5 1,816 34.6 174.4 197.2 224.0 Esec1 152.0 20 11.7 142.7 149.2 161.0 Esec2 192.7 83 40.5 161.2 182.4 225.8 Leached 179.5 11 31.7 153.4 185.4 208.2 All Grps 199.5 1,930 35.1 172.8 196.2 223.3

Figure 5.11. Probability Plot for DSE by minzone in pormin.

5.2.4 DSE FOR MINZONE IN PORPOST

Table 5.5 shows the basic statistics of DSE for minzones in porpost, whereas the probability plot (Figure 5.12) displays the statistical distribution of these data. Analogous to the pormin situation (5.2.3), regarding the low number of samples for supergene minzones (esec1, esec2 and leached), all the minzones in the lithology porpost are considered as an individual unit.

Table 5.5. DSE basic statistics by minzone in porpost.

Standard Minzone Means N Q Median Q deviation 25 75 Prim 205.8 2,767 38.0 175.9 202.7 234.0 Esec1 147.5 2 7.3 142.4 147.5 152.6 Esec2 216.9 32 37.0 183.3 211.1 247.3 All Grps 205.9 2,801 38.0 175.9 202.7 234.1

Figure 5.12. Probability Plot for DSE by minzone in porpost.

5.2.5 DSE FOR MINZONE IN TUFF

Table 5.6 presents the basic statistics of DSE for minzones in tuff, while the probability plot (Figure 5.13) demonstrates the statistical distribution of these data. Minzone are divided into two groups based on the number of samples and the differences in statistics and distribution of DSE between primary and supergene minzones, with higher and lower DSE values, correspondingly.

Table 5.6. DSE basic statistics by minzone in tuff.

Standard Minzone Means N Q Median Q deviation 25 75 Prim 216.4 12,793 38.0 187.7 217.6 247.0 Esec1 195.3 483 38.9 161.0 189.2 224.1 Esec2 200.8 1,789 39.6 168.3 196.9 231.0 Leached 151.9 4 13.7 143.2 147.8 160.6 All Grps 213.9 15,069 38.7 183.8 214.9 244.8

Figure 5.13. Probability Plot for DSE by minzone in tuff. Finally, Table 5.7 displays the basic statistics by the seven combinations of the attributes lithology and minzone. These combinations are termed from A1 to A7.

Table 5.7. DSE basic statistics by the seven lithology-minzone combinations.

Lithology Minzone Mean N Combination Breccia All 182.6 601 A1 Supergene 188.8 300 A2 Andesite Primary 197.5 13,141 A3 PorMin All 199.5 1,930 A4 PorPost All 205.9 2,801 A5 Supergene 199.5 2,276 A6 Tuff Primary 216.4 12,793 A7 All Grps 33,842

5.3 DSE FOR ALTERATION IN LITHOLOGICAL-MINZONE COMBINATION

5.3.1 DSE FOR ALTERATION IN BRECCIA (A1)

Table 5.8 exhibits the basic statistics of DSE for alteration in breccia (combination A1), whereas the probability plot (Figure 5.14) demonstrates the statistical distribution of these data. Considering the low number of samples (N=601) and the equivalence in statistics and distribution of DSE, all the alterations in the combination A1 are grouped as one unit.

Table 5.8. DSE basic statistics by alteration in breccia.

Standard Alteration Means N Q Median Q deviation 25 75 Biotite 189.3 29 40.3 154.9 187.8 216.4 Quartz-sericite 183.9 156 34.1 155.6 176.4 206.2 Argillic 179.3 341 36.4 152.1 165.6 201.4 Albite 192.9 74 35.3 170.3 185.6 211.2 Propylitic 150.3 1 0.0 150.3 150.3 150.3 All Grps 182.6 601 36.1 155.1 174.5 203.6

Figure 5.14. Probability Plot for DSE by alteration in breccia.

5.3.2. DSE FOR ALTERATION IN ANDESITE IN SUPERGENE (A2)

Table 5.9 shows the basic statistics of DSE for alteration in andesite in minzone supergene (combination A2), whereas the probability plot (Figure 5.15) exhibits the statistical distribution of these data. Regarding the low number of samples (N=300) and the fact that most of the samples are associated with one alteration (biotite), all the alterations in the combination A2 are aggregated as a unique unit.

Table 5.9. DSE basic statistics by alteration in andesite in supergene.

Standard Alteration Means N Q Median Q deviation 25 75 Biotite 188.1 222 34.2 163.0 181.1 204.1 Quartz-sericite 167.8 8 39.5 143.1 151.6 178.6 Argillic 156.5 1 0.0 156.5 156.5 156.5 Albite 196.2 54 42.7 159.1 191.8 239.5 Propylitic 184.8 15 29.4 160.3 181.4 193.9 All Grps 188.8 300 35.9 160.4 181.8 206.8

Figure 5.15

Figure 5.15. Probability Plot for DSE by alteration in andesite in supergene.

5.3.3 DSE FOR ALTERATION IN ANDESITE IN PRIMARY (A3)

Table 5.10 shows the basic statistics of DSE for alteration in lithology andesite in minzone primary (combination A3), while the probability plot (Figure 5.16) shows the statistical distribution of these data. Due to the number of samples and the similarities on statistics and distribution of DSE, alterations are combined in two groups. The first, which corresponds to lower DSE values, is comprised of biotite, quartz-sericite, argillic and propylitic. The second contains the alterations with the higher DSE values albite and potassic.

Table 5.10. DSE basic statistics by alteration in andesite in primary.

Standard Alteration Means N Q Median Q deviation 25 75 Biotite 197.5 11,715 32.3 173.5 194.0 218.4 Quartz-sericite 195.7 111 33.8 170.1 193.9 214.9 Argillic 177.9 203 29.4 155.8 173.9 192.3 Albite 204.2 699 38.3 174.1 202.1 233.5 Propylitic 187.1 211 27.9 166.4 186.0 207.1 Potassic 210.1 202 38.8 178.9 204.5 238.7 All Grps 197.5 13,141 32.9 173.1 193.9 218.8

Figure 5.16. Probability Plot for DSE by alteration in andesite in primary.

