Saimm 202302 feb by SAIMM

VOLUME 123 NO. 2 FEBRUARY 2023

The Southern African Institute of Mining and Metallurgy OFFICE BEARERS AND COUNCIL FOR THE 2022/2023 SESSION Honorary President

Nolitha Fakude President, Minerals Council South Africa

Honorary Vice Presidents

Gwede Mantashe Minister of Mineral Resources and Energy, South Africa Ebrahim Patel Minister of Trade, Industry and Competition, South Africa Blade Nzimande Minister of Higher Education, Science and Technology, South Africa

President Z. Botha

President Elect W.C. Joughin

Senior Vice President E. Matinde

Junior Vice President G.R. Lane

Incoming Junior Vice President T.M. Mmola

Immediate Past President I.J. Geldenhuys

Honorary Treasurer W.C. Joughin

Ordinary Members on Council W. Broodryk Z. Fakhraei R.M.S. Falcon (by invitation) B. Genc K.M. Letsoalo S.B. Madolo F.T. Manyanga M.C. Munroe

G. Njowa S.J. Ntsoelengoe S.M. Rupprecht M.H. Solomon A.J.S. Spearing A.T. van Zyl E.J. Walls

Co-opted to Members K. Mosebi A.S. Nhleko

Past Presidents Serving on Council N.A. Barcza R.D. Beck J.R. Dixon V.G. Duke R.T. Jones A.S. Macfarlane M.I. Mthenjane

C. Musingwini S. Ndlovu J.L. Porter M.H. Rogers D.A.J. Ross-Watt G.L. Smith W.H. van Niekerk

G.R. Lane–TPC Mining Chairperson Z. Botha–TPC Metallurgy Chairperson M.A. Mello–YPC Chairperson K.W. Banda–YPC Vice Chairperson

PAST PRESIDENTS *Deceased

* W. Bettel (1894–1895) * A.F. Crosse (1895–1896) * W.R. Feldtmann (1896–1897) * C. Butters (1897–1898) * J. Loevy (1898–1899) * J.R. Williams (1899–1903) * S.H. Pearce (1903–1904) * W.A. Caldecott (1904–1905) * W. Cullen (1905–1906) * E.H. Johnson (1906–1907) * J. Yates (1907–1908) * R.G. Bevington (1908–1909) * A. McA. Johnston (1909–1910) * J. Moir (1910–1911) * C.B. Saner (1911–1912) * W.R. Dowling (1912–1913) * A. Richardson (1913–1914) * G.H. Stanley (1914–1915) * J.E. Thomas (1915–1916) * J.A. Wilkinson (1916–1917) * G. Hildick-Smith (1917–1918) * H.S. Meyer (1918–1919) * J. Gray (1919–1920) * J. Chilton (1920–1921) * F. Wartenweiler (1921–1922) * G.A. Watermeyer (1922–1923) * F.W. Watson (1923–1924) * C.J. Gray (1924–1925) * H.A. White (1925–1926) * H.R. Adam (1926–1927) * Sir Robert Kotze (1927–1928) * J.A. Woodburn (1928–1929) * H. Pirow (1929–1930) * J. Henderson (1930–1931) * A. King (1931–1932) * V. Nimmo-Dewar (1932–1933) * P.N. Lategan (1933–1934) * E.C. Ranson (1934–1935) * R.A. Flugge-De-Smidt (1935–1936) * T.K. Prentice (1936–1937) * R.S.G. Stokes (1937–1938) * P.E. Hall (1938–1939) * E.H.A. Joseph (1939–1940) * J.H. Dobson (1940–1941) * Theo Meyer (1941–1942) * John V. Muller (1942–1943) * C. Biccard Jeppe (1943–1944) * P.J. Louis Bok (1944–1945) * J.T. McIntyre (1945–1946) * M. Falcon (1946–1947) * A. Clemens (1947–1948) * F.G. Hill (1948–1949) * O.A.E. Jackson (1949–1950) * W.E. Gooday (1950–1951) * C.J. Irving (1951–1952) * D.D. Stitt (1952–1953) * M.C.G. Meyer (1953–1954) * L.A. Bushell (1954–1955) * H. Britten (1955–1956) * Wm. Bleloch (1956–1957) * H. Simon (1957–1958) * M. Barcza (1958–1959) * R.J. Adamson (1959–1960)

* W.S. Findlay (1960–1961) * D.G. Maxwell (1961–1962) * J. de V. Lambrechts (1962–1963) * J.F. Reid (1963–1964) * D.M. Jamieson (1964–1965) * H.E. Cross (1965–1966) * D. Gordon Jones (1966–1967) * P. Lambooy (1967–1968) * R.C.J. Goode (1968–1969) * J.K.E. Douglas (1969–1970) * V.C. Robinson (1970–1971) * D.D. Howat (1971–1972) * J.P. Hugo (1972–1973) * P.W.J. van Rensburg (1973–1974) * R.P. Plewman (1974–1975) * R.E. Robinson (1975–1976) * M.D.G. Salamon (1976–1977) * P.A. Von Wielligh (1977–1978) * M.G. Atmore (1978–1979) * D.A. Viljoen (1979–1980) * P.R. Jochens (1980–1981) * G.Y. Nisbet (1981–1982) A.N. Brown (1982–1983) * R.P. King (1983–1984) J.D. Austin (1984–1985) * H.E. James (1985–1986) H. Wagner (1986–1987) * B.C. Alberts (1987–1988) * C.E. Fivaz (1988–1989) * O.K.H. Steffen (1989–1990) * H.G. Mosenthal (1990–1991) R.D. Beck (1991–1992) * J.P. Hoffman (1992–1993) * H. Scott-Russell (1993–1994) J.A. Cruise (1994–1995) D.A.J. Ross-Watt (1995–1996) N.A. Barcza (1996–1997) * R.P. Mohring (1997–1998) J.R. Dixon (1998–1999) M.H. Rogers (1999–2000) L.A. Cramer (2000–2001) * A.A.B. Douglas (2001–2002) S.J. Ramokgopa (2002-2003) T.R. Stacey (2003–2004) F.M.G. Egerton (2004–2005) W.H. van Niekerk (2005–2006) R.P.H. Willis (2006–2007) R.G.B. Pickering (2007–2008) A.M. Garbers-Craig (2008–2009) J.C. Ngoma (2009–2010) G.V.R. Landman (2010–2011) J.N. van der Merwe (2011–2012) G.L. Smith (2012–2013) M. Dworzanowski (2013–2014) J.L. Porter (2014–2015) R.T. Jones (2015–2016) C. Musingwini (2016–2017) S. Ndlovu (2017–2018) A.S. Macfarlane (2018–2019) M.I. Mthenjane (2019–2020) V.G. Duke (2020–2021) I.J. Geldenhuys (2021–2022)

Branch Chairpersons Botswana DRC Johannesburg Namibia Northern Cape North West Pretoria Western Cape Zambia Zimbabwe Zululand

Being established Not active N. Rampersad Vacant I. Tlhapi I. Tshabalala Vacant A.B. Nesbitt J.P.C. Mutambo (Interim Chairperson) A.T. Chinhava C.W. Mienie

Honorary Legal Advisers M H Attorneys

Auditors

Genesis Chartered Accountants

Secretaries

The Southern African Institute of Mining and Metallurgy 7th Floor, Rosebank Towers, 19 Biermann Avenue, Rosebank, 2196 PostNet Suite #212, Private Bag X31, Saxonwold, 2132 E-mail: journal@saimm.co.za

Editorial Board S.O. Bada R.D. Beck P. den Hoed I.M. Dikgwatlhe R. Dimitrakopolous* L. Falcon B. Genc R.T. Jones W.C. Joughin A.J. Kinghorn D.E.P. Klenam H.M. Lodewijks D.F. Malan R. Mitra* H. Möller C. Musingwini S. Ndlovu P.N. Neingo M. Nicol* S.S. Nyoni M. Phasha P. Pistorius P. Radcliffe N. Rampersad Q.G. Reynolds I. Robinson S.M. Rupprecht K.C. Sole A.J.S. Spearing* T.R. Stacey E. Topal* D. Tudor* F.D.L. Uahengo D. Vogt* *International Advisory Board members

Editor /Chairman of the Editorial Board R.M.S. Falcon

Typeset and Published by The Southern African Institute of Mining and Metallurgy PostNet Suite #212 Private Bag X31 Saxonwold, 2132 E-mail: journal@saimm.co.za

VOLUME 123 NO. 2 FEBRUARY 2023

Contents Journal Comment: The Competent Person by S.M. Rupprecht. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

President’s Corner: A Culture of Growth by Z. Botha . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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NEWS OF INTEREST Selling the family Silver by I. Robinson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Review on the Book: State Governance of Mining, Development and Sustainability by T.-L. Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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ROFESSIONAL TECHNICAL AND SCIENTIFIC P PAPERS A critical comparison of interpolation techniques for digital terrain modelling in mining by M.A. Raza, A. Hassan, M.U. Khan, M.Z. Emad, and S.A. Saki. . . . . . . . . . . . . . . . . . . . . . . .

This research examines digital terrain model (DTM) production methods for the modelling of a surface for mining applications. Real data from a mine site is used, as a case study, to create DTMs using various interpolation techniques in Surfer software. The significant variation in the resulting DTMs demonstrates that developing a DTM is not straightforward and that it is important to choose the method carefully because the outcomes depend on the interpolation techniques used. In mining instances, where volume estimations are based on the produced DTM, this can have a significant impact.

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THE INSTITUTE, AS A BODY, IS NOT RESPONSIBLE FOR THE STATEMENTS AND OPINIONS ADVANCED IN ANY OF ITS PUBLICATIONS. Copyright© 2023 by The Southern African Institute of Mining and Metallurgy. All rights reserved. Multiple copying of the contents of this publication or parts thereof without permission is in breach of copyright, but permission is hereby given for the copying of titles and abstracts of papers and names of authors. Permission to copy illustrations and short extracts from the text of individual contributions is usually given upon written application to the Institute, provided that the source (and where appropriate, the copyright) is acknowledged. Apart from any fair dealing for the purposes of review or criticism under The Copyright Act no. 98, 1978, Section 12, of the Republic of South Africa, a single copy of an article may be supplied by a library for the purposes of research or private study. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without the prior permission of the publishers. Multiple copying of the contents of the publication without permission is always illegal. U.S. Copyright Law applicable to users In the U.S.A. The appearance of the statement of copyright at the bottom of the first page of an article appearing in this journal indicates that the copyright holder consents to the making of copies of the article for personal or internal use. This consent is given on condition that the copier pays the stated fee for each copy of a paper beyond that permitted by Section 107 or 108 of the U.S. Copyright Law. The fee is to be paid through the Copyright Clearance Center, Inc., Operations Center, P.O. Box 765, Schenectady, New York 12301, U.S.A. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale.

FEBRUARY 2023

VOLUME 123

The Journal of the Southern African Institute of Mining and Metallurgy

The necessity of 3D analysis for open-pit rock slope stability studies: Theory and practice by A. McQuillan and N. Bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

When geotechnical analysis is completed, the three-dimensional geological, hydrogeological, and structural models are often simplified to two-dimensional sections. In this paper we demonstrate that this simplification can lead to the wrong failure mechanism being identified and/or a conservative factor of safety being calculated, leading to an over-estimation of stability. Through case studies, we show how three-dimensional analysis methods are more suited to rock slopes, particularly those with anisotropic material strength, when singularities such as geological faults are present, and with nonlinear slope geometry. The effect of petrographically determined parameters on reductant reactivity in the production of high-carbon ferromanganese by S. Soqinase, J.D Steenkamp, P. den Hoed, and N. Wagner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

In pyrometallurgical processes, it is of interest to evaluate the reactivity of the carbonaceous reductants towards substances such as slag. In this study we compare the petrographically determined organic composition of coal to reductant reactivity towards high-carbon ferromanganese slag, using two South African medium-rank C bituminous coals and an anthracite sample. The reactivity tests revealed that the coal sample containing a greater proportion of vitrinite was the most reactive reductant. The anthracite sample, consisting of the highest inert maceral proportions, was the least reactive reductant. Hyperspectral core scanner: An effective mineral mapping tool for apatite in the Upper Zone, northern limb, Bushveld Complex by H. Mandende, C. Ndou, and T. Mothupi. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Reliable new sources of rare earth elements (REEs) are required to meet global demand and to avoid a supply shortage. This study investigates the effectiveness of hyperspectral imaging (HSI) in the long-wave infrared bandwidths in identifying apatite in the Upper Zone of the Bushveld Complex. The HSI results were validated using mineralogical and geochemical data. HSI is shown to be an effective tool for mapping apatite in the Upper Zone, although a pure apatite spectral signature was not obtained. Material characteristics of Ti-6AL-4V samples additively manufactured using laser-based direct energy deposition by M.G. Willemse, C.W. Siyasiya, D. Marais, A.M. Venter, and N.K.K. Arthur . . . . . . . . . . . . . . . . . . . . . . . . .

This project focused on the characterization of the evolution of residual stresses in Ti-6Al-4V ELI additivemanufactured test samples. Four square thin-walled tubular samples were deposited to different build heights on the same baseplate, using the direct energy deposition laser printing process. The residual stresses were analysed by the neutron diffraction technique and correlated to qualitative predictions obtained using the ANSYS software suite. Good qualitative agreement between the stress measurements and predictions were observed. Determination of the erosion level of a porphyry copper deposit using soil geochemistry by F. Moradpouri, S.M.H. Ahmadi, R. Ghaedrahmati, and K. Barani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Determination of the erosion surface of a metalliferous deposit using geochemical halos can reduce the risk of exploration operations. The aim of this paper is to determine the erosion surface of the North ROK porphyry deposit in British Columbia using linear productivity (LP), which is the content of an element deﬁning the halo multiplied by the width of the halo. A total of 2045 soil samples were analysed for 36 elements using ICP-MS. Cu, Mo, Pb, and Zn were chosen to calculate the LP and total LP. Probability plot modelling and thresholds values were used to map the distribution of each element in a GIS to calculate the total LP, which indicated that the erosion surface is supra-ore. Boreholes data was used to validate the obtained results.

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Journ

ent Comm

The Competent Person

he SAMREC Code (2016) defines a Competent Person as one having a minimum of five years of relevant experience in the style of mineralization or type of deposit under consideration. In addition, a Competent Person must be registered with a professional organization (SACNASP, ECSA, SAGC) or a member or a fellow of a learned society (GSSA, SAIMM, IMSSA) or Recognised Professional Organisation (RPO). These bodies have enforceable disciplinary processes, including the power to suspend or expel a member. In recent years, the role of the Competent Person has undergone scrutiny regarding the quality of work being presented and whether Competent Persons are overstating their level of relevant competency. Some of the problems identified are as follows:  Incorrectly claiming relevant competency in a deposit type or situation under consideration  Poor application of Reasonable Prospects of Eventual Economic Extraction (RPEEE) to justify Mineral Resource classification, and improper classification of Mineral Resources  Documentation of overly optimistic mining schedules, estimation of capital expenditure, and operating costs  Overly technically worded technical reports inclusive of sale pitches, unrealistic, or misleading statements;  Poor reporting of Environmental, Social, and Governance (ESG) issues  Failure to communicate risks related to mineral deposits and projects adequately and clearly  Failure to use multidisciplinary technical specialists to improve the quality of the technical report. Self-assessment of relevant competency is important and is also connected to ethical considerations. Competent Persons must be clearly satisfied in their own minds that they can face their peers and demonstrate competency. The investment community is seeking transparency from Competent Persons, with many calling for the inclusion of detailed CVs to demonstrate a Competent Person’s relevant experience. The application of RPEEE can widely vary between Competent Persons. The Competent Person must consider the geoscientific knowledge and the modifying factors, both technical and economic aspects. The establishment of RPEEE demands an Initial Assessment, not simply an inventory of mineralized material above a stated cut-off grade. The application of modifying factors in technical studies is critical. The Competent Person must ascertain that the inputs used in technical studies are appropriate and not overly optimistic. It is recommended that technical specialists assist Competent Persons in ensuring all technical inputs are appropriate and realistic, and the associated risks are highlighted. Key inputs include ramp-up schedule, development rates, estimation of mining loss and dilution (i.e. estimation of ROM grade), metallurgical recovery factors, price assumptions, operating and capital cost estimates, economic evaluation, and risk identification. The Competent Person must employ the plain English principle to improve the readability of technical reports so as to benefit investors who lack a scientific background. Other technical reports can be written in such a manner that they resemble a prospectus rather than a technical report. In some cases, material misstatements, omissions, and misrepresentation can occur, either by accident or deliberately. The Competent Person must be diligent in investigating and reporting all material aspects and must conduct sufficient examinations to ensure conditions are as reported by the project owner or registrant. What may not be a ‘big deal’ to an owner may be material to an investor. Competent Persons must ensure they are not unduly influenced by project owners. ESG issues have become relevant due to the increasing global awareness of human beings’ impacts on our planet. Under the SAMREC Code, ESG issues are considered fundamental contributors to Modifying Factors that play an essential role in determining RPEEE for Mineral Resources and the declaration of Mineral Reserves. It is important to note that all projects embody risk; therefore, Competent Persons must ensure all material risks are identified and discussed. The days of a single or two-person Competent Persons team are of the past; technical reports require several specialists that should sign off on their specific areas of expertise. Promoting continuous professional development to ensure Competent Persons are knowledgeable about current reporting trends remains paramount. This is especially important for Competent Persons on operations which may not have internal training programmes. In the end, Competent Persons must use their professional judgement in providing adequate disclosure of all material aspects, bearing in mind that the ‘Competent Person must be clearly satisfied in their minds that they can face their peers and demonstrate competence’ (SAMREC, 2016). Competent Persons must demonstrate a level of ethics. The author is reminded of a quote from Theodore Roosevelt – ‘Knowing what’s right doesn’t mean much unless you do what’s right’. Knowing the SAMREC Code is not enough; one must also abide by it. S.M. Rupprecht

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The Journal of the Southern African Institute of Mining and Metallurgy

A Culture of Growth*

How do we establish a culture of economic growth in South Africa?

t’s

den Presi

*This article is based on literature only, this is not my own work, but built on the wonderful work already out there in the public domain

er Corn

received a great amount of feedback on my previous article, ‘The Burning Question’, and it seems like most of my colleagues are concerned about the lack of growth opportunities within South Africa. What stimulates economic growth in any social setting? I enjoyed an article from the University of KwaZulu-Natal, by Dr Tony Ngwenya, where he states that with a population of about 350 000 people, Iceland has one of the lowest Gini coefficient ratios (a measure of statistical dispersion intended to represent the wealth inequality within a social setting) in the world. South Africa is approximately 160 times larger than Iceland, but it is very apparent that we do not share the same rate of entrepreneurial inclusivity. So naturally this prompts the question: what structural impediments cause South Africa to lag behind a country 160 times smaller than itself?

It’s difficult to answer this question, since I’m not sure what it is that stimulates economic growth and creates economic opportunity. According to the Global Competitiveness Index Report (2018/2019), infrastructure and primary education can be categorized as major contributors in the case of South Africa. In various other articles, mention is also made of access to finance, as well as an entrepreneurial curriculum from an early stage, which confirms the Global Competitiveness Index Report’s mention of primary education. One point was very clear – there is a great call for entrepreneurship to become the main engine that drives growth in South Africa. The Global Entrepreneurship Monitor (GEM) states that many of the world’s governments, think tanks, and international organizations now look towards entrepreneurship as the solution to ending social inequity, promoting women’s empowerment, and implementing business solutions to the world’s environmental challenges (5 ways we can build South African entrepreneurship in the ‘new economy’, Published August 2020, by Bheki Mfeka). This seems to be a very tall order indeed! Entrepreneurship involves an individual identifying an opportunity and then using their ability and motivation to grow their business, bearing most of the risks and enjoying most of the profits. The entrepreneur is commonly seen as a source of new ideas, goods, services, and business. I can only imagine that such an individual will need to be planted in very fertile ground to be able to grow a new business that will empower women and end social inequity. This fertile ground that I’m referring to is called an entrepreneurial culture. Does South Africa have this? A healthy entrepreneurial culture? Unfortunately, I don’t believe we do. Entrepreneurial culture can be described as an environment where someone is motivated to innovate and take risks (EFEB Network, Greek Association of Women Entrepreneurs). It is also described as a set of values, skills, and power of a group that is characterized by risk (Qaiser et al., 2019, Factors affecting “entrepreneurial culture”, Journal of Innovation and Entrepreneurship). Clearly, the definition of this specific culture shows that the environment must support active risk-taking. How is this established? Christo Botes (from Business Partners) says entrepreneurship is moulded by intention, opportunity, skills, and resources (article by Tom Jackson, September 2016). However,

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President’s Corner (continued) although 40.9% of South African adults perceived good entrepreneurial opportunities, and 45.4% perceived they had the capabilities to start a business; only 7% of entrepreneurs were engaged in early-stage entrepreneurial activity in 2015. Why is there such an immense disconnect? Furthermore, the 2015-2016 GEM South Africa report shows a very low mean score of 2.8 in terms of encouraging entrepreneurial risk-taking. That is an astronomical gap between perception, execution, and support. Could it possibly be that we do not accept and buffer failure and that we do not encourage, especially our youth, to learn from failure? It seems that our failure rate in the small, micro, and medium enterprises (SMMEs) sector is fairly high. This sector has been identified as a key vehicle for addressing low levels of unemployment and economic growth, despite the formidable challenges this sector face. The Business Monitor International (BMI) survey estimated that an average of 80% of the collapsed entities in 2013 were owned by non-matric holders (Amra et al., 2013). The most successful, innovative, and more labour-absorptive small businesses were those that were run by educated and skilled owners and personnel. Despite the well documented significance of training, 90% of a sample of 100 small business entrepreneurs dismissed the need for skills training (Fatoki, 2012). This simply confirms what Christo Botes recommends: more emphasis on business and entrepreneurial-based education in schools via formalized programmes and additions to the national curriculum. I agree with this statement – relying solely on tertiary education to instil enthusiasm for entrepreneurship in graduates is unrealistic. What if I’m no longer in primary school? What if I’m not even a graduate? I am in fact already an employee. In this case, literature recommends that employees should be given a chance to participate in decision-making that contributes towards company goals. Incorrect decisions should be inspected so that there is an opportunity to learn for them. Again, knowledge (training) of employees should be updated as they must be familiar with new research in their specific area (Qaiser et al., 2019). It might be prudent to ask if your company allows this. Research from the University of Birmingham shows that when employees feel they have control over their work environment, they are also more likely to come up with ideas on how to improve the company. It is definitely clear that the competencies associated with entrepreneurship are shaped and determined by the skills set acquired both formally and informally. Our South African policy-makers need to self-reflect in terms of the training our entrepreneurs have access to and the skills they acquire, so that they can outsmart their global counterparts in the bigger entrepreneurial schemes. So, where do we want to be? Where should South Africa be going? I want this country to become a net exporter of value-added manufactured goods and shift away from the simple pitto-port model. This is my wish for our country.

Z. Botha President, SAIMM

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The Journal of the Southern African Institute of Mining and Metallurgy

SELLING THE FAMILY SILVER

oes South Africa really take beneficiation seriously? Here is a story about one company, just as an example of where, in my opinion, things might have gone wrong. In 1998 Samancor was the world’s largest ferro-alloy producer, producing alloys of chrome and manganese. It was South African owned and controlled, with its origins in the creation of South African Manganese in 1926. However, in December 1998 its major shareholder, London-listed Billiton (formerly Gencor), took over the company and de-listed it from the Johannesburg Stock Exchange (JSE). It was established as the vehicle to promote Billiton’s global chrome and manganese businesses. Billiton, which subsequently merged with Australian mining company BHP to become BHP Billiton, did not retain its interest in chrome and in June 2005 it sold its majority interest in Samancor Chrome to the Kermas Group, a company domiciled in the UK with substantial interests in Kazakhstan. Kermas remained secretive, never issuing company reports nor providing access to journalists and analysts. Over the years ferrochrome producers in South Africa struggled to maintain production levels due to the rising cost and erratic supplies of power from Eskom. However, a multitude of small chrome ore producers obligingly supplied China with cheap ore to produce ferrochrome. In mid-2021 there were about 20 chrome recovery plants which produce fine chromite from UG2 platinum tailings, and also about 20 formal and informal washing plants for the production of chrome concentrates from primary sources. Eventually, in 2012, China overtook South Africa as the world’s largest ferrochrome producer. At the end of September 2019 the Association of Mineworkers and Construction Union (AMCU) launched an application in the Johannesburg High Court accusing Samancor of having deprived minority shareholder Ndizani Trust of ‘well over US$100 million in dividends and/or other revenue from 2005 and to the present’. One of the witnesses supporting the affidavit – and the whistleblower – was Miodrag Kon, who was appointed a director of Kermas SA in June 2005. Kon detailed a long list of corrupt practices by the company. Finally, in 2021 Kermas was sold to a Chinese consortium fronted by Chinese state-owned Sinosteel. China’s acquisition of Samancor resulted from a change in policy regarding ferro-alloys. After building up its own capacity to become independent of imports, China decided to close its highly polluting facilities and resume imports – preferably from a company which it controlled itself. Samancor’s transformation from a proud and very successful South African company to a mere supplier to China represents the continuation of the trend to surrender domestic control of mining/metallurgical companies to foreign owners whose primary loyalty is towards their own shareholders and international, rather than South Africa’s national, interests. Samancor’s acquisition by the Chinese follows the transfer of the ownership of South Africa’s steel industry to foreign control – Iscor to India’s Arcelor Mittal, Highveld Steel and Vanadium to Russia’s Evraz, Columbus Stainless Steel to Spain’s Acerinox. The major beneficiaries of the decline in South Africa’s ferro-alloy production, in my view, have primarily been the producers of chrome and manganese ores, whose entry into the market has been promoted by the government’s policy of BEE and who have been granted mining licences by the Department of Mineral Resources and Energy (DMRE). The production of manganese alloys suffered a much more catastrophic decline than the production of ferrochrome but, as in the case of chrome ore, there was an escalation in the number of producers of manganese ore. At the beginning of this century there were only four manganese mines in the country but there are now about 24, with none of the newcomers, largely funded by manganese traders, listed on the JSE. This has led to a situation where a plethora of producers supply chrome and manganese ore at bargain basement prices to smelters either based overseas or, if in South Africa, controlled by foreign owners who are not obliged to provide any public information about their activities. This, in my opinion, represents a further surrender of our economic sovereignty and abject submission to foreign interests.

* Dr Ian Robinson is the author of The Fall of a Giant, The Story of the Disintegration of the South African Mining Industry. The views presented are those of the author and do not necessarily reflect those of the SAIMM.

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Review on the Book: State Governance of Mining, Development and Sustainability by Tracy-Lynn Field (Professor, School of Law, University of the Witwatersrand), 2019, 394 pp Professor Field’s lengthy and detailed book considers in depth the dilemma of jurisdictions in reconciling the duty of promoting mining and the obligation of regulating the industry. The book is extensively researched, clearly reasoned, and thought-provoking. However it does not cover smallscale or artisanal mining and does not consider non-fuel extraction. Due to the difficulty of accurately translating technical and legal language, consideration is mainly given to English-speaking jurisdictions. The central theme is the move from ‘mining extractivism’ (the colonial exploitation of resource-rich countries and export of unbeneficiated products, thereby enriching foreign investors with consequent meagre local benefits) to ‘neoextractivism’ (mineral exploitation equitably benefiting all stakeholders). Some thought is given to post extractivism (minimizing extraction and consequent environmental impact by means of reducing, recycling, and reusing). The first two chapters present discourses for and against mining respectively. The next four consider mining rights, taxation, environmental issues, and mine closure in great detail. It is noted that as a result of popular perceptions of mining being a dirty, dangerous, environmentally destructive industry, several international industry initiatives such as codes of practice for cyanide and tailings storage facility (TSF) management have been implemented during recent decades in order to reduce reputational risk and comply with moral obligations. Furthermore, in many, if not most, jurisdictions, state support of ‘double movement’ responsibility is sadly lacking. Examples are incomplete or non-existent cadastres, inadequate geological mapping, and poor regulatory monitoring and enforcement. The list of topics covered and examples given is extensive. For instance, among others, full elaboration is given to mining rights, regulatory uncertainty, stakeholder expectations, environmental issues, upfront impact assessments, worker health and safety, meaningful consultation, ownership ‘free carry’, responsible sourcing (e.g. ‘green gold’, ‘conflict diamonds’), the resource curse, taxation models, corruption, and mine closure. Satisfactory mine closure is identified as one of the most problematic undertakings when one considers upfront agreement on outcomes, enforcement, adequate and secure funding, change of ownership, changing legislation, time scales, post-closure remediation and so forth. ‘State Governance of Mining, Development and Sustainability’ makes for essential reading by legislators, state ministries, mining company boards and their executives, as well as service providers.

P.H. Radcliffe January 2023

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The Journal of the Southern African Institute of Mining and Metallurgy

A critical comparison of interpolation techniques for digital terrain modelling in mining by M.A. Raza1, A. Hassan2, M.U. Khan1, M.Z. Emad1, and S.A. Saki1

Affiliation:

niversity of Engineering & U Technology, Lahore. 2 University’ de Liege, Belgium. 1

Correspondence to: M.U. Khan

Email:

usman@uet.edu.pk

Dates:

Received: 16 Aug. 2022 Revised: 16 Nov. 2022 Accepted: 18 Nov. 2022 Published: February 2023

How to cite:

Raza, M.A., Hassan, A., Khan, M.U., Emad, M.Z., and Saki, S.A. 2023 A critical comparison of interpolation techniques for digital terrain modelling in mining. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 2, pp. 53–62

DOI ID:

http://dx.doi.org/10.17159/24119717/2271/2023

ORCID:

M.A. Raza http://orcid.org/0000-0001-53738795 M.U. Khan http://orcid.org/0000-0002-62606679 M.Z. Emad http://orcid.org/0000-0001-85378026

Synopsis Digital modelling of a surface is crucial for Earth science and mining applications for many reasons. These days, high-tech digital representations are used to produce a high-fidelity topographic surface in the form of a digital terrain model (DTM). DTMs are created from 2D data-points collected by a variety of techniques such as traditional ground surveying, image processing, LiDAR, radar, and global positioning systems. At the points for which data is not available, the heights need to be interpolated or extrapolated from the points with measured elevations. There are several interpolation/extrapolation techniques available, which may be categorized based on criteria such as area size, accuracy or exactness of the surface, smoothness, continuity, and preciseness. In this paper we examine these DTM production methods and highlight their distinctive characteristics. Real data from a mine site is used, as a case study, to create DTMs using various interpolation techniques in Surfer® software. The significant variation in the resulting DTMs demonstrates that developing a DTM is not straightforward and it is important to choose the method carefully because the outcomes depend on the interpolation techniques used. In mining instances, where volume estimations are based on the produced DTM, this can have a significant impact. For our data-set, the natural neighbour interpolation method made the best predictions (R2 = 0.969, β = 0.98, P < 0.0001).

Keywords digital terrain model, interpolation, topographic surface.

Introduction Representation of the Earth’s surface or terrain in an uncomplicated way and with high fidelity is crucial Earth scientists and engineers for many reasons. The representation of the Earth has evolved from simple paintings in ancient times to highly advanced digital representation in the form of digital terrain models (DTMs). A DTM is a representation of the topographic surface and is defined as the digital description of the terrain using a set of spot heights over a reference surface (Hirt, 2014). The concept of DTMs was first introduced during the late 1950s (Miller, 1958) and since then has come a long way. Photogrammetric techniques paved the way for producing DTMs (Thursston and Ball, 2007), which in turn have been extremely useful in geoscience applications since the 1950s and have become a major tool in geographical information processing (Weibel and Heller, 1991). DTMs are considered 2.5D models instead of fully 3D because they assign a unique height value to geodetic or planar coordinates, and thus topographic surfaces are usually shown as continuous surfaces or fields (Weibel and Heller, 1991; Hirt, 2014). Along with DTMs, terms like digital surface models (DSMs) and digital elevation models (DEMs) are also commonly used, which should be distinguished from each other. A DSM is a depiction of a surface with all of its natural and built/artificial features such as vegetation and buildings, whereas a DTM is a bare earth surface. A DTM shows the development of a geodesic surface that augments a DEM and includes features of the natural terrain such as waterways and ridges. So a DEM can be created by interpolating a DTM but the reverse is not possible (GEODETICS, 2022). DEM, meanwhile, is a generic term that is used for a DTM as well as a DSM. It is synonymous with DTM if surface features like vegetation and building heights are removed during surveying, and if not, it is the same as DSM (Hirt, 2014; Maune, 2007). Irrespective of the terminology, all these terrain models are based on surface data-points.

DTM data sources Data acquisition is a crucial task for creation of accurate map and terrain models. This has prompted the development of methods that provide maximum detail with high precision and accuracy. The usual techniques for data acquisition include traditional ground surveying, image processing (photogrammetry), LiDAR, radar- (radar interferometry), and global positioning systems (GPS) (Hirt, 2014).

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A critical comparison of interpolation techniques for digital terrain modelling in mining Generally, traditional ground surveys have been the most common and cost-effective data-acquisition methods for limited areas and small projects and are more common for mining projects. Optical instruments such as theodolites, tachometers, and surveyor’s levels have been utilized largely in the past; however, their use is decreasing because of their lower time efficiency and accuracy (Kennie and Petrie, 2010). Ground-based surveys are nowadays conducted with modern electronic equipment, which offers high-speed working and efficiency. The photogrammetric technique involves aerial or satellite images of the Earth’s surface. These imaging techniques have benefitted from recent technological improvements and choosing between the two can be challenging. However, in general, the resolution of aerial images is higher than that of satellite images available for public use. LiDAR (light detection and ranging) systems utilize a laser scanner, an inertial measurement unit (IMU), and a global positioning system (GPS) coupled with a computer to ensure that all the measurements are synchronous with respect to time. The procedure for LiDAR is such that an aircraft or helicopter flies above the area of interest and laser scan it from side to side. This results in a set of points recorded which contain the location and elevation information. The spatial density of these points is generally within one metre (Réjean, Pierre, and Mohamed, 2009). Radar interferometry is another method used for DTM data acquisition. This method can be used over land, sea, and ice surfaces. These radars use the microwave region of the electromagnetic spectrum, the same as SAR (synthetic aperture radar) systems. In principle, they are very similar to LiDAR in that they also utilize the features of back-reflected waves to determine surface features (Bamler, 1997). Wilson (2012) discusses the methods and data sources to generate DEMs using LiDAR and similar methods. Recently, unmanned aerial vehicles (UAVs) and drones have become popular for topographic surveying and the creation of DTMs in mining and other fields. The success of these approaches hinges on their lower cost, flexibility, speed, and precision (Park and Choi, 2020; Yan, Zhou, and Li, 2012; Wajs, 2015). These devices use several downward-facing sensors and cameras to capture images during flight. The data is synchronized with a global information system (GIS) for accuracy. The gathered data is then processed using purpose-built modern software for DTM creation. In high-production open pit mining operations, such as strip mining, these techniques become especially useful as the volume computations can be done rapidly for accurate material excavation and overburden removal.

Sampling From the 1970s onward, much research work was carried out on surface modelling and contouring from DEM and many interpolation techniques were proposed (Li, Zhu, and Gold, 2004). Methods such as different types of moving averages, height interpolation by finite element projective interpolation, kriging, and several triangulation methods were introduced. But with time it was realized that for a given topography, sampling is the critical factor (Li, Zhu, and Gold, 2004). As a result, attention shifted toward quality control and sampling methods. Sampling has evolved into a whole new discipline and researchers have developed methods for the selection of suitable sampling techniques. Selective sampling, regular sampling patterns, and progressive and composite sampling are some of the popular photogrammetric sampling techniques. In selective sampling, commonly employed in field surveying, the points that are 54

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considered important are surveyed so as to have adequate coverage and required density. This method offers the advantage of high constancy with fewer points. The method is generally more useful for regions with major discontinuities and rugged terrain (Weibel and Heller, 1991). Regular sampling, also known as systematic sampling, as the name implies, uses a fixed distance between sampling points, which can be arranged as grids or profiles, square or rectangular. As the sampling interval is constant, it must be ensured that an adequate distance is selected in order to detect most of the discontinuities (Weibel and Heller, 1991; Li, Zhu, and Gold, 2004). It is a simple method that can be used in an automatic mode, but is restricted to fairly low and homogeneous terrains. In regions where discontinuities are more marked and the terrain is rugged, this might result in insufficient points to generate a high-fidelity terrain model (Weibel and Heller, 1991). In progressive sampling, a low-density grid is sampled initially, and wherever necessary a repetitive densification of the grid is performed; the whole area is surveyed until the required accuracy is achieved (Weibel and Heller, 1991, Li, Zhu, and Gold, 2004). DTM data is judged by its distribution, density, and the accuracy with which it is measured (Li, Zhu, and Gold, 2004). Data can be distributed in various patterns but a particular pattern must fit the specific terrain being investigated. Density of sampled data is represented as either sampling interval or the number of points per unit area. Accuracy of the sampled data depends on the surveying method, quality of instrumentation, techniques used and the skill level of the surveyor. Data acquired in dynamic mode is likely to be less accurate than in static mode. Generally, it is considered that the field survey method is the most accurate, but this depends on the quality of the instrumentation used (Li, Zhu, and Gold, 2004).

Surface modelling Surface modelling or surface reconstruction is the process by which the representation of terrain is obtained (Li, Zhu, and Gold, 2004). This reconstructed surface is the DTM surface that is generated from the original raw data and structured through a few popular approaches such as triangular irregular networks (TINs) and gridbased data structures (Li, Zhu, and Gold, 2004; Weibel and Heller, 1991). In TINs, the points or vertices are chosen and joined together in a series to form a network of triangles and therefore the surface is represented in the form of contiguous, non-overlapping triangles (ESRI, 2017). TINs have an advantage over grid-based models in their ability to describe the surface at different resolutions because in certain cases higher triangle resolution is required, such as for mountain peaks. (ET Spatial Technologies, 2017). TINs are also capable of working with any data pattern and can incorporate features like break lines (Li, Zhu, and Gold, 2004). Several methods have been developed to create these triangles but the most widely adopted is Delaunay triangulation, used by ArcGIS. Delaunay triangulation is based on the principle that a circle drawn through three nodes will not contain any other node This is known as the empty circumcircle principle (ESRI, 2017; ET Spatial Technologies, 2017; Li, Zhu, and Gold, 2004, as illustrated in Figure 1. The major advantage that this triangulation method offers over the others is that it produces as many equiangular triangles as possible and significantly reduces the chances of long, skinny triangles (ESRI, 2017;, ET Spatial Technologies, 2017). Moreover, there are certain interpolation techniques such as natural neighbour, which can only be applied to Delaunay-conforming triangles (ESRI, 2017). TIN is a frequently used vector data format for DEM and requires less The Journal of the Southern African Institute of Mining and Metallurgy

A critical comparison of interpolation techniques for digital terrain modelling in mining Interpolation techniques and mathematical models

Figure 1—An invalid (a) and valid (b) Delaunay triangle

computer memory than the gridded elevation models. However, because of the irregularity of the TIN, the organization, storage, and application of data are more complicated than that of the regular grid DEM (Liang and Wang 2020). The other widely used approach is grid-based surface modelling where points are joined in the form of matrices, either regular squares or rectangles (Weibel and Heller, 1991;, Li, Zhu, and Gold, 2004). Handling of these matrices is simpler but a high point density is required to obtain a terrain of desired accuracy (Weibel and Heller, 1991). Grid-based modelling results in a series of contiguous bilinear surfaces (Li, Zhu, and Gold, 2004). Grid-based surface modelling is highly compatible with grid or progressive sampling techniques, and some software packages accept only gridded data (Li, Zhu, and Gold 2004).

Interpolation of data In digital terrain modelling, interpolation serves the purpose of calculating elevations at the points for which data is not available from the points which have known elevations. There is a need to form the missing links between the points for which data is acquired to cover the unobserved part; the data that is estimated using interpolation to create DTMs. Interpolation is extremely important in terrain modelling processes such as quality control, surface reconstruction, accuracy assessment, terrain analysis, and applications (Li, Zhu, and Gold, 2004).

Visualization of DTMs After collecting the data, and creating the surface and interpolation models, the DTM has to be visualized so that it can be understood in the best possible way. The approaches used include texture mapping, rendering, and animation (Li, Zhu, and Gold, 2004)). Technological advances have made DTM visualization relatively easy and multiple tools and software are available for presenting the data in 3D and creating a DTM. GIS is the most commonly used.

Applications of DTMs DTMs have wide-scale uses in various disciplines of science and engineering such as mapping, remote sensing, civil engineering, mining engineering, geology, geomorphology, military engineering, land planning, and communications (Li, Zhu, and Gold, 2004;, Catlow; 1986, Petrie and Kennie, 1987). DTMs have made a significant contribution in the mining industry since the first time they were employed. Initial land surveys, reserve estimation, mine planning and, when the mining starts, setting up the equipment and the scheduling of mine machinery, all involve the use of DTMs. but the foremost application is in reserve estimation. A complete knowledge of the topographic surface of the region is necessary in defining the extent of the region and for large volume calculations. DTMs can also be used for highwall face and tunnel design and to calculate the volume of earthworks required for the completion of these tasks. The Journal of the Southern African Institute of Mining and Metallurgy

Interpolation is an integral part of constructing a digital terrain model as it approximates data in the regions where none exists. After creating a grid (surface modelling) to represent a surface, we are left with plenty of nodes for which data is necessary and which is estimated using several interpolation techniques. This is even required for LiDAR although the point density is very high, but here it is intended to stick with the methods used for traditional field survey techniques and to interpolate the data for creating DTMs. The interpolation techniques that will be considered are IDW (inverse distance weighted), natural neighbours, kriging, and splines. Different criteria for classifying interpolation techniques are applied across the globe in diverse fields. Some of them are discussed below. There are many ways in which interpolation techniques can be classified, such as based on area size, accuracy or exactness of the surface, smoothness, continuity, and preciseness. Several interpolation techniques have been developed by mathematicians and researchers and to date, even after much work, no technique is considered as the general best (Weibel and Heller, 1991). An interpolator is either global or local if it is based on the scope or area of the field (Li, Zhu, and Gold, 2004; Gentile, Courbin, and Meylan, 2013). Global interpolators are those which use all of the measured points or the whole sampled region to estimate values for the unknown points, whereas local interpolators use a patch or some points close to the targeted value (Gentile, Courbin, and Meylan, 2013). Burrough et al. (2015) suggest that global interpolators are suitable for describing the general trend of terrain, while local interpolators are preferable for variations over patches and utilizing spatial relationships between the data. Based on the interpolated value, they are either exact, where the interpolated value for an already sampled point will be the same as the measured, or approximate, where the interpolated value differs from the known measured value (Gentile, Courbin, and Meylan,, 2013). In other words, exact interpolators result in DTM surfaces that pass through every sampled point while approximate interpolators follow a trend instead and may not necessarily pass through all the original points (Maguya, Junttila, and Kauranne, 2013). This is because of the fact that some methods incorporate certain smoothing functions just to smooth out the sharp changes that might be incorporated (Gentile, Courbin, and Meylan, 2013). All these interpolation techniques basically have a mathematical or statistical model designed to subsume different parameters which affect the interpolation results. Based on these models, interpolation techniques are either deterministic or stochastic. Stochastic or geostatistical methods are those that are capable of yielding the estimated value as well as the associated error whiledeterministic methods, on the other hand, do not include any assessment of the error which could be associated with the estimated value (Gentile, Courbin, and Meylan, 2013). Interpolation methods are concerned with finding out if the values are interrelated, i.e. correlation and dependency (Childs, 2004). This correlation is then used to measure the similarity index within an area, the level, strength, and nature of interdependence between the variables (Childs, 2004). This section focuses on the mathematical or statistical models of the above techniques.