5.3.4 DSE FOR ALTERATION IN PORMIN (A4)

Table 5.11 presents the basic statistics of DSE for alteration in lithology pormin (combination A4), whereas the probability plot (Figure 5.17) displays the statistical distribution of these data. Considering most of the samples are related to one alteration (biotite), all the alterations in the combination A4 are combined as solely one unit.

Table 5.11. DSE basic statistics by alteration in pormin.

Standard Alteration Means N Q Median Q deviation 25 75 Biotite 201.7 1,382 35.2 174.7 197.4 226.2 Quartz-sericite 181.9 112 37.9 150.1 171.6 206.1 Argillic 195.1 89 36.8 164.9 192.3 221.5 Albite 197.2 228 32.5 173.2 196.9 217.9 Propylitic 195.5 98 27.5 174.1 197.2 213.9 Potassic 213.4 21 34.3 177.1 208.7 231.5 All Grps 199.5 1,930 35.1 172.8 196.2 223.3

Figure 5.17. Probability Plot for DSE by alteration in pormin.

5.3.5 DSE FOR ALTERATION IN PORPOST (A5)

Table 5.12 shows the basic statistics of DSE for alteration in lithology porpost (combination A5), while the probability plot (Figure 5.18) exhibits the statistical distribution of these data. Considering most of the samples are related to one alteration (biotite), all the alterations in the combination A5 are combined as a singular unit.

Table 5.12. DSE basic statistics by alteration in porpost.

Standard Alteration Means N Q Median Q deviation 25 75 Biotite 200.5 1,733 35.7 173.5 196.0 223.2 Quartz-sericite 210.2 114 43.9 169.8 212.4 248.8 Argillic 212.5 170 37.2 183.4 215.3 239.9 Albite 209.6 527 39.5 177.9 207.8 243.5 Propylitic 225.3 180 34.5 200.1 228.3 251.4 Potassic 236.0 77 43.8 217.4 251.1 271.2 All Grps 205.9 2,801 38.0 175.9 202.7 234.1

Figure 5.18. Probability Plot for DSE by alteration in porpost.

5.3.6 DSE FOR ALTERATION IN TUFF IN SUPERGENE (A6)

Table 5.13 shows the basic statistics of DSE for alteration in lithology tuff in minzone supergene (combination A6), whereas the probability plot (Figure 5.19) exhibits the statistical distribution of these data. Regarding the number of samples and its distribution, all the alterations in the combination A2 are collected as a unique unit.

Table 5.13. DSE basic statistics by alteration in tuff in supergene.

Standard Alteration Means N Q Median Q deviation 25 75 Biotite 201.8 58 40.1 169.7 197.4 229.0 Quartz-sericite 203.0 593 40.6 167.2 201.5 236.1 Argillic 190.4 332 38.2 158.8 182.0 216.7 Albite 200.3 1,276 39.2 167.8 196.1 230.0 Potassic 188.6 17 27.5 168.9 183.2 213.4 All Grps 199.5 2,276 39.6 166.2 195.0 229.7

Figure 5.19. Probability Plot for DSE by alteration in tuff in supergene.

5.3.7 DSE FOR ALTERATION IN TUFF IN PRIMARY (A7)

Table 5.14 displays the basic statistics of DSE for alteration in lithology tuff in minzone primary (combination A7), while the probability plot (Figure 5.20) shows the statistical distribution of these data. Due to the number of samples and the similarities in statistics and distribution of DSE, alterations are combined in two groups. The first, which corresponds to lower DSE values, is comprised of biotite and argillic. The second contains the alterations with the higher DSE values albite, potassic, quartz-sericite, and propylitic.

Table 5.14. DSE basic statistics by alteration in tuff in primary.

Standard Alteration Means N Q Median Q deviation 25 75 Biotite 201.5 1,058 38.8 168.5 198.9 231.7 Quartz-sericite 214.7 1,075 41.2 181.1 219.7 248.1 Argillic 194.4 790 38.0 161.4 191.9 222.2 Albite 219.8 9,573 36.5 193.4 221.0 249.1 Propylitic 223.1 55 39.2 199.1 220.3 257.5 Potassic 227.1 242 34.9 199.3 232.3 257.0 All Grps 216.4 12,793 38.0 187.7 217.6 247.0

Figure 5.20. Probability Plot for DSE by alteration in tuff in primary.

To conclude, Table 5.15 displays the basic statistics of DSE for the nine combinations of the attributes lithology, minzone, and alteration. These combinations are designated from B1 to B7.

Table 5.15. DSE basic statistics by nine lithology-minzone-alteration combinations.

Lithology Minzone Alteration Mean N Combination Breccia All All 182.6 601 B1 Supergene All 188.8 300 B2 Andesite Biotite+QS+Ar+Propylitic 196.9 12,240 B3 Primary Albite+Potassic 205.5 901 B4 PorMin All All 199.5 1,930 B5 PorPost All All 205.9 2,801 B6 Supergene All 199.5 2,276 B7 Tuff Biotite+Argillic 198.5 1,848 B8 Primary QS+Propilitic+Potassic+Albite 219.5 10,945 B9 All Grps 33,842

5.4 DSE FOR ARGILLIC IN LITHOLOGICAL-MINZONE- ALTERATION COMBINATION

5.4.1 DSE FOR ARGILLIC INTENSITY IN BRECCIA (B1)

Table 5.16 exhibits the basic statistics of DSE for argillic intensity in breccia (combination B1), whereas the probability plot (Figure 5.21) displays the statistical distribution of these data. Considering the low number of samples (N=601) and most of these are related to intensity high, all the alterations in the combination B1 are grouped as one unit.

Table 5.16. DSE basic statistics by argillic intensity in breccia.