Inverse distance weighting Inverse distance weighting (IDW) is a local interpolation method that gives exact measurement values and utilizes a deterministic model. There are specific algorithms that can be used to achieve VOLUME 123

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A critical comparison of interpolation techniques for digital terrain modelling in mining smoothness (Gentile, Courbin, and Meylan, 2013). IDW assumes that the values which are closer to the point to be interpolated will be somewhat similar to those which are further away. Based on this assumption that the nearest points will influence the results greatly, IDW uses them to assign values for unmeasured locations. IDW is an example of a deterministic method, therefore the results will be same even if interpolation is repeated several times. According to its mathematical model, IDW is represented by Equation [1]. [1] where Z(so) is the value that needs to be estimated at location so, N is the number of samples chosen in a particular search distance, λi is the weight assigned to each sampled point, and Z(si) is the known measured value at location si (Erdogan, 2009, Jones et al., 2003). The equation that is developed for calculating weights involves an inverse relation with exponents (x) of distance (d) between the known value and the point to be predicted. Equation [2] is used to calculate the assigned weights, λi. [2] The exponent parameter x indicates the degree of influence of the surrounding points on the estimated value (Priyakant, Rao, and Singh, 2003). The weights sum to unity, showing that the method is unbiased (Gentile, Courbin, and Meylan, 2013). It is evident from Equations [1] and [2] that an increase in distance d will decrease the influence on the interpolated value (Burrough et al., 2015). It is also true that higher values of x will result in smaller weight values assigned for distant points, and lower values in larger weights (Erdogan, 2009, Aguilar et al., 2005). Therefore, the extreme values in the terrain will be sharper and it can be said that the parameter x controls the degree of smoothness in the IDW case. The value of x used typically varies between 1 and 4 with 2 the most commonly used, the reason why this technique is often referred to as inverse distance square (IDS) (Aguilar et al., 2005; Kravchenko and Bullock, 1999; Gentile, Courbin, and Meylan, 2013). Different x values and their impact on interpolation estimate quality have been studied by many researchers and it has been found that the power factor can be of great significance, or in some cases (Aguilar et al., 2005) may not affect the results very much. The other very important factor associated with IDW is the minimum number of points to be taken into consideration (Kravchenko and Bullock, 1999; Gentile, Courbin, and Meylan, 2013) as more points result in increased smoothing (Gentile, Courbin, and Meylan, 2013). Although the choice of x and N is tricky, methods such as cross-validation and jackknifing can be used to select the most appropriate values for these two most important parameters (Tomczak, 1998). The size and shape of the search radius are also very important and should be chosen very carefully. If there is no observable directional influence on the weights of data, the shape of the search radius should preferably be a circle, and if otherwise, it should be adjusted likewise (ESRI, 2017). Size is also an indication of the degree of influence the distant point has on the location to be interpolated. IDW is widely used because of its simplicity, lower computational time, and its ability to work with scattered data (Gentile, Courbin, and Meylan, 2013), but there are also some drawbacks associated with it. These are the selection of interpolation parameters, exact interpolation which refers to no smoothing, its deterministic nature as it doesn’t possess the ability to incorporate 56

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errors, and above all, IDW is highly sensitive to outliers and clustered data which can result in biased results, because of which IDW interpolated surfaces consist of features such as peaks and dips (Gentile, Courbin, and Meylan, 2013). Although IDW itself is an exact interpolator, some algorithms have been developed to incorporate a smoothing factor and the equation can also be written as Equation [3] (Gentile, Courbin, and Meylan, 2013; Garnero and Godone, 2013). Typically, a value between 1 and 5 is taken for s and it reduces the influence of any one sample for interpolated value (Li, Liu, and Chen, 2011). [3]

Splines Splines are basically polynomials of degree k which are fitted between each point to define the surface completely (Gentile, Courbin, and Meylan, 2013, Li and Heap, 2011). The places where two separate polynomials meet are called ‘knots’ and these knots can have a huge impact on the interpolation results (Li and Heap, 2011). The challenge is always to gradually smooth out the surface at these knots, and the method revolves around making the polynomial function, its first-, and in some cases, the second-order derivative, continuous at these arbitrarily chosen knots (Gentile, Courbin, and Meylan, 2013). However, this piecewise polynomial reference is different from that in raster interpolation where it refers to radial basis functions (Skytt, Barrowclough, and Dokken, 2015), which will be the area of focus here. Splines is the method that estimates the values using mathematical functions which smooth the surface and minimize the curvature of the surface (Childs, 2004). Splines have many variates and they produce surfaces which pass through all the sampled points and smooth the rest of it (Childs, 2004; Garnero and Godone, 2013). It is often referred to as a bending sheet (Childs, 2004) which is shaped to pass through all the sampled points and results in a smooth surface. Splines are global; they result in approximately estimated values and the model used is deterministic (Gentile, Courbin, and Meylan, 2013). Splines have a basic form similar to IDW, in which weights are assigned according to the distance between known and unknown points (Garnero and Godone, 2013) as given by Equation [4]. [4] where Φ(r) represents the interpolation function and r shows the Euclidean distance between the known point si and the unknown point so which is represented as || si - so (Garnero and Godone, 2013). Although this is considered as standard, other types of distance function can also be utilized (Gentile, Courbin, and Meylan, 2013). The weights must be assigned in a manner such that the function chosen gives the exact measured value as this type of interpolation is supposed to be passing through all the known points (Garnero and Godone, 2013). This leads to n number of equations with n number of unknowns, which can be worked to acquire a unique solution (Garnero and Godone, 2013; ESRI, 2017). There are many spline functions that have been developed to improve the method further and make it adjustable for given conditions (Gentile, Courbin, and Meylan, 2013; Garnero and Godone, 2013). In the above-stated mathematical expressions r is the Euclidean distance, σ is the tension parameter, E1 is the exponential integral function, CE is defined as the Eulero constant which has a value of 0.577215, and K0 is termed the modified Bessel function The Journal of the Southern African Institute of Mining and Metallurgy

A critical comparison of interpolation techniques for digital terrain modelling in mining (Gentile, Courbin, and Meylan, 2013). The tension parameter, σ, controls the smoothness of a function. The higher its value the better the smoothing, which can have adverse effects in a sense that the depiction of the data may not show the actual variation of the data (ESRI, 2017). This, however, is not true for the inverse multiquadratic method where the reverse is considered true (ESRI, 2017; Garnero and Godone, 2013). Keeping in view the challenge at hand of choosing an appropriate value for the smoothing factor, the same techniques of cross-validation and jack-knifing or trial and error are used. In ArcGIS, these functions are listed under radial basis functions, and a function can also be selected using crossvalidation (ESRI, 2017). Many consider multi-quadratic to be the best function (Yang et al., 2004). Splines offer some advantages over the other techniques in that the roughness of the terrain can be smoothed out efficiently and it is also capable of capturing broad and detailed features (Gentile, Courbin, and Meylan, 2013). The availability of many functions makes this method somewhat more flexible and adjustable to the data. This method works best for the terrains which have gentle slope variation and where the changes occur gradually over considerable horizontal distances (ESRI, 2017). It is also suitable for handling large data-sets (ESRI, 2017). A feature of this method that it can under- and over-estimate the given data for unknown points to make it a better fit for hills and smooth slopes. Splines can also be used along with other interpolation techniques to smooth an already created surface (Erdogan, 2009). Although splines outweigh other techniques in many respects, they do have their fair share of disadvantages. These include considerable variations in elevation within a short horizontal distance (ESRI, 2017), inability to give an account of errors because of their deterministic nature (Gentile, Courbin, and Meylan, 2013), empirical choice of the function and parameters selected (Gentile, Courbin, and Meylan, 2013), and their handling of clustered and isolated data swiftly (Gentile, Courbin, and Meylan, 2013). Furthermore, overall smoothing may still be too high (Gentile, Courbin, and Meylan, 2013) if the chosen values of parameters are not optimal.

Kriging Kriging is an extensively used method (Meyer, 2004) that is favoured by many authors. Bailey (1994, p. 32) maintains that ‘there is an argument for kriging to be adopted as a basic method of surface interpolation in geographic information systems (GIS) as opposed to the standard deterministic tessellation techniques that currently prevail and which can produce artificially smoothed surfaces’. Kriging, unlike the other methods under discussion, is a family of geostatistical or stochastic methods (Gentile, Courbin, and Meylan, 2013; ESRI, 2017). Kriging tries to identify the spatial correlation between the data, in order to come to a better conclusion. This suggests that all the points around an unknown point may not necessarily influence it in the same manner. Therefore, this correlation is modelled as a function of the distance (Burrough et al., 2015). The value at any location is assumed to incorporate a certain component of the trend and a random variable following a special distribution (Clark, 1979). Kriging is a method in which the value at an unknown point is estimated in two steps, i.e., calculating weights and then estimating the value. Determination of weights utilizes a function named the semivariogram γ(h) (sometimes referred to as just variogram), and the process as variogram modelling, and is represented by Equation [5] (Clark, 1979), where ‘n’ denotes the number of paired samples. The Journal of the Southern African Institute of Mining and Metallurgy

[5] Variogram modelling is completed by constructing an ‘experimental variogram’ γ^(h), and then fitting an ‘authorized variogram’ γ(h), model against it (Gentile, Courbin, and Meylan, 2013). An experimental variogram (sometimes referred to as an empirical variogram) is subjected to the conditions and is calculated from the sample data rather than being theoretical (Clark, 1979). An authorized variogram, on the other hand, is any one of a few standard variogram models that have been developed theoretically (Gentile, Courbin, and Meylan, 2013; Clark, 1979). Semivariograms enable understanding the trend in data to further use it for defining two very important features – sill and range. Kriging has many forms but Equation [6] can be considered the basis for all of them (Li and Heap, 2011). Here, μ is the stationary mean which is supposed to be constant over the whole domain and is calculated as the average of the data (Li and Heap, 2011). λi is the kriging weight, n denotes the number of known points used for the estimation of the unknown in a particular search window, and μ(so) is the mean of the samples within the search window (Li and Heap, 2011). [6] Among all the variants, ordinary kriging (OK) is the most widely used (Gentile, Courbin, and Meylan, 2013). Although many kriging methods are approximate, OK is an exact method and estimates the values locally (Gentile, Courbin, and Meylan, 2013). OK, based on its geostatistical properties, assumes the model as Equation [7]. [7] where, μ is the constant because of the intrinsic stationarity, also known as a deterministic trend (Erdogan, 2009), but is unknown (Gentile, Courbin, and Meylan, 2013; ESRI, 2017), while ε(s) is a random quantity drawn from the probability distribution (Gentile, Courbin, and Meylan, 2013), ε(s) is also called autocorrelated errors (Erdogan, 2009). Kriging is sometimes referred to as BLUE (best linear unbiased estimator) (Gentile, Courbin, and Meylan, 2013). Kriging is the best method if there is a directional bias or spatial autocorrelation is present in the data (Childs, 2004). In kriging, unlike IDW, the estimated values can be greater than the sample values and the surface does not necessarily pass through all those sample points (Childs, 2004). Kriging is also capable of giving a quantifiable account of interpolation errors in kriging variance (Gentile, Courbin, and Meylan, 2013). Although kriging is highly favourable in plenty of conditions, it is an overall complex method which requires extreme care when spatial correlation structures are being modelled (Gentile, Courbin, and Meylan, 2013).

Comparison of interpolation techniques Methodology For a comparison of interpolation techniques, we used a real data-set from a large mining site. The data was collected using traditional and GPS-based surveying techniques. Using this data, several topographic surfaces were created using SURFER® 9 utilizing various interpolation techniques. SURFER® 9 has multiple built-in interpolation techniques that make it easier to create surfaces using one method with a simple one-click operation, which makes it possible to handle and tinker with the methods under consideration. VOLUME 123

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A critical comparison of interpolation techniques for digital terrain modelling in mining The data The raw data used for this analysis is presented in Figure 2. The points show little scatter and are confined in a positively sloping trend within a bigger arbitrary rectangular region roughly 500 × 500 m in areal extent. We used this data to create a rectangular region using extrapolation. This will help in understanding the differences encountered while extrapolating the surface for the rectangular region using these points. Although the differences in elevations are not enormous, there are drops and rises in elevations within the data, with the difference between the maximum and the minimum elevation being around 30 m, which will help in identifying the key features related to each method. Keeping in view the distribution of the data in Figure 2, the interpolated and the extrapolated regions can be analysed separately. Although extrapolated regions cannot be trusted for their accuracy because of data scarcity, they will help in understanding the key features of these techniques. The inverse distance weighted to power (IDW) technique is worked by using the values 1, 2, and 4 for power parameter x. It is alredy understood that x refers to the weight that is to be given to the near and far points.

Results and discussion The surfaces created using various interpolation techniques are presented in this section.

Interpolation using inverse distance weighting The surfaces created using inverse distance weighting with power factors (x) of 1, 2, and 3 are presented in Figure 3. The parameter x controls the smoothing (Gentile, Courbin, and Meylan, 2013) and this is clearly visible in the interpolated region. The created surface is smoother where the degree of roughness increases with the power factor x. It can also be seen that with increasing values of x, sharp features such as pits become evident within the same region.

Moving towards the extrapolation region, the degree of smoothness behaves differently to that in the interpolated regions. This is due to the fact that IDW, with higher power values, assigns lower weights to the more distant points. Therefore, as the data becomes more distant, the surface starts to behave smoothly even for sharp changes in elevation. This observation is consistent with both sides of the sampled data. Another important parameter involved in IDW is the search radius, which in this case seems to have little effect on the generated surface, due primarily to the fact that the data is abundant for the region where it exists. However, if the search radius is too low, this can have an impact on the extrapolated surface such that the results may not be obtained for regions such as corners that might become offshore to a certain search radius limit. One such example is shown in Figure 4, where the power factor is kept as 2 while the search radius is taken as 150 yards instead of 342 for Figure 3 .

Interpolation using splines Compared to IDW, splines show inconsistent behaviour between the different variants such as multiquadratic, inverse multiquadratic, and thin plate splines as shown in Figure 5. SURFER® 9 does not provide the option of using splines with tensions and completely regularized splines. This inconsistent behaviour culminates in the extrapolated region where there are large differences in elevation within a very short horizontal distance. In the interpolated region, however, the three kernel functions performed similarly. A key feature associated with splines is their ability to over- and under-estimate the sampled points for an unknown point. The minimum and maximum elevation values among all the data-points are 450.02 and 483.33 yards respectively. Thin plate splines have been estimated as less as 375 yards and as high as 495, which is the greatest among the three variants utilized. The multiquadratic function also exhibited the same feature but only to a small extent, which seems more practical compared to thin plate splines where

Figure 2—Spread of the data projected on a horizontal plane

Figure 3—Plan view of 3D surfaces formed by IDW with different values of power factor x. (a) x = 1, (b) x = 2, and (c) x = 3 58

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The Journal of the Southern African Institute of Mining and Metallurgy

A critical comparison of interpolation techniques for digital terrain modelling in mining Interpolation using kriging

Figure 4—IDW interpolated surface with shortened search radius the difference is too great to be considered practical, especially in the extrapolated region. It needs to be noted, however, that inverse multiquadratic did not exhibit the same feature. The multiquadratic function tested for twice the initial value of R2, i.e. R2 = 54 (Figure 5d) yielded minimum and maximum values of 436 and 490 respectively, compared with 446 and 484 for R2 = 27 (Figure 5a).

Figure 5a— Surface created using multiquadratic spline (R2 = 27)

Figure 5c—Surface created using thin plate spline The Journal of the Southern African Institute of Mining and Metallurgy

In interpolating with kriging, the most important factor to consider is the selection of an appropriate variogram model. Kravchenko and Bullock (1999) observed better soil parameter estimates with kriging and noted that kriging produced more accurate estimates compared to IDW when the variogram and number of neighbouring points were selected carefully. With the given set of points, the linear model proved to be the best fit while others (exponential and spherical) failed to predict the trend completely. Figures 6a and 6b represent the modelled surfaces using a spherical and an exponential variogram respectively. Kriging produced a smoother surface with slight underestimation of the interpolated values. Even in the extrapolated region, surfaces are smoother than those with splines, and to some extent with IDW. The smoothness of the surface in this case for kriging is due to the fact that the datapoints are closely spaced and kriging treats the clustered location more like a single point. These points are sampled because of the changes in their elevations, which kriging fails to pinpoint clearly. Figure 6c shows a surface produced using the best fit variogram linear model. The linear model is shown in Figure 7.

Interpolation using natural neighbour technique Natural neighbour interpolation (NNI) performs fairly well apart from in the extrapolated region where there are no results at all. Figure 8 represents the surface created utilizing NNI, which is

Figure 5b—Surface created using inverse multiquadratic spline

Figure 5d—Surface created using multiquadratic spline (R2 = 54) VOLUME 123

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A critical comparison of interpolation techniques for digital terrain modelling in mining

Figure 6a—Surface produced using exponential variogram model

Figure 6b—Surface produced using spherical variogram model

Figure 6c—Kriging modelled surface (linear variogram)

Figure 8—Surface created using natural neighbour interpolation Figure 7—Linear variogram modelling

smooth compared with IDW and splines. NNI was also capable of estimating small changes in elevation and still producing a smoother surface. As expected, it did not over- or underestimate the data at all. Because of the simple procedure, the computational time for this method was much less. One of the possible reasons for the surface being smooth may be the small horizontal distance between the data-points. NNI handles the scattered data well because it creates polygons and when data-points are too close to each other, there might be some numerical instability and errors in rounding off. 60

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Predicting best fit through regression modelling To determine which interpolation method predicted/estimated the original heights/elevations (Z values) the best, we conducted a stepwise regression analysis by including the Z value estimates using inverse distance weighting (EST_IDW1, EST_IDW2, EST_IDW3 with weights 1, 2, and 3 respectively), kriging (EST_KRG), and natural neighbour (EST_NNI). The analysis (Table I) indicated EST_NNI as the best predictor for the original Z values (R2 = 0.969, β = 0.98, P < 0.0001). This may be because of the fact that the dataThe Journal of the Southern African Institute of Mining and Metallurgy

A critical comparison of interpolation techniques for digital terrain modelling in mining Table I

Stepwise regression analysis predicting Z for five interpolation methods Model

Model summary R2

0.984a

Adjusted R2

0.969

Std. error of the estimate

0.969

0.97133

aPredictors: (Constant), EST_NNI

Coefficientsa Model

Unstandardized coefficients B

1 (Constant) EST_NNI

Standardized coefficients

Std. error

-13.142 1.028

Sig.

Beta

3.422 0.007 0.984

-3.841 143.151

0.000 0.000

aDependent variable: Z_actual Table II

Stepwise regression analysis predicting Z for inverse distance weighting interpolation methods Model

Model summaryb R square

0.728a

Adjusted R square

0.530

Std. error of the estimate

0.529

4.03066

aPredictors: (Constant), EST_NNI bDependent variable: Z_actual Coefficientsa Model

Unstandardized coefficients B

1 (Constant) EST_IDW2

37.324 .921

Std. Error

Standardized coefficients

Sig.

Beta

15.851 .033 .728

2.355 27.700

.019 .000

aDependent variable: Z_actual

set was large and closely spaced enough to provide the best estimate. All the interpolation methods produced very close estimates of the Z values. As inverse distance weighting is a popular interpolation method for DTMs created for mining purposes because of its simplicity to comprehend and use, we compared the three inverse distance weighted estimates (EST_IDW1, EST_IDW2, and EST_IDW3). Among these, the inverse distance squared method (EST_IDW2) proved to be the best estimator for the given set of data (R2 = 0.530, β = 0.728, P < 0.0001) (Table II).