Argillic Standard Means N Q Median Q Intensity deviation 25 75 Low 196.4 65 34.5 172.2 192.2 213.8 Medium 174.6 55 28.8 155.5 166.4 183.2 High 181.7 481 36.6 153.5 170.5 204.4 All Grps 182.6 601 36.1 155.1 174.5 203.6

Figure 5.21. Probability Plot for DSE by argillic intensity in breccia.

5.4.2 DSE FOR ARGILLIC INTENSITY IN ANDESITE IN SUPERGENE (B2)

Table 5.17 shows the basic statistics of DSE for argillic intensity in lithology andesite in minzone supergene (combination B2), whereas the probability plot (Figure 5.22) exhibits the statistical distribution of these data. Regarding the low number of samples (N=300) and the fact that most of the samples are associated with one argillic intensity (low), all the alterations in the combination B2 are aggregated as a unique unit.

Table 5.17. DSE basic statistics by argillic intensity in andesite in supergene.

Argillic Standard Means N Q Median Q Intensity deviation 25 75 Low 191.5 224 36.9 161.5 185.6 212.5 Medium 181.6 73 31.8 160.0 176.2 196.8 High 159.7 3 22.5 139.1 156.5 183.7 All Grps 188.8 300 35.9 160.4 181.8 206.8

Figure 5.22. Probability Plot for DSE by argillic intensity in andesite in supergene.

5.4.3 DSE FOR ARGILLIC INTENSITY IN ANDESITE IN PRIMARY WITH BIOTITE, QUARTZ-

SERICITE, ARGILLIC OR PROPYLITIC (B3)

Table 5.18 exhibits the basic statistics of DSE for argillic intensity in andesite in minzone primary with biotite, quartz-sericite, argillic or propylitic alteration (combination B3), while the probability plot (Figure 5.23) shows the statistical distribution of these data. Argillic intensities are combined in two groups since the number of samples and the similarities on statistics and distribution of DSE. The first, which corresponds to lower DSE values, comprises high and medium argillic intensity. The second contains the argillic intensity low, which expresses the higher DSE values.

Table 5.18. DSE basic statistics by argillic intensity in andesite in primary with biotite, quartz-sericite, argillic or propylitic.

Argillic Standard Means N Q Median Q Intensity deviation 25 75 Low 198.1 11,308 32.2 174.3 194.9 219.0 Medium 183.6 729 30.6 160.0 178.0 201.0 High 179.4 203 30.7 157.0 175.9 193.5 All Grps 196.9 12,240 32.3 172.9 193.6 217.8

Figure 5.23. Probability Plot for DSE by argillic intensity in andesite in primary with biotite, quartz-sericite, argillic or propylitic.

5.4.4 DSE FOR ARGILLIC INTENSITY IN ANDESITE IN PRIMARY WITH ALBITE OR

POTASSIC (B4)

Table 5.19 displays the basic statistics of DSE for argillic intensity in andesite in minzone primary with albite or potassic alteration (combination B4), while the probability plot (Figure 5.24) shows the statistical distribution of these data. Regarding the number of samples and its distribution, all the argillic intensity in the combination B4 are collected as a unique unit.

Table 5.19. DSE basic statistics by argillic intensity in andesite in primary with albite or potassic.

Argillic Standard Means N Q Median Q Intensity deviation 25 75 Low 206.0 827 38.0 175.9 203.2 235.1 Medium 201.2 73 42.7 162.1 193.7 235.1 High 151.1 1 0.0 151.1 151.1 151.1 All Grps 205.5 901 38.4 175.0 202.5 235.1

Figure 5.24. Probability Plot for DSE by argillic intensity in andesite in primary with albite or potassic.

5.4.5 DSE FOR ARGILLIC INTENSITY IN PORMIN (B5)

Table 5.20 displays the basic statistics of DSE for argillic intensity in pormin (combination B5), whereas the probability plot (Figure 5.25) exhibits the statistical distribution of these data. Considering most of the samples are related to the argillic intensity low, all the argillic intensities in the combination B5 are combined as solely one unit.

Table 5.20. DSE basic statistics by argillic intensity in pormin.

Argillic Standard Means N Q Median Q Intensity deviation 25 75 Low 200.6 1,650 34.7 174.6 197.4 223.6 Medium 195.6 174 37.4 165.6 190.5 226.2 High 189.4 106 36.3 157.0 184.6 217.1 All Grps 199.5 1,930 35.1 172.8 196.2 223.3

Figure 5.25. Probability Plot for DSE by argillic intensity in pormin.

5.4.6 DSE FOR ARGILLIC INTENSITY IN PORPOST (B6)

Table 5.21 displays the basic statistics of DSE for argillic intensity in pormin (combination B6), whereas the probability plot (Figure 5.26) shows the statistical distribution of these data. Considering most of the samples are associated with the argillic intensity low, all the argillic intensities in the combination B6 are combined in one unit.

Table 5.21. DSE basic statistics by argillic intensity in porpost.

Argillic Standard Means N Q Median Q Intensity deviation 25 75 Low 206.0 2,302 37.4 176.7 202.4 233.3 Medium 201.9 327 41.3 166.7 199.8 236.0 High 212.4 172 38.7 183.3 215.3 242.6 All Grps 205.9 2,801 38.0 175.9 202.7 234.1

Figure 5.26. Probability Plot for DSE by argillic intensity in porpost.

5.4.7 DSE FOR ARGILLIC INTENSITY IN TUFF IN SUPERGENE (B7)

Table 5.22 shows the basic statistics of DSE for argillic intensity in tuff in minzone supergene (combination B7), whereas the probability plot (Figure 5.27) exhibits the statistical distribution of these data. Argillic are compiled in two groups since the number of samples and the similarities in statistics and distribution of DSE. The first, which corresponds to lower DSE values, encompasses high and medium argillic intensity. The second comprehends the argillic intensity low, which shows the higher DSE values.

Table 5.22. DSE basic statistics by argillic intensity in tuff in supergene.

Argillic Standard Means N Q Median Q Intensity deviation 25 75 Low 206.0 1,426 39.6 173.9 204.3 236.6 Medium 183.5 373 32.6 156.5 177.5 205.1 High 192.4 477 39.6 159.6 183.8 220.2 All Grps 199.5 2,276 39.6 166.2 195.0 229.7

Figure 5.27. Probability Plot for DSE by argillic intensity in tuff in supergene.

5.4.8 DSE FOR ARGILLIC INTENSITY IN TUFF IN PRIMARY WITH BIOTITE OR ARGILLIC (B8)

Table 5.23 shows the basic statistics of DSE for argillic intensity in tuff in minzone primary with biotite or argillic alteration (combination B8), whereas the probability plot (Figure 5.28) displays the statistical distribution of these data. Considering the number of samples and its distribution, all the argillic intensity in the combination B8 are collected as a single unit.

Table 5.23. DSE basic statistics by argillic intensity in tuff in primary with biotite or argillic.

Argillic Standard Means N Q Median Q Intensity deviation 25 75 Low 199.5 959 38.3 167.4 195.5 227.9 Medium 208.4 138 40.7 173.9 210.5 244.7 High 195.4 751 38.3 162.7 192.9 223.9 All Grps 198.5 1,848 38.6 165.8 195.4 227.4

Figure 5.28. Probability Plot for DSE by argillic intensity in tuff primary with biotite or argillic.

5.4.9 DSE FOR ARGILLIC INTENSITY IN TUFF IN PRIMARY WITH QUARTZ-SERICITE,

PROPYLITIC, ALBITE OR POTASSIC (B9)

Table 5.24 displays the basic statistics of DSE for argillic intensity in tuff in minzone primary with quartz-sericite, propylitic, albite or potassic alteration (combination B9), whereas the probability plot (Figure 5.29) exhibits the statistical distribution of DSE. Since the number of samples and the similarities in statistics and distribution of these groups, argillic are compiled in two groups. The first, which corresponds to lower DSE values, includes high and medium argillic

56 intensity. The second comprehends the argillic intensity low, which shows the higher DSE values.

Table 5.24. DSE basic statistics by argillic intensity in tuff in primary with quartz- sericite, propylitic, albite or potassic.

Argillic Standard Means N Q Median Q Intensity deviation 25 75 Low 221.3 9,585 36.3 195.4 222.9 250.3 Medium 207.8 1,263 39.7 175.4 205.9 239.6 High 186.9 97 33.6 161.3 182.1 208.9 All Grps 219.5 10,945 37.0 192.3 221.1 249.2

Figure 5.29. Probability Plot for DSE by argillic intensity in tuff primary with quartz- sericite, propylitic, albite or potassic.

To sum up, Table 5.25 shows the basic statistics of DSE for the twelve defined combinations of the attributes lithology, minzone, alteration and argillic intensity. These combinations represent the final domains and are designated from D1 to D12. In addition, Figure 5.30 displays the spatial distribution of these twelve DSE domains.

Table 5.25. Basic statistics of DSE by the twelve lithology-minzone-alteration-argillic intensity combinations.

Lithology Minzone Alteration Argillic Intensity Mean N Domains Breccia All All All 182.6 601 D1 Supergene All All 188.8 300 D2 High+Medium 182.7 932 D3 Andesite Biotite+QS+Argillic+Propylitic Primary Low 198.1 11,308 D4 Albite+Potassic All 205.5 901 D5 PorMin All All All 199.5 1,930 D6 PorPost All All All 205.9 2,801 D7 High+Medium 189.1 867 D8 Supergene All Low 205.9 1,409 D9 Tuff Biotite+Argillic All 198.5 1,848 D10 Primary High+Medium 206.3 1,360 D11 QS+Propilitic+Potassic+Albite Low 221.3 9,585 D12 All Grps 33,842

Figure 5.30. Plan view showing the distribution of domains for 33,842 DSE data.

6 REGRESSION MODELS FOR DSE

Regression analysis permits the understanding of the dependence of a response variable on one or more predictors, including prediction of future values of the response variable. The simplest scenario considers the use of simple linear regression, which only includes one predictor. Nevertheless, many real-world problems show a better performance using more complex technics (Cook and Weisberg, 1994; Weisberg, 2005).

Regarding the nature of the prediction task, “regression is used when quantitative outputs want to be predicted, whereas classiﬁcation when qualitative outputs are predicted” (Hastie et al., 2009). Among the quantitative algorithms for carrying out regression, it is possible to mentioned simple or multiple linear regression, CART (Classification and Regression Tree), Artificial Neural Networks, whereas for classification, logistic classification or CART are common technics.

Considering that DSE values corresponding to a quantitative and continuous variable, in this research three different algorithms are considered for the prediction of this variable:

• Multiple Linear Regression. • Regression Tree. • Artificial Neural Networks.

As previously indicated (Chapter 1.3), data from the grade control block model is used for generating the regression model to predict DSE values for the blocks into 5YP. Figure 6.1 displays the spatial distribution of the blocks for both grade control and 5YP models.

Figure 6.1. Spatial distribution for both grade control and 5YP block models.

The statistical distribution by domains for both grade control and 5YP block models is presented in Figure 6.2. The most important differences between both block models are the diminishing of domain 12 (tuff in primary with quartz-sericite, propylitic, albite or potassic and low argillic) and increasing of domain 4 (andesite in primary with biotite, quartz-sericite, argillic or propylitic with low argillic intensity) for 5YP.

Figure 6.2. Distribution of domains for: (A) grade control block model (actual data); (B) 5YP, corresponding to blocks to be estimated.

For building the regression model are considered the variables displayed in Table 6.1, which as previously indicated are contained in the grade control block model.

Table 6.1. Variables from the grade control block model.