Conclusions An overview of the common interpolation techniques used for creating digital terrain models (DTMs) in mining was presented. Asample data-set from an actual mine site was interpolated and extrapolated using inverse distance weighting (IDW), splines, kriging, and natural neighbour techniques in Surfer® 9. The results showed that the creation of a DTM is not a straightforward exercise, and one must be careful in selecting the method, as the results The Journal of the Southern African Institute of Mining and Metallurgy

vary based on the choice of interpolation method and the data-set. This can have a huge impact in mining situations where volume calculations are based on the DTM created. The selected method must also incorporate both data interpolation and extrapolation. Although the IDW methods are most commonly employed for DTM creations in mining, this study shows that the results are strongly influenced by the search radius and the power factor of IDW. In general, kriging and natural neighbour produced better results for extrapolation, as these techniques do not overestimate or underestimate the data-points. The selection of any method must take into account various interpolation techniques and then gauge their benefits before finalizing a specific interpolation method for DTM creation. For our data-set, the natural neighbour interpolation method produced the best estimates. For future research, the authors plan to compare the findings with a high-resolution satellite image or through field visits for higher fidelity. This, along with detailed statistical analysis and simulations, will help further refine the technique. These findings should help field mining and exploration engineers to produce better resource and volume estimates. VOLUME 123

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A critical comparison of interpolation techniques for digital terrain modelling in mining References Aguilar, F.J., Agüera, F., Aguilar, M.A., and Carvajal, F. 2005. Effects of terrain morphology, sampling density, and interpolation methods on grid DEM accuracy. Photogrammetric Engineering & Remote Sensing, vol. 71. pp. 805–816. Bailey, T.C. 1994. A review of statistical spatial analysis in geographical information systems. Spatial Analysis and GIS. Fotheringham, S. and Rogerson. P, (eds). CRC Press. pp. 13–44. Bamler, R. 1997. Digital terrain models from radar interferometry. https://phowo. ifp.uni-stuttgart.de/publications/phowo97/bamler.pdf Bohling, G. 2007. Introduction to geostatistics. Open File Report no. 26. Kansas Geological Survey. 50 pp. Burrough, P.A., McDonnell, R., McDonnell, R.A. and Lloyd, C.D. 2015. Principles of Geographical Information Systems. Oxford University Press. Catlow, D. 1986. The multi-disciplinary applications of DEMs. Proceedings of Auto-Carto London. Volume 1. Hardware, Data Capture and Management Techniques. Blakemore, M. (ed.). pp. 447–454. https://cartogis.org/docs/ proceedings/archive/auto-carto-london-vol-1/pdf/the-multi-disciplinaryapplications-of-dbms.pdf Childs, C. 2004. Interpolating surfaces in ArcGIS spatial analyst. ArcUser, JulySeptember 2004. pp. 32–35. Clark, I. 1979. Practical Geostatistics. Applied Science Publishers, London. Erdogan, S. 2009. A comparision of interpolation methods for producing digital elevation models at the field scale. Earth Surface Processes and Landforms, vol. 34. pp. 366-376. ESRI. 2017. ArcGIS Documentation. https://desktop.arcgis.com/en/documentation/ ET Spatial Technologies. 2017. Triangulated irregular network http://www.ianko.com/resources/triangulated_irregular_network.htm Garnero, G. and Godone, D. 2013. Comparisons between different interpolation techniques. Proceedings of the International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, vol. XL-5/W3. pp. 27–28. https://d-nb.info/1144994764/34 Gentile, M., Courbin, F., and Meylan, G. 2013. Interpolating point spread function anisotropy. Astronomy & Astrophysics, vol. 549. A1. 20 pp. https:// www.aanda.org/articles/aa/full_html/2013/01/aa19739-12/aa19739-12.html Geodetics. 2022. DEM, DSM & DTM: Digital elevation model – Why it’s important https://geodetics.com/dem-dsm-dtm-digital-elevation-models/ Hirt, C. 2014. Digital terrain models. Encyclopedia of Geodesy. Grafarend, E.W. (ed.). Springer, Berlin, Heidelberg. https://ddfe.curtin.edu.au/gravitymodels/ ERTM2160/pdf/Hirt2015_DigitalTerrainModels_Encylopedia_av.pdf Johnston, K., Ver Hoef, J.M., Krivoruchko, K., and Lucas, N. 2001. Using ArcGIS geostatistical analyst. Esri Press, Redlands, CA. https://downloads2.esri. com/support/documentation/ao_/Using_ArcGIS_Geostatistical_Analyst.pdf Jones, N.L., Davis, R.J., and Sabbah, W. 2003. A comparison of three‐dimensional interpolation techniques for plume characterization. Groundwater, vol. 41. pp. 411–419. Kennie, T.J.M. and Petrie, G. 2010. Engineering Surveying Technology, Taylor & Francis. Kravchenko, A. and Bullock, D.G. 1999. A comparative study of interpolation methods for mapping soil properties. Agronomy Journal, vol. 91. pp. 393–400. Krivoruchko, K. and Gotway, C.A. 2004. Creating exposure maps using kriging. Public Health GIS News and Information, vol. 56. pp. 11–16. Li, D., Liu, Y., and Chen, Y. 2011. Computer and Computing Technologies in Agriculture IV: 4th IFIP TC 12 Conference. CCTA 2010, Nanchang, China, October 22-25, 2010, Part II, Selected Papers, vol. 345. Springer.

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Li, J. and Heap, A.D. 2011. A review of comparative studies of spatial interpolation methods in environmental sciences: Performance and impact factors. Ecological Informatics, vol. 6. pp. 228–241. Li, Z., Zhu, Q., and Gold, C. 2004. Digital Terrain Modeling: Principles and Methodology, CRC Press. Liang, S. and Wang, J. 2020. Geometric processing and positioning techniques. Advanced Remote Sensing (2nd edn). Academic Press. pp. 59–105. Maguya, A.S., Junttila, V., and Kauranne, T. 2013. Adaptive algorithm for large scale dtm interpolation from lidar data for forestry applications in steep forested terrain. ISPRS Journal of Photogrammetry and Remote Sensing, vol. 85. pp. 74–83. Maune, D.F. 2007. Digital Elevation Model Technologies and Applications : The DEM Users Manual. American Society for Photogrammetry and Remote Sensing, Bethesda, MD. Meyer, T.H. 2004. The discontinuous nature of kriging interpolation for digital terrain modeling. Cartography and Geographic Information Science, vol. 31. pp. 209–216. Miller, C.L. 1958. The theory and application of the digital terrain model. MS thesis, Massachusetts Institute of Technology. Park, S. and Choi, Y. 2020. Applications of unmanned aerial vehicles in mining from exploration to reclamation: A review. Minerals, vol. 10. p. 663. Petrie, G. and Kennie, T. 1987. An introduction to terrain modeling: Applications and terminology. Terrain Modelling in Surveying and Civil Engineering: A Short Course. University of Glasgow. Priyakant, N.K.V., Rao, L., and Singh, A. 2003. Surface approximation of point data using different interpolation techniques–A GIS approach. http://www. geospatialworld.net/article/surface-approximation-of-point-data-usingdifferent-interpolation-techniques-a-gis-approach/ Réjean, S., Pierre, B., and Mohamed, R. 2009. Airborne LIDAR surveys – An economic technology for terrain data acquisition.: https://www.geospatialworld. net/article/airborne-lidar-surveys-an-economic-technology-for-terrain-dataacquisition/ Skytt, V., Barrowclough, O., and Dokken, T. 2015. Locally refined spline surfaces for representation of terrain data. Computers & Graphics, vol. 49. pp. 58–68. Thursston, J. and Ball, M. 2007. What is the role of the digital terrain model (DTM) today? http://sensorsandsystems.com/what-is-the-role-of-the-digitalterrain-model-dtm-today/ Tomczak, M. 1998. Spatial interpolation and its uncertainty using automated anisotropic inverse distance weighting (IDW)-cross-validation/jackknife approach. Journal of Geographic Information and Decision Analysis, vol. 2. pp. 18–30. Wajs, J. 2015. Research on surveying technology applied for DTM modelling and volume computation in open pit mines. Mining Science, vol. 22. pp. 75–83. Weibel, R. and Heller, M. 1991. Digital terrain modeling. Geographical Information Systems: Principles and Applications. Maguire, D.J., Goodchild, M.F., and Rhind, D.W. (eds). Longman, London. Wilson, J.P.J.G. 2012. Digital terrain modeling. Geomorphology, vol. 137. pp. 107–121. Yan, X.M., Zhou, Z.L., and Li, X.B. 2012. Three-dimensional visual modeling technology and application of open pit mining boundary. Advanced Materials Research. Trans Tech, Stafa-Zurich, Switzerland. pp. 790–793. Yang, C.-S., Kao, S.-P., Lee, F.-B., and Hung, P.-S. 2004. Twelve different interpolation methods: A case study of Surfer 8.0. Proceedings of the XXth ISPRS Congress. International Society for Photogrammetry and Remote Sensing, Hannover, Germany. pp. 778–785. u

The Journal of the Southern African Institute of Mining and Metallurgy

The necessity of 3D analysis for open-pit rock slope stability studies: Theory and practice by A. McQuillan1 and N. Bar1

Affiliation:

ecko Geotechnics, St Vincent and G the Grenadines, Australia.

Correspondence to: A. McQuillan

Email:

alison@geckogeotech.com

Dates:

Received: 26 Oct. 2022 Revised: 8 Jan. 2023 Accepted: 23 Jan. 2023 Published: February 2023

How to cite:

McQuillan, A. and Bar, N. 2023 The necessity of 3D analysis for open-pit rock slope stability studies: Theory and practice. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 2, pp. 63–70

DOI ID:

http://dx.doi.org/10.17159/24119717/2425/2023

ORCID:

A. McQuillan http://orcid.org/0000-00021645-6497 N. Bar http://orcid.org/0000-00017948-2468

Synopsis Geotechnical models developed during the planning stages of open pit mines are three-dimensional so as to capture the spatial variation in lithological, structural, hydrogeological, and geomechanical conditions. Geological models that describe the lithological and structural (faulting and folding) characteristics of a deposit are always 3D. Likewise, boreholes and piezometers used to develop geomechanical properties and groundwater models are drilled at spatial offsets across the deposit to understand the lateral and vertical characteristics. Yet when geotechnical analysis is completed, often the three-dimensional geological, hydrogeological, and structural models as well as geometrically complex 3D mine designs for optimizing economic mineral recovery and overburden removal are simplified to two-dimensional sections. In this paper we demonstrate that this simplification can lead to the wrong failure mechanism being identified, analysed, and/or a conservative factor of safety being calculated and hence an over-estimation of slope stability. Through case studies we show how three-dimensional analysis methods are more suited to rock slopes, particularly those with anisotropic material strength, when singularities such as geological faults are present, and nonlinear slope geometry. When the same slopes are analysed in two dimensions, the failure mechanism calculated is often fundamentally incorrect. The case studies further reveal that the factor of safety calculated in three dimensions is not always higher than the two-dimensional factor of safety.

Keywords slope stability, 3D, limit equilibrium, finite element, open pit, rock mechanic.

Introduction Several methods exist to analyse slope stability. Available methods can be broadly categorized into empirical, kinematic, limit equilibrium (LE), and numerical methods. Stability analyses can further be calculated in two dimensions (2D) or three dimensions (3D) using deterministic and/or probabilistic inputs. All of these methods have their advantages and limitations. Of the available methods, 2D LE analysis is traditionally the most widely applied to slope stability, with stability being assessed and reported in terms of a factor of safety (FOS) (McQuillan, Canbulat, and Oh, 2020). In this paper we demonstrate the variation in FOS calculated between 2D and 3D slope stability analysis methods. Through case studies, it is shown how 3D analysis methods are more suited to rock slopes, particularly those with anisotropic material strength and nonlinear slope geometry. When analysing the same slopes in 2D, the failure mechanism calculated is fundamentally incorrect. The case studies presented further demonstrate that the 3D FOS is not always higher than the 2D FOS. The only way to determine the 3D FOS with confidence is to analyse the scenario in true 3D, not by applying a rule of thumb or assuming a general percentage increase to 2D FOS. If the slope under investigation includes any of the following features, 3D stability analysis should be included in the geotechnical design review process. i. Nonlinear slope geometry (Bar and Weekes 2017, Dana et al., 2018) ii. Spatially or laterally varying geological and hydrogeological conditions iii. Spatially varying material strengths, including anisotropic material behaviour in the same unit iv. Singularities and persistent geological structures, striking and intersecting up to 50° from the slope orientation (McQuillan et al., 2018) v. Highly variable 2D results within close spatial proximity to each other (Bahsan and Fakhriyyanti, 2018; Chakraborty and Goswami, 2021). The recommendation of 3D analysis is not limited to 3D LE and 3D numerical analysis. Empirical methods that consider the 3D geometry of slope stability can be just as valuable (Romana, 1993; McQuillan et al., 2018).

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The necessity of 3D analysis for open-pit rock slope stability studies: Theory and practice 3D modelling for slope stability analysis 3D LE analysis methods were first presented in 1969 (Anagnosti, 1969). Kalatehjari and Ali (2013) provide a summary of the development and application of 3D LE analysis from Anagnosti’s (1969) publication through to the developments in the early 2010s. Dana et al. (2018) further provide a summary of the developments of 3D slope stability analysis methods (LE and FE) from the 1960s to 2010s and comment on how the different methods affect stability results. To have confidence in the results of 2D or 3D models, validation should be completed with a fundamentally different type of analysis (e.g. finite element, finite difference). Similarity in results between methods should increase confidence in the results of either analysis method (Ugai and Leshchinsky, 1995; Kainthola et al., 2013). Results of 3D modelling should also be validated against the known behaviour of slopes. Recent examples of 3D back-analysis of excavated slopes with complex failure mechanisms are presented for Venetia diamond mine (Bar et al., 2022a), Bingham Canyon copper mine (Telfer and Schumacher, 2022), and Pueblo Viejo gold mine (Bar et al., 2022b).

for the weathered horizon, and dragline operations for the main pass horizon down to the target coal seams. The weathered horizon consists primarily of a matrix-cemented coarse sandstone. The main pass overburden is interbedded sandstone and siltstone. Persistent bench-scale joints are present in the main pass highwall, with joint sets oriented 87°/169° and 87°/093° (dip/dip direction). The intersection of these sets contributed to a wedge-mechanism slope failure (Figure 1). The stability of the main pass highwall is assessed using 3D LE analysis to show the limitations of 2D analysis for this type of 3D failure mechanism and slope geometry. In Slide3, joints can be accommodated in the slope stability calculation as either a ubiquitous material model (e.g. Generalised Anisotropic function) or as explicit joints (e.g. Weak Layer function). This model applies explicit joint orientations as measured from post-failure field survey (McQuillan and Guy 2022). Material properties applied are summarized in Table I. Results of this analysis method are displayed in Figure 2. A critical FOS of 0.78 is calculated. The failure mechanism is predicted to be sliding along the subvertical joint planes and shear through

Case studies Three case studies are presented to demonstrate real-world examples of the following scenarios. i. Simplifying real-world geometry to a 2D section does not model the true failure mechanism, and results in a mechanistically incorrect analysis of the slope under investigation. ii. 3D analysis does not always result in a higher stability factor, especially where the slope under investigation has variable surface geometry and sub-surface geology iii. Analysing the slope using two different methods, 3D LE and 3D FE, can be useful to validate predicted failure mechanisms and stability factors. The case study sites exhibit the following conditions: i. Nonlinear slope geometry. ii. Anisotropic material behaviour, including singularities (bench-scale geological structures) intersecting the slope excavation at acute angles. 3D LE (Slide3), 3D FE (RS3), 2D LE (Slide2), and 2D FE (RS2) modelling software from Rocscience, Inc (2022) were used to calculate the 3D and 2D FOS and SRF respectively.

Figure 1—Slope failure with wedge-style back scarp failure mechanism

Case study 1 Case study 1 presents an example of where simplifying slope conditions to 2D results in a mechanistically incorrect analysis of the real-world problem. Case study 1 is sourced from an open-cut coal mine and features a near-90° elbow in the slope design. The multi-bench slope is excavated using truck and shovel operations

Figure 2—Perspective view of 3D LE results applying joints as explicit weak layers (lime planes), at orientations defined in Table I. Critical FOS 0.78. Critical slip surface is bounded at the sides by subvertical joints and projected to shear through the CMR at the base

Table I

Material properties – Case study 1 Material

Failure criterion

Fresh coal measure rock (CMR) Mohr-Coulomb Joint Mohr-Coulomb Joint orientations Weak layer Coal Mohr-Coulomb 64

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Unit weight (kN/m3)

Cohesion (kPa)

Friction angle (o)

24 15 Joint set 1: Dip = 87o; Dip Direction = 169o Joint set 2: Dip = 87o; Dip Direction = 093o 15

110 2

30 12

The Journal of the Southern African Institute of Mining and Metallurgy

The necessity of 3D analysis for open-pit rock slope stability studies: Theory and practice the rock mass at the base of the critical slip surface. As the joints applied in this model are true to their actual field location, the model is indicating that failure at this measured intersection of joint sets is possible (i.e. FOS < 1) and risk management strategies should be applied. Controls may include exclusion zones based on the critical failure surface volume (or volume of failure surface with FOS < 1.0), which are readily calculated using 3D analysis. The modelled failure mechanism in Figure 2 is threedimensional. For comparison, multiple 2D sections were cut through the critical failure surface to show the difference in FOS between 2D and 3D analysis methods. Sections were cut at the intersection of the two joints, and then either side of this central section. Results of the 2D LE analysis for each 2D section are presented in Figure 3. Simplifying this wedge failure mechanism to a 2D problem (i.e. by cutting a section through the line of intersection of the two joints) results in a FOS of 0.63, section B. This is less than the FOS of 0.78 calculated using 3D methods, but is not directly comparable as the mechanics and forces in the 2D and 3D models are different. Most critically, simplifying to a 2D section for analysis does not represent the actual failure mechanism realized by the intersection of the two persistent geological structures. Where sections are cut either side of the line of intersection of the two joint sets, these sections similarly result in a lower FOS than the 3D analysis, and are again not representative of the real

mechanics and forces involved in the failure that will form at the intersection of the two joints. If such conditions exist, 2D analysis is not suitable for slope stability analysis, as 2D analysis is modelling apparent dip and dip direction only.

Case study 2 Case study 2 presents a situation where the 3D SRF is lower than the 2D SRF. The study is representative of a mine waste dump being extended over natural mountainous topography to take advantage of a short haul-dump circuit. The natural slope geometry consists of competent bedrock material, below an approximately 10 m layer of colluvium soil. Material properties applied to 3D FE modelling are summarized in Table II. Dump design and slope dimensions are illustrated in Figure 4. Dump stability was assessed using 3D FE methods. In case study 2, both the downslope and cross-slope natural topography vary significantly, leading to a situation where the local 2D conditions resulted in lower shear stresses than the combined 3D section of the slope that the dump was to be constructed over. This resulted in the 3D SRF being lower than the 2D sections cut through the same section of slope. A comparison of SRFs calculated from 3D FE and 2D FE analysis, at four different locations across the dump design is summarized in Figures 5 and 6. In three of the four 2D sections analysed the critical SRF was equal to or greater than the 3D SRF.

Figure 3—2D LE slope stability results. Top: images display plan view location of 2D sections cut. Bottom: images displays Slide2 analysis results. A: Section offset south of intersecting joints, FOS 0.63; B: section at intersection of joints, FOS 0.52; C: section offset north of intersecting joints, FOS 0.55

Table II

Material properties - Case study 2 Material

Waste rock Colluvium soil Bedrock

Failure criterion

Mohr-Coulomb 20 21.5 38.5 Mohr-Coulomb 20 0 33 Generalized Hoek-Brown 95 55 10

Unit weight (kN/m3) Peak cohesion (kPa)

0.5

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Peak friction angle (o)

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UCS (MPa)

GSI

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The necessity of 3D analysis for open-pit rock slope stability studies: Theory and practice

Figure 4—Perspective view of final dump design (left), natural topography is displayed by green contours. Section view of final dump design (right) showing spoil material to be dumped over natural colluvium soil and bedrock units

Case study 3 Case study 3 shows an example of how 3D FE analysis can be used to validate the results of 3D LE analysis. The study is representative of a mine waste dump of relatively low strength material. A portion of the dump is constructed over a residual mud pile. The stability of the waste dump is evaluated using 3D LE and 3D FE analysis. Applied material properties are summarized in Table III. The 3D LE analysis results are presented in Figures 7 and 8. The critical FOS is 2.24, with the critical slip surface sliding through the ponded mud at the base of the dump. Another low FOS and larger slip surface, also sliding through the ponded mud, is identified with a FOS of 2.39. The results of 3D FE analysis are presented in Figures 9 and 10. A critical SRF (Hammah et al., 2005) of 2.41 was calculated. Maximum shearing is modelled to occur primarily through the

Figure 5—Perspective view of 3D FE analysis results, showing a critical SRF of 0.88 through the spoil material. 3D results display contours of predicted total displacement. Warmer colours (red, yellow, green) indicate higher predicted displacement, cooler colours (blue) indicate lower predicted displacement

Figure 6—2D FE analysis results, showing variance in critical 2D SRF across the 3D model. 2D SRF through the centre of the 3D model (top left), 2D SRF 45 m from the centre slice (top right), 2D SRF 75 m from the centre slice (bottom right), 2D SRF 100 m from centre slice (bottom left)

Table III

Material properties – Case study 3 Material

Failure Criterion

Unit weight (kN/m3)

Cohesion (kPa)

Friction angle (o)

Subsoil Waste rock Mud Basement

Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb

19 20 12 22

28 26 0 121

19 15 8 29

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The Journal of the Southern African Institute of Mining and Metallurgy

The necessity of 3D analysis for open-pit rock slope stability studies: Theory and practice

Figure 7—Perspective view of 3D LE results. Critical FOS slip surface = 2.24 (light blue polygon). Larger area low FOS slip surface = 2.39 (green polygon)

Figure 8—Section view through critical slip surface, showing the majority of the critical slip surface is sliding through mud at the base of waste material

Figure 9—Perspective view of 3D FE results. Critical SRF = 2.41. 3D results display contours of predicted total displacement. Warmer colours (red, yellow, green) indicate higher predicted displacement, cooler colours (blue) indicate lower predicted displacement

mud pile at the base of the dump. A difference of 17% was observed between the 3D FE critical SRF and 3D LE critical FOS. However, a comparison of the results of 3D LE (Figures 7, 8) and 3D FE (Figures 9, 10) shows that there is reasonable correlation between the results of these different methods, as regards both the size and location of predicted shearing and displacement. A lower critical SRF is expected with finer mesh settings (Bahsan and Fakhriyyanti, 2018; Dana et al., 2018) and 10-noded elements applied. A 5 m, 4-noded element, graded mesh was applied to this case study. The Journal of the Southern African Institute of Mining and Metallurgy

Discussion Case study summary The three case studies show the advantages of 3D stability analysis and limitations of 2D stability analysis. The case studies have demonstrated that for slopes with (i) 3D failure mechanisms, resulting from anisotropic material strength and/or persistent geological structure and (ii) slopes with nonlinear slope geometry, 3D analysis methods provide a more realistic VOLUME 123

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The effect of petrographically determined parameters on reductant reactivity in the production of high-carbon ferromanganese by S. Soqinase1,2, J.D Steenkamp1,2, P. den Hoed2, and N. Wagner3

Affiliation:

Mintek, Randburg, South Africa Department of Chemical and Metallurgical Engineering, University of the Witwatersrand, Johannesburg, South Africa. 3 DSI-NRF CIMERA, Department of Geology, University of Johannesburg, Johannesburg, South Africa. 1

Correspondence to: S. Soqinase

Email:

sandas@mintek.co.za

Dates:

Received: 19 Sep. 2022 Accepted: 31 Jan. 2023 Published: February 2023

How to cite:

Soqinase, S., Steenkamp, J.D., den Hoed, P., and Wagner, N. 2023 The effect of petrographically determined parameters on reductant reactivity in the production of high-carbon ferromanganese. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 2, pp. 71–80

DOI ID:

http://dx.doi.org/10.17159/24119717/2321/2023

Synopsis In pyrometallurgical processes, metal oxides are reduced from molten slag through carbothermic reduction. It is of interest to evaluate the reactivity of the carbonaceous materials towards substances such as slag. Characterization techniques such as coal petrography can provide insight into the influence of feed coal properties and how they potentially dictate reductant performance. This study aimed to compare the petrographically determined organic composition of coal to reductant reactivity. Two South African medium-rank C bituminous coals and one anthracite sample were investigated together with high-carbon ferromanganese industrial slag. The reductant reactivity tests were conducted at 1500°C in a muffle furnace to assess the potential of carbonaceous reductant in reacting with the main slag components. SEM-EDS was applied to understand the extent of MnO (and to a lesser extent, SiO2) reduction from the slag. Coal 2, consisting of a greater proportion of vitrinite (59.5 vol% on a mineral matter-free basis and 54.7 vol% including mineral matter) was the most reactive reductant. The anthracite sample, with the highest inert maceral proportions (71.8 vol% including mineral matter and 76.8 vol% on a mineral matter-free basis), was the least reactive reductant.