Variable Attribute type Description Statistical type

Domain geological 12 domains from this research (Chapter 5) Qualitative/Categorical ascu assay soluble copper in sulphuric acid (%)

au assay gold (ppm) cncu assay soluble copper in cyanide (%)

hg assay mercury (ppm) mo assay molybdenum (ppm) Predictor

scu assay total soluble copper (%) Quantitative/Continuous tcu assay total copper (%)

density physical density (g/cm3) dwi geometallurgical drop weight index (kWh/t)

is50 geotechnical Point Load Index (MPa) dse operational drilling specific energy (psi) Response

The grade control block model contains different kind of predictors: geological, geometallurgical and geotechnical, as well as assays. Additionally, this includes DSE values estimated via square inverse distance. 5YP block model comprehends the same variables, except for DSE, which is calculated using an average by domain.

For this research, the concept “model” is considered as the result of the combination of data and a modelling tool (Figure 6.3).

Figure 6.3. Concept of model considered in this research.

The first step for constructing the DSE regression model using the grade control block model is splitting the 65,535 blocks data base into two groups, termed train and test (Figure 6.4). The former includes about 90% of the data (58,887 blocks) and is used for building the model. The latter contains approximately 10% of the data (6,648 blocks) and is utilized for validating the model. It is important to highlight that the information contained in the test group and used during the validation process, corresponds to “fresh” data never “seen” for the model.

Figure 6.4. Distribution of samples (blocks) for train and test groups. To assess the capacity of the different models to predict DSE on the test group are used four statistics. Mean absolute error (Equation 6) is a measure of accuracy for the prediction (Hyndman and Athanasopoulus, 2014). For similar purpose but independent of the scale of the variable, mean absolute percentage error (Hyndman and Athanasopoulus, 2014) allows determining the performance of the predictive model (Equation 7).

1 Equation 6 푀퐴퐸 = ∑푛 푎푏푠 (푦 − 푦̂ ) 푛 푗=1 푗 푗 100 Equation 7 푀퐴푃퐸 = ∑푛 푎푏푠 [(푦 − 푦̂ )/푦 ] 푛 푗=1 푗 푗 푗 Where,

푦푗 = 푎푐푡푢푎푙 푣푎푙푢푒

푦̂푗 = 푝푟푒푑𝑖푐푡푒푑 푣푎푙푢푒

푛 = 푛푢푚푏푒푟 표푓 푎푐푡푢푎푙 − 푒푠푡𝑖푚푎푡푒푑 푝푎𝑖푟푠

Sample correlation coefficient (r), is a measure of the linear correlation between two variables (X and Y), with interval values between +1 and −1, where 1 is a perfect positive correlation, 0 is no correlation, and −1 is a perfect negative correlation (Equation 8). Correlation measures the changing of a variable when another variable change (Pyle, 1999).

푛 ∑푖=1(푥푖− 푥̅)(푦푖− 푦̅) Equation 8 r = 푛 2 푛 2 √∑푖=1(푥푖− 푥̅) √∑푖=1(푦푖− 푦̅)

Where,

푛 = 푛푢푚푏푒푟 표푓 푠푎푚푝푙푒푠

푥푖, 푦푖 = 𝑖푛푑𝑖푣𝑖푑푢푎푙 푠푎푚푝푙푒푠

푛 1 푥̅ = 푠푎푚푝푙푒 푚푒푎푛 = ∑ 푥 푛 푖 푖=1

Finally, the coefficient of determination (r2) corresponds to the quantity of the variance in the dependent variable that is predictable or explained by the response variable. Also, could be considered as the “explanatory power” for one variable to explains another (Pyle, 1999).

6.1 REGRESSION MODEL FOR DSE BASED ON MULTIPLE LINEAR REGRESSION

Simple linear regression can be expressed as a function of slope (1) and the intercept (0) of a straight line (Figure 6.5), considering the Equation 9.

Equation 9 Y = 0 + 1X

Figure 6.5. Simple linear regression. Modified from Weisberg, 2005. Multiple linear regression “generalizes the simple linear regression model by allowing for many terms in a mean function rather than just one intercept and one slope” (Weisberg, 2005). The universal multiple linear regression model with response Y and terms X1,...,Xp can be expressed as shown in Equation 10.

Equation 10 Y = 0 + 1X1 + … +pXp

If p=2, the multiple linear regression can be represented as a plane in three dimensions (Figure 6.6).

Figure 6.6. A linear regression when p=2 (Weisberg, 2005).

If p>2, the multiple linear regression can be characterized as a hyperplane, “the generalization of a p-dimensional plane in a (p+1)-dimensional space” (Weisberg, 2005).

For multiple linear regression is only possible to use quantitative variables. For this reason, for carrying out the regression model for DSE, it is necessary to develop individual models for each of the twelve domains defined in Chapter 5. The correlations between the response variable (DSE) and the predictors for the twelve domains is shown in Table 6.2. For building the multiple linear regression for each domain, are solely considered predictors with significant correlation at p<0.05.

Table 6.2. Linear correlations between DSE and predictors. Blue and red shade cells, positive and negative correlations, respectively. Significant correlation at p<0.05 is labelled in red font colour. Blank cell corresponding to predictors with no variance (constant value).

6.1.1 DSE VALIDATION FOR MULTIPLE LINEAR REGRESSION

Figure 6.7 displays the comparison in the test group (6,648 blocks) between the actual DSE values and the predicted DSE values through the multiple linear regression model.

Figure 6.7. Scatterplot for DSE in the test group, comparing the actual data and the result of the prediction using the multiple linear regression model.

Finally, the results of validation for the model based on multiple linear regression are presented in Table 6.3. The results show a moderately unbiased model, considering similar mean values for actual and predicted DSE. Besides, the correlation coefficient is 0.59, explaining 35% (r2) of the variability of actual DSE data. Likewise, as an average, the error of the model is 25.9 DSE points, equivalent to 14.7%.

Table 6.3. Statistics results for the actual data (test group) and the result of the prediction using the multiple linear regression model.

DSE test group DSE prediction Mean DSE 188.1 190.3 r 0.59 r 2 0.35 MAE 25.9 MAPE 14.7%

6.2 REGRESSION MODEL FOR DSE BASED ON REGRESSION TREE

Classification and Regression Tree or CART (Breiman et al., 1984), is a broadly used statistical technic for generating regression models with a structure based on a tree (Hand et al., 2001). Each node in the tree defines a binary test for an individual variable (Figure 6.8).

Figure 6.8: An example of regression tree, with quantitative variables in the terminal nodes. From Jeraldo, 2015.

The structure of the tree is a consequence of the data itself rather than predefined. Based on a splitting criterion, data is partitioned into two subsets of maximum heterogeneity. This splitting criterion is recursively applied up to obtaining the most balanced tree regarding performance and complexity, considering that excessively complicated tree might result in overfitting, whereas too simple structure could lead a regression tree with inadequate predictive capacity (Hand et al., 2001).

For this research, nodes of the tree correspond to both qualitative (domains) and quantitative (assays, geotechnical, etc.) predictors. The first eleven nodes for the regression tree model for predicting DSE are shown in Figure 6.9. For each node are displayed identification (ID), the number of samples (N), sample mean (Mu) and variance (Var). Diminishing in heterogeneity due to splitting and generation of new nodes can be identified, for instance, node 1 (ID=1) has variance 1,469, whereas the variance of node 9 (ID=9) is 731.

Figure 6.9. First eleven nodes of the regression tree generated for the prediction of DSE.

6.2.1 DSE VALIDATION FOR REGRESSION TREE

Figure 6.10 displays the comparison in the test group (6,648 blocks) between the actual DSE values and the predicted DSE values through the regression tree model.

Figure 6.10. Scatterplot for DSE in the test group, comparing the actual data and the result of the prediction using the regression tree model.

To conclude, the results of validation for model based on regression tree is presented in Table 6.4. The results show an unbiased model, considering similar mean values for actual and predicted DSE. Also, the correlation coefficient is 0.5, explaining 25% (r2) of the variability of actual DSE data. Furthermore, as an average, the error of the model is 26 DSE points, equivalent to 15.3%.

Table 6.4. Statistics results for the actual data (test group) and the result of the prediction using regression tree model.

DSE test group DSE prediction Mean DSE 182.9 183.5 r 0.50 r 2 0.25 MAE 26.0 MAPE 15.3%

6.3 REGRESSION MODEL FOR DSE BASED ON ARTIFICIAL NEURAL NETWORKS

Artificial neural networks emulate in a simple manner the way the animal brain and nervous system work (Hagan et al., 2014). The brain comprises of a large number (roughly 1011) of vastly linked elements (in the order of 104 connections per element) called neurons, which can be divided into three components: dendrites, cell body, and axon (Figure 6.11). Dendrites are tree-like receptors of nerve fibres that transmit electrical signals towards the cell body. In the cell body, these signals con be considered as sums and thresholds. Axon is a sole long fibre that conveys the signals from the cell body to other neurons. In this context, a synapsis can be considered as the point of interaction between an axon of one neuron and a dendrite of another. The extraordinary capacity of processing of neural networks is based not only on the enormous number of neurons but also in the massive number of interconnections among them (Hagan et al., 2014).

Figure 6.11. Diagram of biological neurons. From Hagan et al., 2014.

Despite their simplicity, artificial neural networks present two important parallels with the biological neural network. Firstly, the basic unit of both networks is straightforward computational designs exceedingly interconnected. Secondly, the connections between neurons regulate the function of the network (Hagan et al., 2014). A neural network initiates with an input layer (Figure 6.12), equivalent to the natural dendrite, in which each node corresponds to a predictor.

Figure 6.12. Layout of an artificial neural network, including variables of this research.

The input nodes are linked to the nodes of the hidden layer, analogous to the cell body. The neurons of hidden layer are the main processing units and receive the signal corresponds to the product of each node from the input layer multiplied by a factor, determining a connection weight Wxy (Figure 6.13). A training method allows the determination of connection weights, which correspond to the unknown parameters. Over this value is applied a nonlinear function termed activation function, which continues its trajectory towards the output layer. This layer is comparable to the axon of the natural neuron. The output layer comprises a single response variable (Hagan et al., 2014). The process of constructing an artificial neural network is iterative up to appropriate performance is reached.

Figure 6.13. Layout of an artificial neural network. Neurons in input layer are multiplied by a weight (Wxy). This signal is processed in the neurons of the hidden layer via a nonlinear activation function. Finally, the result is combined for generating the response in the neuron of the output layer.

6.3.1 DSE VALIDATION FOR ARTIFICIAL NEURAL NETWORK REGRESSION

Figure 6.14 displays the comparison in the test group (6,648 blocks) between the actual DSE values and the predicted DSE values through the artificial neural networks model.

Figure 6.14. Scatterplot for DSE in the test group, comparing the actual data and the result of the prediction using the artificial neural networks model.

To sum up, the results of validation for model based on artificial neural networks is presented in Table 6.5. The results show a relatively unbiased model, considering comparable mean values for actual DSE and prediction values. Also, the correlation coefficient is 0.66, explaining 44% (r2) of the variability of actual DSE data. Moreover, as an average, the error of the model is 21.8 DSE points, equivalent to 13.0%.

Table 6.5. Statistics results for the actual data (test group) and the result of the prediction using artificial neural networks model.