Keywords reductant reactivity, MnO reduction, coal petrography, high-carbon ferromanganese slag.

Introduction High-carbon ferromanganese (HCFeMn) is a manganese alloy commonly produced in submerged arc furnaces (SAFs) in which metal oxides are reduced by carbon, from coke or coal char, to form a slag phase (Ostrovski and Swinbourne, 2013). Excavation of an industrial HCFeMn SAF revealed different reaction zones within the furnace interior (Olsen and Tangstad, 2004; Ringdalen, Tangstad, and Brynjulfsen, 2015). The two main reaction zones are the prereduction zone, where the charge is solid, and the coke bed zone, where ore, slag, and fluxes are molten (Olsen and Tangstad, 2004). There are two possible mechanisms of MnOx reduction suggested, which are indirect reduction through the gas phase and direct reduction at the interface between carbon and slag (Rankin and Deventer, 1980; Rankin and Wynnyckyj, 1997). The reduction of the higher manganese oxide compounds to MnO occurs through the release of upflowing CO gas in the pre-reduction zone (Suharno et al., 2018). The main reaction in the coke-bed zone is the reduction of MnO from liquid slag, by either solid carbon or solute carbon, to form metallic manganese (Kim, 2018; Lindstad, Tangstad, and Olsen, 2007) as seen in Equation [1]. [1] The reaction ultimately controls the distribution of manganese between slag and alloy (Ringdalen and Tangstad, 2009). Various parameters have a bearing on the rate of carbothermic reduction of MnO from liquid slags. The parameters studied, are influenced by the reaction kinetics and thermodynamics, including temperature (Olso, Tangstad, and Olsen, 1998), slag composition, the basicity of the slag (Kolbeinsen et al., 2006), and activity of MnO in slag. Several studies have been conducted to understand the mechanisms of MnO reduction by carbon from high-carbon ferromanganese slags (Rankin and van Deventer, 1980; Coetsee, 2018; Safarian et al., 2008, 2009; Sun et al., 2010 ; Safarian and Tangstad, 2010). The significance of carbonaceous reductant is its role in the reduction of oxide compounds through the gasification of reductant and direct reduction of slag with solid carbon. Direct reduction relates to the reaction between the carbonaceous reductant and molten slag (Sahajwalla, Dubikova, and Khanna, 2004; Pistorius, 2002). Generally, reactivity refers to the rate at which a substance can undergo a reaction (Safarian and Tangstad, 2010). Since carbonaceous materials are frequently used in pyrometallurgical processes, it is important to define the reactivity of carbon with specific substances. Reductant reactivity towards slag is defined as the potential of the carbonaceous reductant to react with the main slag components, specifically MnO.

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The effect of petrographically determined parameters on reductant reactivity Significance of petrographic analysis in coal utilization Relating reactivity to petrographically determined constituents is essential to understand the influence of feed coals and how they potentially perform in technological applications. The organic constituents of coal, known as macerals, are formed through biochemical and physicochemical changes in plant matter (Diessel, 1992) and, in turn, form the fundamental basis for petrographic assessment. Each maceral is distinguished by a unique set of physical, chemical, and technological properties for a given rank (Chen and Ma, 2002) which ultimately contribute to the behaviour of the coal. Generally, macerals are divided into reactive and unreactive groups based on changes in structure and chemical composition when heated. Reactive macerals soften, swell, and release volatile matter upon heating, while the inert forms of inertinite macerals at any rank will not combust easily and require more heat (Falcon and Ham, 1988). The changes in the chemical reactivity and structure of the coal’s organic constituents when heated needs to be considered when choosing a carbonaceous reductant since the resulting reductant will reflect the characteristics of the original coal. Extensive research data is available on the structural transformation of macerals and their change in chemical reactivity during processes such as pyrolysis and carbonization. For instance, the metallurgical industry depends on the petrographic assessment of coal for processes such as carbonization to produce quality coke. The thermal behaviour of particles extracted from pyrolysis, combustion, or gasification processes can be assessed petrographically (Bunt, Wagner, and Waanders, 2009; Malumbazo, Wagner, and Bunt, 2012; Alonso et al., 2001). Reactive macerals are known to devolatilize easily with increasing temperature and rank (Falcon and Ham, 1988), consequently swelling and becoming porous. Contrastingly, the principal unreactive maceral such as inertinite undergo little to no change in structure upon heating. This is true for reductant types irrespective of coal rank. Inertinites are generally poor in volatiles, and will not swell and become porous at any temperature, due to their dense structure. It is, therefore, essential to establish the key characteristics of the carbonaceous reductants that influence reductant reactivity towards slag, for selection in the production of HCFeMn. Such a study should include intrinsic coal properties, such as the organic composition, and how they could potentially perform at high temperatures for use as carbonaceous reductants. Understanding

the underlying reasons for the variations in feed carbons and how suitable each will be as a reductant for each process is important.

Experimental procedure Three reductant samples were sourced from a South African producer of manganese ferroalloys. The samples are described as coal 1, coal 2, and anthracite. The industrial HCFeMn slag sample used was sourced from one of South Africa’s HCFeMn producers.

Chemical analysis The bulk chemical composition of the HCFeMn slag sample (Table I) was determined by inductively coupled plasma optical emission spectrometry (ICP-OES). The bulk chemical compositions of the prepared representative coal samples were determined by proximate analysis using standard methods to measure moisture, ash, fixed carbon (by difference), and volatile matter (Table II).

Specific phase chemical analysis SEM-EDS was used for the identification of specific phases in the as-received slag phase and heat-treated slag sample microstructures at different reaction times to assess the extent of reduction. The SEM instrument used was a ZEISS Sigma 300VP with a field emission gun and ZEISS ‘Smart SEM software. The EDS detector used was an Oxford Instruments X-act PentaFET Precision with Oxford INCA software.

Petrographic analysis Representative coal samples (coal 1, coal 2, and anthracite) were crushed and mixed in epoxy resin and prepared as polished sections in accordance with ISO 7404-2. The petrographic analysis was carried out under oil immersion using a Zeiss Axio Imager M2m petrographic microscope fitted with a Fossil Hilgers system, at a magnification of 500×. Maceral group analysis and rank determination were conducted following SABS ISO 7404 parts 3 and 5 respectively.

Equipment The carbonaceous reductant reactivity tests were conducted in an Ultrafurn gas-tight muffle furnace (Figure 1), with workable chamber dimensions (H × W × D) of 175 mm × 195 mm × 175 mm, equipped with molybdenum disilicide (MoSi2) heating elements. A CAHO P961 programmable controller was used to set the heating

Figure 1—Schematic diagram of gas-tight furnace set-up used for the carbonaceous reductant reactivity tests 72

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The effect of petrographically determined parameters on reductant reactivity rate of 10°C/min to the target reaction time and set temperature. The reactivity test matrixes, one for each reductant, with the HCFeMn slag heated to 1500°C for periods of 72 to 360 minutes at 72-minute intervals are presented in Table III. Crucibles were prepared from large lumps of each carbonaceous reductant type (dimensions 25-27 mm inner diameter, 7-10 mm thickness, and height 50 mm) as seen in Figure 2. Once prepared, the reductant crucibles were filled with slag. The combined mass of the crucible and slag was recorded. The mass of the slag before the reaction was determined by difference. The charged crucibles were placed into size A5 alumina crucibles, which served as containment vessels in case of leakages, and aided in positioning the crucibles in the furnace chamber. To scavenge any oxygen that could potentially enter the chamber, a refractory board, with reactive carbon placed on top, was used as a lid to the alumina crucible. The furnace was heated gradually at a rate of 10°C/min to 1500°C under an inert atmosphere. Once the reaction time lapsed, heating was stopped. The sample was kept inside the chamber and allowed to cool overnight to room temperature while the argon gas flowed continuously. Once cooled, the reacted reductant crucible plus slag was removed from the alumina crucible and the combined mass of the crucible and slag was determined by weighing. The mass of slag and reductant after reaction allowed for the determination of mass loss percentage (Equation [2]) as a function of reaction time. [2]

where Δm = (Initial mass of reductant crucible + slag) – (final mass of reductant crucible + slag) (g) mi = initial mass of reductant crucible + slag (g)

Results and discussion Material characterization Chemical analysis The representative HCFeMn slag sample was analysed by ICP-OES. The slag bulk chemical analysis indicated an average MnO content of 23.4% (Table I). The proximate analysis for the parent coal samples is provided in Table II. The results indicate that the volatile matter was the highest in coal 2 at 29.3, followed by coal 1 at 27.7%. The anthracite sample had the least volatile matter at 5.4% and the highest fixed carbon (78.1%). The moisture and ash contents were similar in all three parent coals. The moisture contents ranged between 3.2% and 3.9% and the ash yield between 16.3% and 17.4%.

Specific phase chemical analysis The specific phase chemical analysis results quantified by SEM-EDS for the as-received HCFeMn slag are presented in Figure 3. The Table I

Bulk chemical composition of the HCFeMn slag by ICP-OES (%) Sample ID MnO FeO CaO MgO SiO2 Al2O3 K2O TiO2 BaO

Average Std dev.

23.4 0.8 29.4 7.1 0.36 0.05 0.34 0.16

34.5 0.25

3.9 0.04

0.2 0.2 0.6 0.01 0.00 0.01

Proximate analysis (% dry basis) Moisture Volatile matter Ash

Fixed carbon

Table II

Proximate data for the coals tested Sample Figure 2—(a) Reductant crucible prepared from the large coal lumps (b) filled with HCFeMn slag

200 mm

Coal 1 Coal 2 Anthracite

3.2 3.9 3.9

27.7 29.3 5.4

16.3 17.4 16.3

55.0 52.1 78.1

10 mm

Figure 3—SEM micrographs of the as-received HCFeMn slag , acquired at 20.0 kV. (a) Secondary electron image, Scale bar indicates 200 μm. (b) Backscattered electron image of area A of primary phase (1) and secondary phase (2). Scale bar indicates 10 μm The Journal of the Southern African Institute of Mining and Metallurgy

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The effect of petrographically determined parameters on reductant reactivity analysis revealed two phases –a primary phase and a secondary phase. The primary phase had a higher SiO content while the secondary phase had a higher MnO content. On average the two phases consisted of 27.3% MnO and 32.8% SiO2. The Fe-Mn-C alloy in the as-received slag (Figure 4) consisted predominantly of Fe at greater than 80 wt.%. Fe in the as-received slag is indicative of the presence of a metallic phase in the slag. The presence of metallic Fe in the system has been shown to accelerate the carbon/slag interactions (Teasdale and Hayes, 2005).

Petrographic analysis The reflectance measurement results of the parent samples (Table IV) classified coal 1 and coal 2 as medium-rank C bituminous coals. The anthracite sample is classified as high-rank coal with a vitrinite reflectance measurement of 2.9 RoVmr%. The classification follows the international classification of in-seam coals (United Nations Economic Commission for Europe, 1998). The boundaries that separate the different categories of coal rank are justified by important changes in coal properties or behaviour (Pinheiro, 2006). Volatile matter and fixed carbon are found to have opposing effects (Figure 5). Generally, as rank increases, volatile matter content decreases, leading to a reciprocal carbon content enrichment due to the geochemical changes the coal undergoes with the progression of rank. The maceral data in Table IV indicates that coal 1 and coal 2 are vitrinite-rich: 44.3 vol.% on a mineral matter free basis and 40.5 vol.% including mineral matter in coal 1, and 59.3 vol.% 54.7 vol.% respectively in coal 2. The anthracite sample has the least vitrinite proportion of 21.3 vol.% including mineral matter and 22.8 vol. % on a mineral matter-free basis and is inertinite-rich. Liptinite content was very low at 0.4 to 4.7 vol.% on both a mineral matter-free basis and including mineral matter. The vitrinite in coal 1 and coal 2 is mainly dominated by bands of collotelinite and collodetrinite as seen in Figure 6 and Table IV. The principal inertinite maceral is inert semifusinite with anthracite comprising the highest proportion.

The total reactive macerals are made up of vitrinite, liptinite, reactive semifusinite, and reactive inertodetrinite. Coal 1 and coal 2 displayed a higher total reactive maceral content compared to anthracite. Coal 1 consisted of 55.2 vol.% total reactive macerals on a mineral matter-free basis and 50.5 vol.% including mineral matter. Coal 2 consisted of 64.5 vol.% on a mineral matter-free basis and 59.5 vol.% including mineral matter. The total inert macerals were the highest in nthracite at 76.8 vol.% on a mineral matter-free basis and 71.8 vol.% including mineral matter. The series of micrographs in Figure 6 identifies the dominant macerals.

Reactivity tests The results in Figure 7 show that after 72 minutes of reaction time, coal 2 exhibited the highest initial mass loss of 38.6%. Coal 1 lost 32.9%, and anthracite had the least mass loss at 12.1%. The initial

Figure 5—Coal rank relationship with volatile matter and fixed carbon for the coals studied

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10 mm

Figure 4—Backscattered electron images acquired at 15.0 kV. (a) Metal prill entrained in the feed , consisting of Fe metal. Scale bars indicate 10 μm (a) and 1 μm (b)

Table III

Reactivity test matrixes Raw materials

HCFeMn slag and anthracite HCFeMn slag and coal 1 HCFeMn slag and coal 2 74

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Temperature (°C)

Reaction times (min)

1500 1500 1500

72, 144, 216, 288, 360 72, 144, 216, 288, 360 72, 144, 216, 288, 360 The Journal of the Southern African Institute of Mining and Metallurgy

The effect of petrographically determined parameters on reductant reactivity Table IV

Maceral group composition (vol.%) and reflectance results (mmf: mineral matterfree basis, Inc. mm: including mineral matter) Maceral group (vol. %)

mmf

Coal 1 Inc. mm

Coal 2 Inc. mm

Vitrinite Collotelinite Collodetrinite Corpogelinite Telinite Pseudovitrinite

44.3 24.1 19.2 0.4 0.4 0.2

40.5 22.0 17.5 0.4 0.4 0.2

59.3 33.6 23.9 1.4 0.2 0.2

54.7 31.0 22.0 1.3 0.2 0.2

22.8 13.9 8.4 0.2 0.0 0.2

21.3 13.0 7.9 0.2 0.0 0.2

Liptinite

4.7

4.3

3.1

2.9

0.4

Sporinite Cutinite

4.3 0.4

3.9 0.4

2.7 0.4

2.5 0.4

0.4 0.0

Inertinite

51.0

46.6

37.6

34.6

76.8

71.8

Fusinite Reactive semifusinite Inert semifusinite Inert inertodetrinite Reactive inertodetrinite Secretinite

14.5 6.0 21.7 7.9 0.2 0.6

13.3 5.5 19.9 7.2 0.2 0.6

8.3 1.9 20.3 6.6 0.2 0.2

7.6 1.7 18.7 6.1 0.2 0.2

3.4 1.5 58.6 9.1 0.2 4.0

3.2 1.4 54.8 8.5 0.2 3.7

mmf

Anthracite Inc. mm

Mineral matter 8.6 7.8 6.5 Rank (mean random reflectance %) Rank category Total* reactive macerals Total inert macerals

0.8 0.7 Med. rank C Med. rank C bituminous bituminous 55.2 51.0

50.5 46.6

64.5 37.6

59.5 34.6

2.9 Anthracite 24.9 76.8

23.3 71.8

*Total reactive macerals = vitrinite + liptinite + reactive semifusinite and reactive inertodetrinite

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Figure 6—Micrographs of coal 1 macerals (magnification 500× under oil immersion, reflected light). (a) Banded, vitrinite bands (collotelinite) and collodetrinite with a vitrinic groundmass and inertinite fragments, (b) smoother band of collotelinite surrounded by inert semifusinite and inertodetrinite, (c) coal 2 images of bands of semifusinite and vitrinite, (d) collotelinite and collodetrinite with a vitrinitic matrix and semifusinite, (e) anthracite images of banded semifusinite at different . (f) secretinite embedded within semifusinite showing internal. Scale bar indicates 100 μm The Journal of the Southern African Institute of Mining and Metallurgy

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Figure 7—Mass loss data and curves Please see the comment opposite

rapid mass loss in coals 1 and 2 can be attributed to the release of volatile matter, which is expected to be driven off at temperatures above 400°C (Speight, 2015). The least initial mass loss observed in anthracite is related to the least volatile matter content (Table III). Thereafter, coal 1 recorded a higher mass loss of 37.0% at 144 minutes and 39.7% at 216 minutes reaction time, compared to 32.8% and 39.7% for coal 2. At 288 and 360 minutes reaction time, the respective mass losses were 41.2% and 39.6% (coal 2) and 34.9% and 39.0% (coal 1). Anthracite underwent the least mass loss at all the reaction times. An almost linear mass loss pattern was observed for anthracite until 216 minutes. Moreover, a linear mass loss was noted in coal 1 at 72-216 minutes reaction time (32.9–39.7%). At higher temperatures, the mass loss was attributed to reduction of MnO in the slag to Mn in the alloy, which is expected to occur at temperatures between 1400 and 1500°C (Ringdalen, Tangstad, and Brynjulfsen, 2015). The differences in reactivities of the reductants at the different reaction times can be attributed to several reasons. In Figure 8, the mass loss profile highlights the influence of the slag and reductant crucible sizes on the mass loss. In coal 2, less mass loss was observed at 144 and 216 minutes compared to the initial 72 minutes reaction time. This is attributed to the reductant crucible mass as seen in

Figure 8, where less mass was consumed compared to the preceding 72 minutes reaction time. At 360 minutes reaction time, lower mass loss was also observed compared to 288 minutes reaction time. This is also due to the lower reductant crucible mass. In contrast, anthracite underwent less mass loss at 288 and 360 minutes compared to the preceding 216 minutes due to the lower slag mass used. Besides the variable reductant crucible and slag masses, other factors such as the method used could have contributed to the sometimes nonlinear mass loss trend observed as a function of time. In addition, the tests were conducted in batch mode and not continuous as in the case of thermogravimetry-type tests. However, despite the stated reasons, the results demonstrate that overall coal 2 underwent the highest mass loss, followed by coal 1 and anthracite with the least mass loss. This ultimately translates to coal 2 being the most reactive carbonaceous reductant, followed by coal 1, and anthracite being the least reactive.

Characterization of post-mortem samples Macroscopic observations Cross-section images with corresponding observations at the different reaction times are presented in Figure 9.