DSE test group DSE prediction Mean DSE 176.0 179.0 r 0.66 r 2 0.44 MAE 21.8 MAPE 13.0%

6.4 REGRESSION MODELS FOR DSE: RESULTS COMPARISON

Table 6.6 presents a summary of the results of the performance of the three models generated for the test group. Additionally, is included the result for the alternative currently in use in CDA: average by domain model. The result of the regression tree model is unsatisfactory, considering an even lower performance for all the statistics than the current average by domain model. Moreover, the multiple linear regression is not better than average by domain model, considering its similar statistical results. However, the use of the artificial neural networks model permits to obtain results significantly better than average by domain model. Using the artificial neural networks model is possible to explain 44% of the variability of actual DSE values for the test group, compared with 31% obtained for the average by domain model. Also, the mean absolute percentage error (MAPE) for the artificial neural networks model is lower than the error obtained for the average by domain model (13% and 14.7%, correspondingly).

Table 6.6. Statistics results in the test group for generated models.

multiple linear artificial neural mean by domain regression tree regression network r 0.56 0.50 0.59 0.66 r 2 0.31 0.25 0.35 0.44 MAE 25.5 26.0 25.9 21.8 MAPE 14.7% 15.3% 14.7% 13.0%

7 DSE PREDICTION FOR 5YP

For the prediction of DSE for 5YP block model, it is considered the artificial neural network model, based on its best performance. The total amount of blocks for 5YP is 41,761. From this, 40,319 blocks are estimated, the equivalent of 96.5% of the total. The difference corresponds to blocks with domains unknown for the model and thus, not estimated.

Figure 7.1 displays the mean for DSE by domain in both the grade control (actual data) and the 5YP block model estimated through artificial neural networks model.

Figure 7.1. Comparison of DSE mean by domain of grade control (actual data) and 5YP (estimated through artificial neural networks model or ANN).

7.1 SPATIAL COMPARISON FOR DSE BLOCK MODELS

Figure 7.2 and Figure 7.3 shows the distribution for the actual DSE data for the grade control block model. All the displayed data corresponds to material already extracted from the CDA open pit.

Figure 7.2. Distribution of DSE data (actual) for the grade control block model.

Figure 7.3. Plan view for distribution of DSE data (actual) for the grade control block model.

Figure 7.4 and Figure 7.5 displays the distribution for the estimated DSE data for the 5YP block model, based on the artificial neural networks model.

Figure 7.4. Distribution of DSE data for the 5YP block model. DSE values were estimated through regression using the artificial neural networks model.

Figure 7.5. Plan view for distribution of DSE data for the 5YP block model. DSE values were estimated through regression using the artificial neural networks model.

For the 5YP block model estimated through the artificial neural networks model (Figure 7.4 and Figure 7.5), it is possible to recognise significant differences for different locations. These differences express the geological characteristics of the materials for the 5YP. On the one hand, “soft” zones (blue colours, DSE<200) are situated in the eastern, northern and western margins of the 5YP, which correspond to upper benches under the influence of supergene process. On the other hand, most of the blocks located in the central portion of the 5YP correspond to “hard” zones (DSE≥200, white to red colours). These blocks of the “hard” zone have a deeper position in the plan and are not as influenced by the supergene process as the peripherical and shallow blocks. Furthermore, in the distribution of DSE values is possible to identify patterns due to the influence of geological domains. For instance, in the western part of the plan, high values are determined by the presence of tuff with albitic alteration and in the eastern part by the north and north-western lineament of the porpost and pormin, respectively.

For the 5YP block model is possible to contrast the results of estimation of DSE through the artificial neural networks model with the model currently used in CDA mine, which corresponds to an average by domain. As can be seen in Figure 7.6 and Figure 7.7, even though the DSE values of the average by domain model show an overall similar spatial distribution for DSE values, the results of the average by domain model not express the variability shown by the results of the artificial neural networks model. This is an important drawback of the average by domain model currently used in CDA mine.

Figure 7.6. Distribution of DSE data for the 5YP block model based on the average by domain model, which is currently used in CDA.

Figure 7.7. Plan view of DSE data for the 5YP block model based on the average by domain model, which is currently used in CDA.

8. DISCUSSION

CDA deposit contains different types of geological attributes (Chapter 2). Lithology includes andesite, tuff, hydrothermal breccia and porphyry. Among the minzone, are identified a well-developed supergene zone, which includes the minzone leached and the enrichment minzones esec1 and esec2, besides primary zones. For alteration, are recognised albite, K-feldspar, biotite, quart- sericite, propylitic and argillic. Structurally, the deposit expresses high complexity. Particularly, the Hermosa Fault corresponds to a dilatational structure that offset and put in contact tuff and andesite. Moreover, this fault controls hydrothermal breccia and quartz-sericite alteration-mineralization process. These geological attributes exercise a strong control over DSE values. This control is used to define DSE domains through exploratory data analysis and additionally, permits demonstrate the coherence of the CDA geological model (Chapter 5).

In terms of the mining process, CDA operates both heap leaching and concentrate processes, producing copper cathodes as well as copper-gold concentrates (Chapter 3). One drawback for CDA mine is the low grades of the deposit (0.4% CuT; 0.12 ppm Au). As an additional disadvantage, CDA mine is situated just 300 m from Andacollo town. This brings about difficulties in terms of maintaining the social licence to operate. Thus, it is important to identify the characteristics of the rock mass affecting not only operational cost but also controlling as much as possible the effects of mining operation on the community and environment.

For drilling, it is important to recognise the resistance of the rocks to penetration. Drilling is time-consuming and affects the dynamics of the downstream operations blasting, loading and hauling. So, it is critical to have in the block model an accurate parameter of rock resistance to drilling. Furthermore, in drilling a high consumption of steel occurs, being necessary the replacement of bars, bits and other parts of the drill rigs. Therefore, to know a priori the resistance of rocks could permit a better planning for the drilling operation and could allow prepare more precise budgets for replacement of tools and for scheduling maintenance for drill rigs.

Blasting is a critical operation because the principal component of operational cost in CDA is milling. On the one hand, the cheapest way to reduce size particles

80 is blasting. On the other hand, Andacollo town was declared PM10 saturated zone in 2009 (PM10 correspond to particles suspended in the atmosphere with a diameter lesser than 10 micrometres). Teck CDA has assumed a commitment with the community and the Chilean government for reducing the emission of particles from the mine. To know the resistance of the rocks is key for controlling blasting. Unappropriated blasting may cause uncontrolled emission of PM10 and in this manner, affects the sustainability of CDA operation.