Figure 8—Mass loss as a function of residence time with coal and slag mass differences 76

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The effect of petrographically determined parameters on reductant reactivity ➤ Coal 1 and coal 2 had similar appearances (with minor variations) compared to the anthracite, which reacted differently. ➤ Overall, and applicable to all the reaction times, coal 1 exhibited more heat-induced cracks and was found to be more porous and brittle to the touch. As a result, most of the slag penetrated through the cracks and settled at the base of the reductant ‘crucible’ or deposited within the cracks. Consequently, it was almost impossible to separate it from the alumina crucible that was serving as a containment vessel. ➤ The slag is characterized by a green colour, which indicates the presence of MnO. In the case of coals 1 and 2 the green slag disappeared after 72 minutes reaction time, which is an indication that there was little or no MnO present. The MnO could either have reacted with the carbon and reported as Mn in the alloy or been lost as part of the volatiles. ➤ In anthracite the change in slag colour from green to grey took place over longer reaction times compared to the coals.

Figure 9—Cross-section images of the heat-treated samples at different reaction times The Journal of the Southern African Institute of Mining and Metallurgy

This is in agreement with the reductant reactivity tests, where anthracite was seemingly the least reactive of the reductants. ➤ The volume and shape changes in anthracite after heat treatment were also less marked compared to the coals.

Specific phase chemical analysis ➤ The results in Figure 10 show that at 72 minutes reaction time, the alloy in coal 1 was mostly present in the slag matrix, with two phases of Si-Mn-C. The slag microstructure differed from that of the as-received sample in that it consisted of a needlelike crystalline phase in a random network of veins. ➤ In coal 2 at 72 minutes reaction time the interface between the coal and slag was clearly defined with alloy forming in between. The coal was porous with metal entrainment between the pores. The alloy was identified as a single-phase alloy. ➤ The slag-anthracite interface is clearly defined with alloy preferentially located between the slag and carbon. The alloy consisted of two phases which are similar in composition, predominantly made up of Si-Mn-Fe. ➤ In coal 2 at 144 minutes reaction time (Figure 11), two slag phases were identified, consisting of a primary slag matrix and a crystalline phase. The slag is also associated with the alloy, which could be a result of the liquid slag penetrating into the liquid alloy with silicon carbide (SiC) distributed within the slag and alloy phases. The alloy is also characterized by a single phase consisting mainly of Si-Mn. ➤ The slag-anthracite boundary is clearly defined, with alloy existing mainly in between, with prills migrating into the slag. The alloy consisted of two phases; the primary alloy phase consisting of Si-Mn-Fe with Mn predominant. The anthracite did not exhibit any pores, but fine metal prills were dispersed throughout. ➤ At the slag-carbon interface of coal 1 (Figure 12) the slag comprised two phases, a primary phase high in CaO and SiO2 and a secondary phase. The alloy consisted of two phases of Si-Mn-Fe. ➤ Coal 2 displays a clear contact with the slag, as seen in the coal exhibiting cracks in Figure 12. The alloy phase is characteristic of a higher Si content than Mn. ➤ The interface between slag and anthracite is defined by the alloy forming in between. The slag microstructure is associated with a spinel phase. ➤ The slag microstructure of coal 1 at 288 minutes reduction time (Figure 13) appeared different from that at 216 minutes. It consisted of a secondary slag phase of elongated crystals high in Al2O3 and CaO and no crystalline phase. Mostly metal prills were observed in the slag matrix, and hardly any large alloy particles at the reaction interface, which could indicate insufficient time for alloy particles to coalesce. ➤ There is no clearly defined reaction interface between coal 2 and slag. The coal integrated with the slag. The slag microstructure also appeared different, consisting of one phase with coal and alloy entrainment. ➤ The anthracite appeared partially consumed with large alloy particles formed, consisting predominantly of Si-Mn. ➤ At 360 minutes reaction time, coal 1 was porous with the slag depositing between the pores (Figure 14). The slag consisted of finely disseminated metal prills with alloy at the interface. The alloy was associated with a SiC phase, which replaces carbon as the stable carbon-containing phase. VOLUME 123

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Figure 10—SEM backscattered electron image at 72 minutes reaction time acquiredat 20.0 kV. (a) Slag, Coal 1 and alloy interface, (b) coal 2-slag interface, (c) slaganthracite interface, Scale bar indicates 100 μm

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Figure 11—SEM backscattered electron image of the interface at 144 minutes reaction time, acquired at 20.0 kV. (a) Coal 2. Scale bar indicates 40 μm. (b) Slaganthracite interface. Scale bar indicates 100 μm

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200 mm

Figure 12—SEM backscattered electron image at 216 minutes reaction time, acquired at 20.0 kV. (a) Coal 1 and slag, Scale bar indicates 100 μm. (b) Coal 2. Scale bar indicates 200 μm. (c) Anthracite-slag interface. Scale bar indicates 200 μm

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Figure 13—SEM backscattered electron image at 288 minutes reaction time, acquired at 20.0 kV. (a) Coal 1. Scale bar indicates 50 μm. (b) Coal 2. Scale bar indicates 100 μm, (c) Anthracite. Scale bar indicates 50 μm

➤ In coal 2 (Figure 14), all the coal appears to have been consumed with no clear reaction interface. The coal was either lost as volatile matter or through a reduction reaction. The slag penetrated into liquid alloy and was composed of a mixture of alloy, SiC, and slag. ➤ There is a clear reaction interface between slag and anthracite with the anthracite partially consumed. Determining MnO concentrations with SEM-EDS from the slag (Table V) proved to be a challenge, especially for the two coals. 78

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The reason could be that the slag was most likely reduced from a two-phase area. Safarian and Tangstad (2010) found that for a slag reduced in a single phase, the chemical composition could be used to evaluate slag-carbon reactivity. However, this is not possible in a two-phase area. The MnO concentrations from the slag (Table V) were mostly determined from the secondary slag phase as it was difficult to determine MnO content from the primary phase. As such, a highly reactive reductant did not equate to a faster MnO reduction rate. However, with anthracite the trend was The Journal of the Southern African Institute of Mining and Metallurgy

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200 mm

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Figure 14—SEM backscattered electron image of the slag-coal interface with alloy at 360 minutes reaction time, acquired at 20.0 kV. (a) Coal 1 and slag interface. Scale bar indicates 100 μm. (b) Slag and alloy phases. Scale bar indicates 100 μm. (c) Slag-anthracite interface. Scale bar indicates 200 μm

more obvious, and the MnO content in the slag decreased with an increase in reduction time as seen in Table V. It was possible to determine the MnO content in slag with the anthracite samples due to the slag being present at all the reduction times with a clearly defined slag/carbon interface. This was not always the case for coal 1 and coal 2 – at longer reduction times the slag/carbon interface was not always defined and sometimes little or no slag was present. The yield of Mn in the alloy varied, with no trend observed except for anthracite. Most of the Mn in alloy measurements were determined at the slag-carbon interface, which had a much higher Mn content than alloy surrounding slag. This is in line with the findings of Safarian and Tangstad (2010). However, although tentative, the results did show an increase in Mn in the alloy, indicative of a reduction reaction. Based on the above observations, a possible mechanism of MnO reduction from the slag can be proposed. ➤ The presence of metal prills in the slag indicates that metal is transferred from the reaction interface to the slag through gas bubbles (Tangstad and Safarian, 2010). ➤ The as-received slag consisted of Fe metal prills, which were occasionally found in the reduced alloy. It has been suggested that the presence of Fe metal prills increases the rate of reduction (Tranell et al., 2007; Skjervheim, 1995). ➤ Safarian et al. (2009) and Tranell et al. (2007) observed that the presence of FeO in the slag system increases the rate of reduction. The as-received slag contained FeO, which could have played a role in the reduction of MnO. FeO is the first oxide in the system to be reduced through contact of the slag with the reductant.

Petrographic analysis related to reductant reactivity Effect of rank The reductant reactivity test results revealed that reactivity decreased with an increase in coal rank, in agreement with a study by Raaness and Gray (1995). The influence of coal rank on reactivity is associated with rank-related properties such as volatile matter and fixed carbon content (O’Keefe and Mastalerz, 2011). Generally, coal 1 and coal 2, which have high volatile matter contents and lower fixed carbon, are more reactive because of the faster rate of devolatilization. On the other hand, the higher-ranked anthracite, which devolatilizes at a higher temperature, was the least reactive.

Effect of maceral composition The organic composition showed some distinct chemical and physical differences between coals 1 and 2. The behaviour of the reductant is influenced by factors such as rank and maceral composition (Ward and Suarez-Ruiz, 2008). Coal 1 and coal 2 The Journal of the Southern African Institute of Mining and Metallurgy

Table V

MnO content in slag at different reduction times (wt.%) Time (min)

0 72 144 216 288 360

Anthracite

Coal 1

Coal 2

21.5 18.3 18.8 9.0 3.4 1.8

21.5 2.0 n.d. 6.9 1.6 n.d.

21.5 17.9 3.5 1.9 n.d. n.d.

n.d. Not determined

Figure 15—Coal type and maceral groups

contained different proportions of total reactive and inertinite macerals. Coal 2, with the highest total reactive macerals (Figure 14), was the more reactive reductant. In contrast, anthracite contained the highest proportion of inertinite, and the reactivity tests confirmed that anthracite was the least reactive reductant. The mass losses observed were due to thermal decomposition and release of volatiles, leading to changes in morphology and molecular structure of the macerals (Falcon, Wagner, and Malumbazo, 2018). Vitrinite is rich in volatile matter and hydrogen in low-rank bituminous coals. Inertinites are generally poor in volatiles. In terms of chemical reactivity, inertinite is more aromatic and richer in carbon-structured molecules (Falcon, Wagner, and Malumbazo, 2018). Anthracite, rich in inert macerals, reported lower volatile matter and thus was less reactive. The relationship of reactive and unreactive macerals to reductant reactivity is explored through the response of the carbonaceous reductants to slag during the reactivity tests. Generally, the reductant with a higher reactive maceral content was VOLUME 123

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The effect of petrographically determined parameters on reductant reactivity found to be the most reactive. Based upon the above observation, a correlation was established between petrographic parameters (coal type and rank) and reductant reactivity. The influence of devolatilization, which depends on the coal rank and proportions of volatile organic matter, was established. However, the role of the macerals in reduction could not be established as the reactivity tests could not indicate which of the individual macerals contributed to the reduction process.

Conclusion Coal 1 and coal 2 exhibited similar chemical properties such as volatile matter and fixed carbon content, derived from proximate analysis. Anthracite contained the least volatile matter and higher fixed carbon. The reactivity tests showed that the reductant reactivity towards slag was higher in lower ranked coals, while lower reactivity was observed in higher ranked anthracite. Coal 1 and coal 2 were characterized by a high proportion of total reactive macerals compared to anthracite. The carbonaceous reductant reactivity towards slag showed a systematic trend, increasing with an increasing proportion of reactive macerals. The maceral analysis results showed that coal 2, with the highest proportion of reactive macerals relative to inert macerals, exhibited the highest mass loss, while anthracite, with the highest inert maceral proportions, was the least reactive. However, anthracite has low reactivity due to its high rank and high heat content. It is believed that coal rank played a larger role in the reductant reactivity than the maceral proportions. Anthracite, irrespective of maceral type, does not form porous chars (Falcon, Wagner, and Malumbazo, 2018). No information could be gathered on how the reactive and inert macerals react with the slag as a result of the reduction, but a relationship between the relative chemical reactivities of macerals and structural changes upon heating was established.

Acknowledgements The PreMa project is funded by the European Union’s Horizon 2020 Research and Innovation Programme under Grant Agreement No. 820561 and by industry partners Transalloys, Eramet, Ferroglobe, OFZ, and Outotec. The paper is published with permission from Mintek.

References

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Coal based reducing agents in ferroalloys and silicon production. New Trends in Coal Conversion: Combustion, Gasification, Emissions and Coking. Woodhead Publishing. pp. 405–435. Teasdale, S.L. and Hayes, P.C. 2005. Kinetics of reduction of FeO from slag by graphite and coal chars. ISIJ International, vol. 45, no. 5. pp. 642–650. Tranell, G., Gaal, S., Lu, D., Tangstad, M., and Safarian, J. 2007. Reduction kinetics of manganese oxide from HC FeMn slags. Proceedings of INFACON XI. pp. 232–240. https://www.pyrometallurgy.co.za/InfaconXI/231-Tranell.pdf United Nations Economic Commission for Europe. 1998. International classification of in-seam coals. Geneva. u The Journal of the Southern African Institute of Mining and Metallurgy

Hyperspectral core scanner: An effective mineral mapping tool for apatite in the Upper Zone, northern limb, Bushveld Complex by H. Mandende1, C. Ndou1, and T. Mothupi1 Affiliation:

C ouncil for Geoscience, Pretoria, South Africa.

Correspondence to: H. Mandende

Email:

hakaymanday@gmail.com

Dates:

Received: 3 Nov. 2022 Accepted: 23 Jan. 2023 Published: February 2023

How to cite:

Mandende, H., Ndou, C., and Mothupi, T. 2023 Hyperspectral core scanner: An effective mineral mapping tool for apatite in the Upper Zone, northern limb, Bushveld Complex. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 2, pp. 81–92

DOI ID:

http://dx.doi.org/10.17159/24119717/1890/2023

Synopsis The technological advances in efficient, rapid, and non-destructive hyperspectral core logging systems for systematic mineral mapping have led to the discovery and exploitation of new mineral deposits Hyperspectral imaging in the long-wave infrared range has been recently used successfully to identify various phosphatebearing minerals (monazite, xenotime, and britholite), with limited work on apatite associated with mafic-ultramafic layered intrusions. In this study we investigate the effectiveness of a hyperspectral imaging (HSI) system with long-wave infrared (LWIR) bandwidthsto identify apatite in the Upper Zone of the Bushveld Complex. The accuracy of the HSI results was validated by mineralogical and geochemical data. The two apatite-enriched zones detected by HSI suggesting widespread development of apatite throughout the uppermost 600 m of the Upper Zone. The lower apatite-enriched zone is approximately 40 m thick, while the upper apatite-enriched zone is about 23 m thick, consistent with previous thickness determinations by traditional logging and analytical methods. Spectral mixing observed in the response of apatite is ascribed either to the common association of apatite and olivine in these rocks, or to differences between the spatial resolution of the hyperspectral image and the size of apatite grains. The VNIR-SWIR wavelength region did not show prominent spectral features of apatite. Nonetheless, HSI in the LWIR range is effective in mapping apatite and should therefore be considered as an exploration tool. This research advances our knowledge of the reflectance spectroscopy of REE-bearing minerals, which makes it easier to detect, identify, and quantify REE-bearing silicate minerals by HSI.

Keywords HSI, hyperspectral imaging system, long-wave infrared, apatite, Bushveld Complex.

Introduction The transition to cleaner energy technologies will see an increase in the demand for critical elements, including the tare earth elements (REEs), due to their importance in low-carbon technologies, particularly solar photovoltaic (PV), wind, and geothermal energy generation. This, combined with the uneven global distribution (China produces approximately 81% of global REE output) has led to a search for potential new sources of REEs. Apatite is in an important mineral in mafic-layered intrusions, often occurring as a cumulus phase in the uppermost highly fractionated Fe-Ti oxide-rich lithological units. Apatite can incorporate a wide spectrum of elements (e.g., F, Cl, S, REEs, Th, U, P, Sr, Pb, Mn, and Nd isotopes), which can be used to constrain magmatic processes, determine magma sources, and trace magma evolutionary paths in mafic layered intrusions. More than 0.35% REEs is typically present in magmatic apatite (Ihlen et al., 2014; Decrée et al., 2022), sometimes reaching substantial concentrations – up to ~19 wt% REE2O3 at Pajarito Mountain, New Mexico (Roeder et al., 1987; Hughes, Cameron, and Mariano, 1991). In the Upper Zone of the Bushveld Complex, apatite is an important cumulus mineral high in the sequence (at depths above about 600 m) within the uppermost olivine-bearing ferrodiorites (Ashwal, Webb, and Knoper, 2005) above the topmost magnetite layer 21. In this study, apatite is of particular interest because it is a potential source of REEs and phosphates, with up to 7 000 ppm REE content in apatite reported from the eastern limb of the Complex and an estimated resource potential of several billion tons of ore grading about 20 vol% combined ilmenite and apatite (von Gruenewaldt, 1993). Traditional methods for determining the mineralogical and ore characteristics of apatite, for example by logging drill core, are usually time-consuming, qualitative, subjective, and require the use of expensive complementary laboratory-based techniques such as chemical assays and detailed mineralogical analyses which include meticulous sample preparation requirements. Reflectance spectroscopy, a rapid non-destructive analytical technique with minimum sample preparation requirements, has been successfully used to study the reflectance of phosphate minerals in the visible to short-wave infrared regions (Turner, Rivard, and Groat2014, 2016; Turner, 2015; Laakso

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Hyperspectral core scanner: An effective mineral mapping tool for apatite in the Upper Zone et al., 2018, 2019). These investigations have mainly focused on monazite, xenotime, and britholite from alkaline, carbonatite , and sedimentary rocks, with fewer studies having applied hyperspectral technology to the detection of magmatic apatite in mafic-ultramafic layered intrusions. In addition, the detection of REE-bearing apatite in the long-wave infrared (LWIR; 8–12 μm) wavelength range is still poorly understood. Reflectance spectroscopy studies the interaction of electromagnetic radiation with matter by recording the reflected energy in different spectral regions, including visible near-infrared (VNIR) and short-wave infrared (SWIR) to long-wave infrared (LWIR) wavelengths (380–1 000 nm, 1 000–2 500 nm, 7 600–12 000 nm). HSI allows for data collection at higher spatial resolution (1–2 mm per pixel) for spectral sensors compared to 30 m per pixel achieved by multispectral sensors. In this study we present the results of apatite mineral mapping of the uppermost Upper Zone intersected by the Bellevue borehole, drilled in the northern limb of the Bushveld Complex, using hyperspectral scanning. A detailed mineralogical and textural characterization using optical microscopy and automated scanning electron microscopy (SEM) combined with whole-rock geochemistry data is included for the evaluation of the results from the newly tested HSI technique. Mineral detection and identification achieved by the analysis of the HSI data in different bandwidths and resolutions is evaluated.

Regional geology The Bushveld Complex (Figure 1), which incorporates the largest mafic-ultramafic layered intrusion in the Earth’s crust, the Rustenburg Layered Suite (RLS; Figure 1a), was intruded at 2057.7 ±1.6 Ma (Olsson et al., 2010; Mungall, Kamo, and McQuade, 2016) into the Kaapvaal Craton, subparallel to the sedimentary layering of the Transvaal Supergroup (Sharpe, 1982) as well as Archaean granite- gneiss basement rocks extending northwards from the farm Drenthe on the northern limb of the Complex (Cawthorn, Barton, and Viljoen, 1985; Zeh et al., 2015; Grobler et al., 2019). Based on variations in the cumulus mineral assemblage from the bottom upwards, the RLS is stratigraphically informally subdivided into five major units (South African Committee for Stratigraphy, 1980) — these are the Marginal, Lower, Critical, Main, and Upper zones. The Marginal Zone, forming the base of the layered sequence, consists of several hundred metres of medium- to fine-grained noritic lithologies. The overlying Lower Zone is dominated by interlayered ultramafic cumulates including orthopyroxenite, dunite, and harzburgites (cf. Cameron, 1978). The Critical Zone, also termed the Grasvally Norite–Pyroxenite–Anorthosite Member (Hulbert, 1983). is famous for its remarkable layering, varied rock sequence, and for chromitites that constitute the world’s largest known chromite deposit (Cameron, 1980), making it a vital part of the RLS. The Grasvally Norite–Pyroxenite–Anorthosite member is subdivided into a pyroxenitic lower Critical Zone dominated by a sequence of layers that include feldspathic pyroxenite, norite, chromitites, and chrome-bearing pyroxenite, and a noritic to anorthositic upper Critical Zone characterized by anorthosite at the base and interlayers of pyroxenite, gabbronorite capped by the upper group chromitites, Merensky Reef, Bastard Reef, and a mottled anorthosite. The Main Zone overlying the Critical Zone comprises a succession of relatively homogeneous gabbroic rocks interlayered with anorthosite.The Upper Zone constitutes a complex sequence of layered rocks, including layers of Ti-magnetite and anorthosite dominated by a monotonous and poorly layered ferrogabbro with 82

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variable amounts of magnetite (Scoon and Mitchell, 2012). The following sections deal only with aspects pertinent to the uppermost 600 m of the Upper Zone of the northern limb (Figure 1b).

Stratigraphy of the uppermost 600 m of the Upper Zone The Bellevue (BV-1) borehole, drilled on the farm Bellevue 808 LR to a depth 2949.50 m, on which this study is based, is unique as it intersects two major apatite-rich zones up to 40 m in thickness. Although apatite appears as a liquidus phase at approximately 1 100 m depth as reported by Ashwal, Webb, and Knoper (2005), of interest to this study is the apatite-enriched sequence above the uppermost massive magnetite layer (approx. 600 m) where apatite constitutes an important cumulus phase (Ashwal, Webb, and Knoper, 2005). The sequence of rocks immediately above the uppermost massive magnetite layer in the Bellevue drill core (Figure 1b) includes magnetite gabbro (Figure 1d), olivine-magnetitegabbro, plagioclase-olivine-gabbro (Figure 1c) and olivinemagnetite-diorite (ferrodiorite), grading to diorites towards the roof contact. Using visually estimated petrographic modes for 430 samples from the Bellevue drill core as plotted by Ashwal, Webb, and Knoper (2005), the apatite was intersected between depths of approximately 577.4 and 440 m within the olivine-magnetite gabbro and between 100 and 300 m associated with the uppermost fractionated fayalite- and/or hornblende-bearing ferrodiorites. In addition, several dolerite sills/dykes (up to 5 m thick) and granitoids (up to 9 m) intrude into the Bushveld cumulate rocks near the top of the sequence and sporadically throughout the Bellevue drill core.

Methodology Sampling Areas mapped as enriched in apatite by the hyperspectral core scanner were sampled for SEM and petrographic mineral analysis. A total of 40 samples were collected from the upper and lower apatiteenriched zones of the Bellevue drill core (BV-1). The location of BV-1 is shown in Figure 1a. The samples were cut into 5 cm pieces of quartered core and mounted in resin to prepare 30 cm polished stubs. The stubs were carbon coated and submitted for automated SEM analysis at the Council for Geoscience mineralogy laboratory.

Analytical techniques Optical microscopy and SEM Petrographic studies were carried out on the polished drill core samples using a standard petrographic microscope (Nikon Eclipse E600 POL). Microanalysis on the selected polished stubs was performed at the Council for Geoscience mineralogy laboratory on a ZEISS SIGMA 300VP FEG-SEM equipped with a backscatter electron (BSE) detector and a Bruker XFlash 30 mm2 EDX detector, with 129 eV energy resolution and based on the ZEISS Mineralogic automated quantitative mineralogy software platform. The acceleration voltage of the primary electron beam was set to 20 kV to ensure X-ray excitation for all relevant elements such as iron. A 120 µm aperture, providing an 80 µA beam current, was used to obtain a high input count rate for the EDX detector. The scanning parameters were a 20 μm step size and a working distance of 10 mm. The high-resolution BSE images were captured first, the EDS spectra were collected and identified by comparison with known phases in the database. The hyperspectral mineralogy was compared with mineralogical (SEM and petrographic) and wholerock geochemical data in order to validate the detected apatite using high-resolution HSI. The Journal of the Southern African Institute of Mining and Metallurgy

Hyperspectral core scanner: An effective mineral mapping tool for apatite in the Upper Zone

Figure 1— (a) Simplified map of the Bushveld Complex showing location of the BV-1 borehole. (b) Lithological log of the Bellevue borehole showing the uppermost differentiates (above 600 m), adapted from the data of Knoper and von Gruenewaldt (1996). Note: The colour key to the lithologies is not arranged chronologically. (cd) Plagioclase-olivine gabbro and layered plagioclase-magnetite gabbro

HSI The spectral data was acquired using the SisuRock hyperspectral scanner at the National Borehole Core Depository (NBCD) of the Council for Geoscience (Figure 2). The cameras in the system cover the VNIR, SWIR, and LWIR sections of the electromagnetic spectrum. An RGB (visible light) camera was fitted to the system to provide natural-colour images. Figure 2 shows the SisuRock system, with the cameras labelled in red. The system’s specifications are listed in Table I. ➤ Approximate pixel size - The data was processed on the mobile processing unit at the NBCD using TerraCore’s Intellicore® processing solution. The five levels of data processing provided by TerraCore are summarized below. Level 1 – Calibration stage: The spectralon-based white panel (100% reflectance) and an aluminium standard panel (used for correcting the LWIR) as well as the dark reference measurements were used to correct the hyperspectral and RGB data from radiance at sensor to reflectance, and a The Journal of the Southern African Institute of Mining and Metallurgy

Figure 2—CGS SisuRock system with the LWIR camera (OWL), the highresolution visible light camera (RGB), and the VNIR and SWIR camera (FENIX) with co-registered VNIR–SWIR spectrometers VOLUME 123

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Hyperspectral core scanner: An effective mineral mapping tool for apatite in the Upper Zone Table I

Specifications of the CGS’s SisuROCK system System parameter

Hyperspectral cameras

RGB camera

Wavelength range

380–2 500 nm (FENIX) 7 700–12 300 nm (OWL)

Not applicable

Infrared zone covered

VNIR/SWIR (FENIX) LWIR (OWL)

Visible

Spectral bandwidth

3.4/6/48 nm

Not applicable

Spectral resolution

3.5/12/100 nm

Not applicable

Spectral bands

88/276/98 bands

3 bands

Image dimensions

384 pixels across track

4 000 pixels across track

Pixel size (spatial resolution)

±1.4 mm @ 32.3° FOV*

±0.12 mm @ 640 mm FOV*

Camera serial number

351021 (FENIX) 920025 (OWL)

L403455K

Camera calibration

Spectral calibration, normalized

White balance

Scan rate

170 mm/s @ 1 mm pixel size

170 mm/s @ 0.10 mm pixel size

Maximum sample size

1 500 mm (length) x 640 mm (width) x 300 mm (height), 50 kg

Operating conditions

Enclosed facility (limited dust), 0 to +40°C, non-condensing

Operating voltage

220/ 240 V; 50/60 Hz

System dimensions

5.5 m x 1.5 m x 2.5 m (l x w x h)

Output file format

BIL file format, ENVI compatible

geometric correction was applied to remove the ‘smile’ inherent in push-broom cameras. All image dimension changes, such as reducing excess imagery around the target material, were undertaken at level 1. Level 2 – Masking stage: This level involved an automated routine which was run to develop a mask that retained only the core and removed the core tray and any other external materials such as wood blocks. Where needed, the mask was fine-tuned manually by the CGS’s processing team. This mask was then applied to the data-set. At this stage, a series of processes was also run to generate unmasked products, including a first-pass automated mineral map. These products can be generated within 24 hours of imaging, and so can be used to aid logging in active drill programmes. Level 2 processing also included registration using depth markers in the core boxes and QA/QC against expected depths from the imagery. Level 3 – Spectral processing stage: During the spectral processing stage, a variety of processing templates were applied. These included the generation of derived spectral parameters such as absorption depth ratios and the extraction of spectral parameters such as absorption depths, widths, and wavelengths in the VNIR–SWIR range and peak heights and wavelengths in the LWIR range. Mineral mapping was conducted via two processing algorithms. The first algorithm applied an automated spectral library matching technique (automated dominant mineral map) using Pearson correlation. This is a linear correlation method where perfectly identical spectra give a correlation coefficient value of 1 (i.e. similarity = 1), while a value of −1 indicates a complete mismatch (Samuel et al., 2021). The second method involved the use of an SOM, which is an 84

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unsupervised clustering technique that ‘utilizes competitive learning for training neurons to represent particular subsets of a data-set well’ (Wong. Abeysinghe, and Hung, 2019). Two types of SOM classification images were produced: (1) box classification images and (2) borehole classification images. The box SOM classification provides discrimination details at a box level and allows discrimination in a core tray, but does not allow correlation across core trays due to the scene dependency. Borehole classification images are generated using the borehole SOM to provide classification correlation across boxes in the drill-hole (Harris, 2020). Level 4 – Spectral interpretation stage: During the spectral interpretation stage, automated dominant mineral map and borehole SOM results were reclassified via a QC process using the Intellicore® software (v1.9.3.89) in order to manage any misclassification typically arising from mineral mixtures. Misclassifications include instances where one spectral profile displays absorption features of two or more minerals. The output spectra from the automated results were compared with those from the US Geological Survey’s VNIR–SWIR spectral library, the John Hopkins University LWIR spectral library, and the TerraCore LWIR spectral library. Mismatches with the library spectra were reclassified as a new mineral, or an assemblage of minerals in the case of mineral mixtures, with the dominant mineral followed by less dominant minerals, according to their spectral response. Mineral identification of the automated products and the SOM results was carried out by a spectral geologist to produce a dominant mineral map and assemblage SOM mineral map. Level 5 – Product generation stage: This level involved product generation from all prior phases, and was staged to ensure a steady flow for use by spectral and project geologists. These products are uploaded into the Intellicore® software. The Journal of the Southern African Institute of Mining and Metallurgy

Hyperspectral core scanner: An effective mineral mapping tool for apatite in the Upper Zone Results Different mineral assemblages present different responses to these spectral cameras, as illustrated in Table II. The LWIR wavelength region is useful in identifying and mapping anhydrous silicates (including quartz and feldspars) and anhydrous sulphates such as barite and anhydrate, while the VNIR–SWIR range is important in identifying and mapping hydrated silicate minerals, especially phyllosilicates and hydrated sulphates, such as gypsum. Unlike the VNIR-SWIR wavelength region, the LWIR range has good detection capabilities for identifying apatite, especially in samples where apatite is relatively abundant. According to Laakso et al. (2018) apatite grains are spectrally featureless in the SWIR wavelength region and thus are undetectable. The detection of apatite in the Bellevue drill core was based on a data mining approach that classifies the data using self-organizing maps (SOMs).

Detection of apatite using spectral data Figure 3 depicts a LWIR spectrum (spectral profile/signature) for apatite from the TerraCore spectral reference library. The signature is characterized by three main features: the peak at 8 980–9 030 nm,

the trough at 9 200–9 215 nm, and the peak at 9 338–9 578 nm. In both the upper and lower apatite zones, the LWIR spectrum appears to indicate a mixture of apatite and olivine, as illustrated in Figure 4. Spectral mixing is described by Kruse (1994) as a consequence of the mixing of materials having different spectral properties within the ground field-of-view (GFOV) of a single image pixel. The response shows a class -6 spectral profile which represents the apatite response overlain by an olivine spectral profile from a spectral reference library compiled by TerraCore. Figure 5 shows an RGB (true colour) image of box 42 with a box SOM pixel spectral profile of apatite detected at the depth interval of 304.8–305.12 m. The point/pixel spectral signature at this depth shows minimal spectral mixing. Barnes, Maier, and Ashwal (2004) noted an oxide-rich unit with a lower part consisting of massive magnetite and ilmenite and an upper part of nelsonite (an apatiterich rock) at a depth of 305 m. The apatite response from the point spectral signature in box 42 was validated by comparing it with the apatite spectral signature from the TerraCore LWIR spectral reference library. Figure 6 shows the results of the comparison.

Table II

S elected mineral groups and their ability to be identified in the VNIR, SWIR, and LWIR (source: TerraCore). Apatite, the focus mineral in this study, is highlighted VNIR response

SWIR response

LWIR response

Silicates Inosilicates Amphibole Actinolite Pyroxene Diopside Cyclosilicates Tourmaline Dravite Nesosilicates Garnet Andradite Olivine Forsterite Zircon Zircon Sorosilicates Epidote Clinozoisite Phyllosilicates Mica Muscovite Chlorite Clinochlore Clay minerals Kaolinite Illite Tectosilicates Feldspar Orthoclase Albite Silica Quartz Carbonates Calcite

Structure

Group

Non-diagnostic Good Non-diagnostic Moderate Good Good Non-diagnostic Non-diagnostic Non-diagnostic Non-diagnostic Non-diagnostic Non-diagnostic Non-diagnostic Non-diagnostic Non-diagnostic

Good Moderate Good Non-diagnostic Non-diagnostic Non-diagnostic Good Good Good Good Good Non-diagnostic Non-diagnostic Non-diagnostic Good

Good Good Moderate Good Good Non-diagnostic Good Moderate Moderate Moderate Moderate Good Good Good Good

Non- silicates Dolomite Non-diagnostic Hydroxides Gibbsite Sulphates Alunite Alunite Barite Borates Borax Halides Chlorides Halite Phosphates Apatite Apatite Amblygonite Hydrocarbons Bitumen Oxides Hematite Spinel Magnetite Sulphides Pyrite

Good Non-diagnostic Non-diagnostic Non-diagnostic Non-diagnostic Non-diagnostic Moderate Moderate Non-diagnostic Good Non-diagnostic Non-diagnostic

Good Good Good Non-diagnostic Good Moderate Moderate Good Good Non-diagnostic Non-diagnostic Non-diagnostic

Moderate Moderate Good Uncertain Uncertain Good Good Uncertain Non-diagnostic Non-diagnostic Non-diagnostic

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Example

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Hyperspectral core scanner: An effective mineral mapping tool for apatite in the Upper Zone 100 80 60 40 20 0

7800

8600

9400

10200

11000

11800

Apatite Figure 3—LWIR spectrum of apatite highlighting the three main spectral features (courtesy of the TerraCore spectral reference library)

Reflectance

7800

8600

wavelength

9400

10200

Class 6

Olivine

11000

11800

Figure 4—Class 6 (blue, representing apatite) LWIR response from the Bellevue borehole. The apatite appears in a mixed phase with olivine (red), as shown by the overlying red spectrum from the TerraCore LWIR spectral reference library

Figure 5—RGB image of box 42 with a pixel point spectral profile generated from the box self-organizing map results showing minimal spectral mixing 86

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Hyperspectral core scanner: An effective mineral mapping tool for apatite in the Upper Zone 100 80 60 40 20 0

7800

8600

9400

10200

Class 4 Apatite

11000

18800

Figure 6—The detected apatite point spectral profile (blue) from the drill core compared with the apatite signature from the TerraCore spectral reference library (red)

Using class 66 of the 100 class borehole SOM results (mixed spectra of apatite and olivine) from the LWIR (OWL) bandwidths, two apatite-enriched zones were mapped (Figure 7). These are

the lower and upper apatite-enriched zones. In the upper apatiteenriched zone, apatite is encountered from 236–259 m. The apatite zone itself is <23 m thick, as the borehole intersected several nonresponsive intervals associated with metasedimentary xenoliths (236.3–236.6 m), pegmatitic patches (239 and 240 m), olivine-free rocks (241.64–241.82 m, 244.15–244.65 m, 244.95–244.50 m), and pegmatite (253.3–256.7 m). Thus, the apatite zone between 248.9 and 259 m is considered a zone of apatite enrichment with minor non-responsive intervals. The lower apatite zone, close to 50 m thick, occurs immediately above the topmost magnetite layer. A non- responsive zone within this zone, between 547 and 558 m (approx. 10 m) was observed, bringing the thickness of the lower apatite zone to about 40 m. The non-responsive interval is characterized by a fine-grained gabbroic rock (548–549 m) and an olivine-magnetite gabbro (549–558 m) as mapped by Knoper and von Gruenewaldt (1996). Interestingly, this apatite-poor zone coincides with the presence of conspicuous olivine at the depth interval of the latter zone (Figure 7). In contrast, the presence of apatite in some intervals coincides with the presence of olivine, as is the case, for instance, at 531–537 m (Figure 7).

Figure 7—Representative apatite mineral map detected using LWIR (OWL) The Journal of the Southern African Institute of Mining and Metallurgy

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Hyperspectral core scanner: An effective mineral mapping tool for apatite in the Upper Zone Discussion

Mineralogical data The mineralogical analysis results show that Fe-Ti oxides (magnetite and ilmenite), feldspar, apatite, olivine, and pyroxene are the most abundant phases in the lower apatite zone (Figure 8). In this zone apatite is mostly concentrated along grain boundaries of olivine, while also occurring as inclusions in Fe-Ti oxides (Figures 9a-b and 11). The common occurrence of apatite along grain boundaries of olivine (Figure 9d) in this zone may explain the mixed apatiteolivine spectral response as illustrated in Figures 4 and 6. The mineralogical analysis results of the upper apatite zone indicate the increased presence of hydrous silicate minerals (hornblende, chlorite, and biotite) with minor quartz and sulphides in addition to Fe-Ti oxides (magnetite and ilmenite), feldspar, apatite, olivine, and pyroxene. Similarly, an apatite-olivine association is commonly observed (Figure 9f) in addition to the frequent occurrence of apatite as inclusions in Fe-Ti oxides (Figures 9g and 9h), and rarely in hydrous silicates (Figure 9c). Sulphides are also observed, occurring mainly as small (>50 μm) rounded inclusions that are usually present as separate grains in ilmenite, magnetite, and silicate minerals, occasionally associated with apatite (Figures 9b, 9g, 9h). The general distribution of apatite shown in the LWIR mineral map (Figure 7) coincides with mineralogical observations of the samples, and its spatial distribution as detected by HIS was thus validated (Figures 8, 9, and 11). Generally, the apatite-rich rocks contain up to 17 vol% apatite (Figure 8).

The presence of apatite in the uppermost Upper Zone of the Bushveld Complex has been observed and described in several

Geochemical data Whole-rock phosphorus (P2O5 wt.%) was also used as a proxy to validate the apatite detected using high-resolution HSI. The P2O5 content was plotted as a function of drill-hole depth. There is a significant correspondence between the apatite mineral phase in the lower apatite zone detected using the hyperspectral scanner and the whole-rock geochemistry (Figure 11). The P2O5 content in the non-responsive interval from 548–558 m ranges between 2.2 to 2.9 wt.% P2O5, which suggests the presence of apatite (Figure 7). While it is unclear why there is no apatite response in this interval, it is possible that this is related to the grade of P2O5. Alternatively, differences in the measured surface area can also create situations in which apatite grains occur within the area measured with XRF, but not within the area measured with HSI. The highest grades of P2O5 (2.61–5.04%) were found towards the base of the lower apatite zone in the interval between 560 and 572 m, which is consistent with the high apatite response detected by HSI (Figure 11).

Figure 9—Photomicrographs of the upper (A-D) and lower (E-H) apatite zones showing the grain size distribution, texture, and mineral associations of apatite in the uppermost Upper Zone. Olv = olivine, Bi = biotite, Plag = plagioclase, Ap = apatite, Fe-Ti oxide = magnetite and or ilmenite. A = BV001 (236 m below the roof contact); B-C = BV016 (251 m below roof contact); D = BV018 (253 m below roof contact); E-F = BV028 (560 m below roof contact); G = BV035 (567 m below roof contact); H = BV039 (571 m below roof contact)

Figure 8—Summary of the modal mineralogy (wt.%). Note: BV02 – BV24 represents upper apatite zone; BV26 – BV40 represents lower apatite zone 88

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50 100 150 200 250 300 Ap-Oliv

350

100%

1.38

2.77

4.15

5.54

Figure 10—Correlation between apatite detected from HSI and whole-rock P2O5 data for the lower apatite zone

Figure 11—Hyperspectral responses of apatite in the LWIR (OWL) of the SisuROCK-2 data-set corresponding to representative mineralogical and geochemical dataset. Note: BV06 and BV040 were sampled at depths 241 m and 572 m, respectively The Journal of the Southern African Institute of Mining and Metallurgy

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Hyperspectral core scanner: An effective mineral mapping tool for apatite in the Upper Zone studies (e.g., Nienaber-Roberts, 1986; Von Gruenewaldt, 1993; Ashwal, Webb, and Knoper, 2005). Apatite was generally determined in these studies by sampling of drill core, followed by mineralogical and geochemical investigations. This. however, is time-consuming and does not provide a detailed spatial distribution of minerals of interest as only small areas are covered. To accurately identify apatite in the uppermost Upper Zone, we imaged the BV-1 drill core in the LWIR region and used mineralogical and geochemical analysis as validation. This methodology is not intended to replace traditional laboratory techniques (optical microscopy, XRF) but rather to reduce reliance on them. In this study, HSI has demonstrated its efficacy in identifying the presence and the spatial distribution of apatite in the uppermost differentiates of the Upper Zone. From this, two apatite enriched layers have been identified, from 236to –259 m and from 527 to 576 m. The context of our findings calls for a discussion of three key observations: (1) spectral mixing of apatite and olivine in the apatite-enriched layers; (2) the near-pure pixel point spectral signature of apatite; and (3) the detection of REEs hosted in apatite using HSI. Firstly, one of the challenges with mapping apatite in mafic layered intrusions such as the Bushveld Complex is that it is commonly associated with silicates (plagioclase, pyroxene. and olivine; Figures 9d-f), hydrous silicates (Figure 9c), Fe-Ti- oxides (Figures 9a-b; g-h), and sulphides (Figures 9b and 9h). These mineral associations can cause spectral mixing. According to Laakso et al. (2018) spectral mixing can cause the appearance and disappearance of spectral features, particularly where the contents of the pixels are shared by two or more minerals. Another possibility for spectral mixing is related to the spatial resolution of the hyperspectral imagery in relation to the grain sizes of individual minerals. In this regard, if the pixel size of an image is larger than the size of single mineral grains, then spectral mixing can occur (Keshava and Mustard, 2002). Figure 4 shows the spectral response of apatite which appears to be in a mixed phase with olivine. The common association of olivine with apatite is interpreted as the reason for the spectral mixture, whereby the spectral response of fluorapatite is overlapped by that of the much larger olivine crystals. As the spatial resolution (1.4 mm) of our hyperspectral image is lower than the average size (Dx(50)) of even the smallest apatite grain in the rock samples analysed by SEM (270–605 µm; Table III), significant spectral mixing is likely to occur. Despite challenges such as spectral mixing, we are confident that the apatite is correctly mapped by HSI as recorded by the positive correlation seen between

Table III

Apatite size distribution Sample Dx(20)

BV-004 BV-006 BV-011 BV-022 BV-028 BV-031 BV-032 BV-033 BV-034 BV-035 BV-040

146 188 207 350 254 220 213 142 149 225 190

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Grain size (μm) Dx(50) Dx(80)

270 351 405 605 484 440 463 283 277 446 406

Dx(95)