For the CDA mine sustainability, DSE corresponds to an adequate parameter to determine the best design for both drilling and blasting activities. Among the advantages of DSE is possible to mention:

✓ Low cost. DSE is a low-cost technology. The costs include the licence, implementation and operation of the Thunderbird® system.

✓ Availability of a large amount of data. In CDA mine, about 100 new data are generated every day. In fact, the amount of DSE is higher than the amount of new copper analysis for grade control.

✓ Robustness. DSE values are based on the average of readings made every 10 cm, for 10 m height bench.

To evaluate the robustness of DSE, comparative analyses were carried out for the three drill rigs and six operators at CDA open pit by different geological attributes (Chapter 4). The results indicate that drill rigs D003 and D006 show similar values of DSE. For D005, a 4% difference of DSE was observed. This difference is not very high, but it is considered significant for this research and thus, DSE values from D005 drill rig were not included in the later analysis. The comparison for the six operators does not shows any clear difference among the DSE results. In this way is proved that in general, the result of DSE has an acceptable accuracy (reproducibility).

The grade control block model contains several variables, including DSE values estimated through square inverse distance. The 5YP block model only includes DSE calculated as an average by domain, because blast holes are solely

81 available for one or two benches depth (grade control block model). Three regression models for predicting DSE in the 5YP block model have been built using variables from the grade control block model (Chapters 6 and 7). To construct the regression models, the data was randomly divided into two: a train group, including about 90% of the blocks (58,887 data), used for building the models; a test group, corresponding to approximately 10% of the original data base (6,648 data), used for validating the models. The results in the test group demonstrate that the models based upon regression tree and multiple linear regression are not better alternatives for estimating DSE compared with the model currently in use in CDA mine, which is based on an average by domain. However, results of the model based on artificial neural networks show better performance than the average by domain model. Indeed, the model based on artificial neural networks displays less error than the average by domain model (13 and 14.7%, respectively). Additionally, correlation for the artificial neural networks model is significantly higher than the average by domain model (0.66 versus 0.56). It permits to explains in a better fashion the variability of DSE: 31% for the average by domain model versus 44% for the artificial neural network model (measured as r2 or coefficient of determination). Consequently, the model based on the artificial neural network is able to reproduce in a better way the variability of DSE. The superior performance of artificial neural networks might be explained by the fact that this algorithm is based on artificial intelligence. In this sense, it learns from the train group the patterns that determine the relationships between the predictors and the response variable DSE.

9. CONCLUSIONS

CDA is a deposit that contains various geological attributes. Lithology, minzone, alteration types and intensity of argillic alteration exercise control over DSE values. This control is used for defining domains that express the different statistical behaviour of DSE values. The defined domains are key as a predictor for later construction of DSE regression model. Also, the close relationship between geological attributes and DSE data demonstrates the coherence of the CDA geological model.

Validating process has proved the reproducibility of DSE data for different drill rigs and operators. A 4% difference for DSE in drill rig D005 respect D003 and D006 was identified. Due to this, DSE from this machinery was not used in this research.

Using assays and geological, geotechnical and geometallurgical variables included in the CDA grade control block model, three regression models have been generated. Division of data in train, for building the model and test, for statistical validation, has permitted to determine which of the three regression models generated show the best performance in predictive terms. Additionally, the statistical validation process has been used for establishing if any of these models express a better performance than the model currently in use in CDA (average by domain). Firstly, the results are robust, considering the large number of samples that the test group includes (6,648). Secondly, two of the models, regression tree and multiple linear regression display a similar or worse performance than the average by domain model. Thirdly, the results of the artificial neural networks model exceed the results of the average by domain model, showing for the test group lesser relative error (13.0 versus 14.7%, respectively) and higher correlation (0.66 versus 0.56, correspondingly). The use of the artificial neural networks model instead the average by domain model permits explain in a better fashion the variability of DSE in 5YP, improving the results from the current 31 to 44%, respectively.

Considering the difficulties of CDA operation, the use of the model based upon artificial neural networks, might allow a better mine planning, impacting significantly on several aspects of the operation: 1) improving budget for drill bits, tools and explosives and scheduling for drill rig maintenance; 2) Refining the schedule for drilling-blasting-loading-hauling operations; 3) Determining for blasting the correct power factor for each polygon, reducing cost for “soft” areas of the plan (low DSE values) and increasing the power factor for “hard” material (high DSE values). Additionally, but no less important, it might allow to reduce the PM10 emissions and, consequently, diminish the probability of events that could affect the relationship with the community and local and national authorities.

Finally, it is important to highlight the advantages of using DSE. Among these is possible to indicate its low cost, a large amount of data generated and

83 robustness. The results of this research show the potential for the using of this technology for facing the financial, community and environmental complexities of the current and future mining industry.

10. RECOMMENDATIONS

✓ To implement in the 5YP the DSE regression model based on artificial neural networks. It will generate a significant improvement for mine planning.

✓ To share the model with drilling and blasting department in CDA mine and explain the advantages of using the DSE values calculated for 5YP block model through artificial neural networks.

✓ To explore the root cause (torque, penetration rate, etc.) for the differences observed between drill rig D005 and the other two machineries (D003 and D006). Set the three pieces of equipment at the same level of DSE for any sort of domain.

✓ The consumption of energy for drill rig D005 is 4.4 and 4% lesser than D003 and D006, respectively. It is identified an opportunity to reduce the operative cost of these two drill rigs. It is estimated that reducing the energy consumption for D003 and D006 drill rigs to the levels of D005 would bring about diminishing of the operative cost of drilling between 50,000 and 100,000 USD.

✓ To incorporate additional variables to the regression model may increase the DSE predictive performance for the model.

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