498 580 778 824 839 828 825 521 503 818 790 VOLUME 123

805 924 1252 1139 1236 1238 1228 832 833 1224 1213

the abundance of apatite mapped and the mineralogical and wholerock P2O5 results. Secondly, the pixel point spectral signature of apatite detected at the depth interval of 304.8–305.12 m shows minor spectral mixing comparable to the apatite pixel spectral profile in the TerraCore LWIR spectral reference library. The rock has been defined by Barnes, Maier, and Ashwal (2004) as an oxide-rich unit with a lower part consisting of massive magnetite and ilmenite and an upper part of nelsonite (an apatite-rich rock). The nelsonite was reported to consist of 60% oxides (predominantly granular ilmenite with some magnetite) and 30% apatite (Barnes, Maier, and Ashwal, 2004). The lack of spectral mixing at this level is difficult to explain but is probably due to the high modal percentage of apatite (approx. 30%) with no silicate mineral association. In addition, apatite in this rock is associated with Fe-Ti oxides, which are non-diagnostic in the LWIR spectral range as indicated in Table II. From this, it seems reasonable to assume that the spectral response of apatite is influenced by mineralogy, in particular mineral associations. Lastly, the VNIR range of the infrared is effective in detecting REE phosphate minerals, including fluorapatite where the absorption features in this range are due to Nd as shown by Turner, Rivard, and Groat (2016). However, in our study the VNIR-SWIR range had limited detection capabilities in mafic-ultramafic rocks dominated by silica, some silicates (nesosilicates such as olivine), and oxides, as these minerals did not show prominent spectral features. Image C in Figure 12 compares the fluorapatite spectral profile (yellow) from the USGS library with the apatite-rich region of interest (ROI) spectral profile (red). The results show the absence of fluorapatite-diagnostic prominent VNIR features related to the LREE (Nd) on the ROI spectral profile (circled in black) and the inconspicuous spectral features in the SWIR range. The apatite LWIR spectral profile in this study can be attributed to the PO4 fundamental vibrations (Christensen et al., 2000). As concluded by Laakso et al (2019), the LWIR range did not show any distinctive spectral features that can be attributed to REEs. Therefore, the detection of REE spectral features was not achieved in this study. Although the automated hyperspectral logging system is fast, reliable, and effective, it does not yield quantitative mineralogical information from the mineral maps and images obtained using the SisuRock system, as the data is limited to the pixel-size resolution and the classification of the pixel arises from the main spectral feature. This is because HSI data processing tools only focus on the spatially distributed mineralogy and mineralogical composition and not the texture, grade, or geometry of the minerals in the drill core. In addition, it is important to mention that HSI is a surface technique and the mineral abundance is based on pixel response. For this reason, absolute mineral abundance cannot be quantified as the pixel size is determined by the camera spatial resolution. In this regard, HIS should be used in conjunction with laboratory analytical methods like SEM, optical microscopy, and XRF. Nonetheless, owing to its non-destructive nature, minimal sample preparation requirements, and rapid acquisition time, HIS provides a suitable solution for mineral mapping for bulk samples or diamond drill core. Although substantial amounts of drill core still need to be sent for in-depth mineralogical and geochemical analyses like SEM, petrography, and whole-rock XRF to determine the mineralogy quantitatively, the cost of chemical assaying is decreased. Instead of sampling the entire core to identify apatiteenriched zones, the SiSuRock hyperspectral scanner can be used to identify target areas for analysis. The Journal of the Southern African Institute of Mining and Metallurgy

Hyperspectral core scanner: An effective mineral mapping tool for apatite in the Upper Zone

Figure 12—RGB image for box 77 (at depth 561-568 m) of the lower apatite zone (A), ROI highlighted in red with the corresponding LWIR spectral profile depicting the spectral mixing of apatite and olivine signatures and the VNIR-SWIR low response spectral profile showing inconspicuous spectral features that cannot be resolved (B), VNIR-SWIR comparison of the ROI spectral profile (red) with the USGS library spectra of fluorapatite (yellow) with prominent VNIR features highlighted (C)

Conclusion and recommendations

Acknowledgments

Hyperspectral imaging (HSI) is shown to be an effective and reliable method to characterize apatite-rich units in the Upper Zone of the Bushveld Complex using the LWIR spectral region, and which can therefore also be used to map apatite in other mafic-ultramafic layered intrusions. HSI of borehole core from the upper 600 m of the Upper Zone delineated two apatite-enriched zones: the lower (531–575 m) and upper (236–259 m) zones. A pure apatite spectral signature was not obtained owing to spectral mixing as a result of the common association between apatite and silicates. Detection of sulphides and oxides is not yet possible by HSI as highlighted in Table II. Oxides are important in the context of apatite as many apatite-rich units succeed Fe-Ti oxide-rich layers. A technique that could identify the fine-grained sulphide and oxide minerals would improve the detection of apatite-enriched zones. This is because a close association between apatite and Fe-Ti oxides is a distinctive feature of apatite mineralization in the upper parts of the Upper Zone. The second part of the work involved the mineralogical and geochemical characterization of the apatite-rich zones detected through HSI. The results show a good correlation with the HSI results. Apatite occurs in common association with oxides, sulphides, hydrous minerals. and silicates, confirming the predominant spectral mixture associated with the apatite-enriched zones. This study demonstrates that the LWIR range shows good apatite detection in mafic- ultramafic rocks, and the association of apatite with silicate minerals, while the SWIR and VNIR ranges did not show prominent spectral features.

The authors wish to thank the Council for Geoscience for permission to publish this paper. Our appreciation goes to Professor Rais Latypov for undertaking a preliminary review of the work, and to Zahn Nel for the language editorial work on the manuscript. We thank Bushveld Minerals Pty Ltd for providing the whole-rock geochemistry data of the apatite enriched zone. Mr Senza Ndumo is thanked for assisting with the logging and sampling of the core.

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Hyperspectral core scanner: An effective mineral mapping tool for apatite in the Upper Zone Decrée, S., Coint, N., Debaille, V., Hagen-Peter, G., Leduc, T., and Schiellerup, H. 2022. The potential for REEs in igneous-related apatite deposits in Europe. Special Publications, vol. 526. The Geological Society, London. Grobler, D.F., Brits, J.A.N., Maier, W.D., and Crossingham, A. 2019. Litho- and chemostratigraphy of the Flatreef PGE deposit, northern Bushveld Complex. Mineralium Deposita, vol. 54, no. 1. pp. 3–28. Harris, P. 2020. Spectral geology manual: CGS spectral geology workshop notes. TerraCore, Johannesburg, South Africa. Hughes, J.M., Cameron, M., and Mariano, A.N. 1991. Rare-earth-element ordering and structural variations in natural rare-earth-bearing apatites. American Mineralogist, vol. 76, no. 7–8. pp. 1165–1173. Hulbert, L.J. 1983. A petrographical investigation of the Rustenburg Layered Suite and associated mineralisation south of Potgietersrus. DSc dissertation, University of Pretoria, South Africa.

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Zeh, A., Ovtcharova, M., Wilson, A.H., and Schaltegger, U. 2015. The Bushveld Complex was emplaced and cooled in less than one million years – Results of zirconology and geotectonic implications. Earth and Planetary Science Letters, vol. 418. pp. 103–114. u

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Material characteristics of Ti-6AL-4V samples additively manufactured using laser-based direct energy deposition by M.G. Willemse1, C.W. Siyasiya1, D. Marais3, A.M. Venter3, and N.K.K. Arthur1,2 Affiliation:

epartment of Materials Science D and Metallurgical Engineering, University of Pretoria, Pretoria, South Africa. 2 CSIR, NLC, Laser Enabled Manufacturing Group, Pretoria Campus, 0001, South Africa. 3 Research and Technology Development Division, The South African Nuclear Energy Corporation (Necsa) SOC Limited, South Africa. 1

Correspondence to: M.G. Willemse

Email:

mattianw@gmail.com

Dates:

Received: 8 Feb. 2021 Revised: 15 Jun. 2021 Accepted: 3 Jul. 2021 Published: February 2023

Synopsis Although additive manufacturing is fast gaining traction in the industrial world as a reputable manufacturing technique to complement traditional mechanical machining, it still has problems such as porosity and residual stresses in components that give rise to cracking, distortion, and delamination, which are important issues to resolve in structural load-bearing applications. This research project focused on the characterization of the evolution of residual stresses in Ti-6Al-4V extra-low interstitial (ELI) additive-manufactured test samples. Four square thin-walled tubular samples were deposited on the same baseplate, using the direct energy deposition laser printing process, to different build heights. The residual stresses were analysed in the as-printed condition by the neutron diffraction technique and correlated to qualitative predictions obtained using the ANSYS software suite. Good qualitative agreement between the stress measurements and predictions were observed. Both approaches revealed the existence of large tensile stresses along the laser track direction at the sections that were built last, i.e., centre of the top layers of the samples. This in addition leads to large tensile stresses at the outer edges (corners) which would have the effect of separating the samples from the baseplate should the stresses exceed the yield strength of the material. Such extreme conditions did not occur in this study, but the stresses did lead to significant distortion of the baseplate. In general, the microstructures and spatial elemental mapping revealed a strong correlation between the macro-segregation of elemental V and the distribution of the β-phase in the printed parts.

Keywords residual stresses, additive manufacturing, Ti-6Al-4V, neutron diffraction, ANSYS Additive Suite, direct energy deposition.

How to cite:

Willemse, M.G., Siyasiya, C.W., Marais, D., Venter, A.M., and Arthur, N.K.K. 2023 Material characteristics of Ti-6AL-4V samples additively manufactured using laser-based direct energy deposition. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 2, pp. 93–102

DOI ID:

http://dx.doi.org/10.17159/24119717/1508/2023

ORCID:

M.G. Willemse http://orcid.org/0000-00031137-2267 C.W. Siyasiya http://orcid.org/0000-00021426-3149 N.K.K. Arthur http://orcid.org/0000-00018400-329X D. Marais http://orcid.org/0000-00018952-6217 A.M. Venter http://orcid.org/0000-00033677-4713

Introduction Since the development of additive manufacturing (AM) in the late 1970s, rapid prototyping has been increasingly pursued as an alternative to traditional manufacturing due to its ability to produce complex geometrical shapes with lower material losses. AM processes may lead to adverse effects such as porosity, cracking, distortion, and delamination in the solid components produced. Residual stress buildup is a major contributor to, and consequence of, these adverse effects because of the severe and rapidly varying thermal cycles the part is subjected to during the deposition and subsequent reheating stages. If not immediately alleviated, this can cause premature failure in use. During the AM process, the occurrence of delamination and distortion not only leads to untimely production delays but requires costly intervention to alter and optimize the deposition parameters. It is thus important to be able to predict such occurrences with modelling, although modelling predictions need to be adequately validated to ensure applicability and reliability. In this project we investigated the effect of part geometry on residual stresses associated with direct energy deposition (DED)-manufactured Ti-6Al-4V components, as well as studying microstructure, composition, and hardness. The main objective was to determine the effects the material build height and subsequently the number of deposited layers had on these physical characteristics of the components. The validity of the residual stress simulations with commercial software was determined by comparing qualitative predicated results against measured values obtained by means of the neutron diffraction technique.

Literature survey Residual stresses Residual stresses are balancing static forces (per unit volume) that exist within a solid material due to inhomogeneous regions of mechanical deformation, thermal treatment, or volume expansion in the absence

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Material characteristics of Ti-6AL-4V samples additively manufactured of external forces (such as gravity, applied mechanical forces or forces associated with thermal gradients). For an object at rest, these internal forces are in equilibrium, i.e., the tensile (positive) and compressive (negative) internal strain fields balance to zero. The resultant residual stresses are elastic and can be as large as the yield strength of the material (Masubuchi, 2013). When the strain fields exceed the material yield, the material deforms plastically to alleviate this, which leads to balancing elastic residual stresses. Complicated thermal cycles are associated with the Laser Engineered Net Shaping (LENS™) additive manufacture process, which comprises heating of powders, their cooling and solidification, as well as reheating with the addition of subsequent build layers. As the material cools and solidifies inhomogeneously, localized shrinkage occurs between the melt pool and the surrounding cooler solidified material, which leads to residual stresses. These stresses may be as large as the yield strength of the material. Generally, during this inhomogeneous melting and cooling, the material deposited last leads to the development of tensile (positive) residual stress as contraction of the material is inhibited by the previously deposited solidified material. Dependent on the magnitudes of the thermal gradients and material melting temperature, Yang, Yang, and Wang (2016) showed that the thermal gradients create forces that are highly directional, leading to anisotropic stresses which correlate with the temperature gradient in the part being produced. Therefore, printing parameters need to be optimized to minimize temperature gradients during the printing process (Ngoveni, Arthur, and Pityana, 2019).

Fatigue behaviour Residual stresses can impact the fatigue life of a part by retarding or accelerating the onset of fatigue. This becomes especially prevalent in the near-surface regions where tensile stresses adversely affect fatigue lifetime through crack initiation and propagation. When a part is in service, the total force acting on it is a combination of the external forces and forces associated with the existing internal residual stress field. Therefore, when a part that has a compressive residual stress in the near-surface region experiences an external tensile load in the same region, the total load will be the vector sum of these forces and thus is effectively reduced. If both force fields, either positive (tensile) or negative (compressive), are aligned, this will increase the total load on the part and rapidly decrease its fatigue life (Masubuchi, 2013).

Direct energy deposition additive manufacturing technique Direct energy deposition (DED) is a laser-based (AM) process which enables the rapid production of metal prototypes from computer-aided design (CAD) files. The LENSTM DED manufacturing process, developed by Optomec, was used in this project. Three-dimensional CAD files are input into the DED system software, which ‘slices’ the object model into thin twodimensional layers. The software controls the laser that creates a heat spot at the build position, as well as the metal powder injection to form the deposition as individual layers of molten material on the baseplate (substrate that supports the build), or over an existing build top layer (substrate) to geometrically correspond to the CAD model slice. The three-dimensional object is incrementally created by sequential stacking of molten layers. The main hardware components in this process include the high-power laser (which provides the heat source) and the material powder which is deposited directly into the heat spot to form the melt pool that solidifies to produce the new layer. The thickness of these layers is 94

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normally in the order of hundreds of micrometres and is defined by the user taking into account the deposition rate and laser focus requirements.

Ti-6Al-4V Ti-6Al-4V ELI (‘extra-low interstitial’, which refers to the low oxygen and iron content to improve the ductility and fracture toughness) (Roy et al., 2018) is a high-purity commercial grade titanium alloy used for medical applications such as orthopaedic pins and screws, surgical staples, etc. It has a superior strength-toweight ratio and is corrosion resistant, which makes it suitable for high-pressure cryogenic vessels and aerospace components (Arthur and Pityana, 2018). Titanium alloys are heat treatable and consist of two main phases: α- phase at ambient temperature and pressure, which has a hexagonal close-packed (hcp) crystal structure; Above 890 °C, an allotropic transformation occurs to the β-phase which has a body centred cubic (bcc) crystal structure (Callister and Rethwisch, 2015). The β-phase is stabilised by elements such as molybdenum, niobium, chromium, iron and vanadium and is known to have a softer crystal structure than that of the α-phase, which is attributed to the presence of a higher amount of slip planes (Liu and Shin, 2019). This suggests that an increased volume fraction of β-phase in the alloy leads to an increase in its ductility (Liu and Shin, 2019). The α-phase, on the other hand, is stabilised by elements such as aluminium, tin, carbon, oxygen, and nitrogen. The phase proportions are dependent on the thermal processing. In addition, by adding alloying elements, the phase proportions can be altered to give rise to specific phases (Peters et al., 2001), which in turn determines the mechanical properties of the material (Yumak and Aslantas, 2020).

Experimental procedure Simulations Qualitative residual stress simulations associated with the DED process were performed with the ANSYS Additive Manufacturing Simulation Suite (ANSYS 2019 R3). This software is an engineering simulation and 3D design package that enables visualization of the effect of real-world physical phenomena on a given part or body prior to manufacture. This can assist in optimizing the manufacturing process by detecting and mitigating adverse consequences in the design constraints before the part is produced. The software can simulate effects applicable to fluids, materials optics, materials, structures, and complete systems. For additive manufacture, it enables optimization of build planning related to the topology of the additively manufactured part and automatically inserts support structures where needed. In addition, it enables predictive validation of the microstructure, part distortion, residual stress formation, and porosity formation as a function of a given printing parameter. Spatial resolution is defined by the mesh sizes in the simulations.

Additive manufactured samples The AM work was performed at the National Laser Centre (NLC), Council for Scientific and Industrial Research (CSIR), Pretoria using an Optomec LENS™ 850-R system fitted with a 1 kW IPG fibre laser (Kumar and Pityana, 2011). Four samples were sequentially built on the same baseplate as shown in Figure 1. Two sets of square tube samples with edges 25 mm long and the tested wall thickness of 6.5 mm were made to different build heights: 10 mm and 25 mm. In The Journal of the Southern African Institute of Mining and Metallurgy

Material characteristics of Ti-6AL-4V samples additively manufactured using laser-based direct Lattice strain values were calculated by referencing respective d-spacings at each measurement position to a stress-free (d0) value determined from Equation [1]. [1]

Figure 1—Photographs of the DED additively manufactured Ti-6Al-4V samples on the Ti-6Al-4V baseplate: (a) side view; (b) top view

addition, each set comprised geometries with sharp corners, as well as with 2 mm filleted outside corners. Depositions were performed as 650 μm wide (x and y directions) and 300 μm high (z direction) layers. The sample wall thicknesses (y-direction) were therefore achieved with 10 side-by–side depositions. All samples were printed on a sandblasted and cleaned Ti-6Al4V substrate plate with dimensions of 150 × 150 × 10 mm3. The laser power was 360 W, and the laser translated at a speed of 10.58 mm/s. The powder feed rate used was 2.51 g/min. All printing parameters used were from Arthur et al. (2016). All subsequent investigations were performed on the as-built samples retained to the baseplate.

Neutron diffraction Residual stress investigations were performed with the neutron diffraction technique using the MPISI instrument at the SAFARI-1 research reactor operated by the South African Nuclear Energy Corporation (Necsa) SOC Limited (Venter et al., 2018). The technique uses the penetrating and diffraction capabilities of thermal neutrons to perform nondestructive investigations of the as-built samples without surface preparation. The instrument was configured to diffract a 1.647 Å wavelength neutron beam from its Si(331) monochromator at a take-off angle of 83.5° through the chamber exit port. All investigations were performed with a neutron gauge volume of 3 × 3 × 5 mm3. The diffracted intensities from the neutron gauge volume at the different measurement positions and sample orientations were measured with a 2D position-sensitive detector set at a centre angle of 76.10° that enabled detection of the Ti(103) α-phase reflection. The interplanar (d) spacing was calculated from the peak centre angle fits, using the Bragg equation.

Stress values were calculated from the strain values by incorporating the relevant diffraction elastic constants for the reflection. Values used were S1 = -2.542 × 10-6 MPa-1 and ½S2 = 10.819 × 10-6 MPa-1 Results are reported as the spatial distributions of the residual stress along the sample lengths and heights in each of the three orthogonal directions of the walls of the printed components. This allows direct comparison to the predictions of the ANSYS simulations. Figure 2 illustrates the sample sections that were investigated with neutron diffraction together with the corresponding measurement grids. Due to the weak diffracted intensities from the material (titanium has a negative scattering length; net intensity is thus from the aluminium content in the material) (Hu et al., 2020), a relatively large neutron gauge volume (3 × 3 × 5 mm3) had to be employed to ensure data acquisition in a reasonable time of 1 hour per measurement position. The instrumental gauge volume was determined by scanning a 2 mm Fe pin across the beam and was confirmed to be within 10%-gauge of the nominal volume definition criterion. Taking cognisance of the sample geometries and thus symmetries, one wall per sample was investigated to further reduce the overall measurement time. All measurements were taken with fully submerged gauge volumes and centralized on the wall thicknesses (y-directions). Stress values were thus averaged over the gauge volume used in analyses and had an experimental uncertainty of ±50 MPa, determined by the fit accuracies of the diffraction peaks. A naming convention was adopted to identify the measurement areas of the samples. The first letter of the name identifies the corner shape, the number represents the sample height, while the last letter represents the cardinal direction (as indicated in Figures 2 and 3). Thus, the samples labelled S10W and F10E represent the sharp cornered samples of 10 mm height, measured along the west direction and the fillet cornered samples of 10 mm height, measured along the east direction, respectively.

Figure 2—(a) Annotated photograph of the AM samples and (b) coordinates where neutron diffraction measurements were taken. Colour coding correlates the measurement regions on the samples (dependent on sample height). Note the measurement reference positions as well as the strain orientations. Measurements were taken along the three orthogonal directions (refer to Figure 3): Longitudinal component = x-direction; normal component = y-direction; transverse component = z-direction The Journal of the Southern African Institute of Mining and Metallurgy

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Material characteristics of Ti-6AL-4V samples additively manufactured

Figure 4—Measurement grid used for taking the hardness measurements

Figure 3—Annotated photograph showing the conventions used to identify each of the measured stress components for the samples

Hardness One surface of each sample was polished using standard metallographic techniques with colloidal silica to provide surfaces that were flat and smooth to within 3 μm. Vickers microhardness tests were performed on these polished surfaces of the sample outside walls to determine the influence of the build height (and thus sequential reheating) on the sample hardness. Measurement positions were along the left (L), right (R), and centre line (C) sections of each sample and separated along the build height into four equidistant regions (Figure 4). Each region was measured three times along the intersecting lines of the grid with average values visualized as spatial maps. All hardness tests were conducted using a load of 500 g.

Scanning electron microscopy (SEM) The outer polished sample surfaces were recorded with highmagnification SEM images and the material composition was determined with energy dispersive X-ray spectroscopy (EDS) analyses at regions that corresponded with the hardness measurements. Investigations were performed with a Jeol JSM IT300 instrument with an Oxford X-max 50 EDS detector. All SEM-EDS data was processed using the Oxford AZtec software. Measurement positions corresponded with the hardness maps. Only one sample of each build height could be investigated due to time constraints.

Results Neutron diffraction Figure 5 and Figure 6 show the results from the neutron diffraction experiments, whereby the residual stress results are given in Figure 5 and Figure 6 displays the results as spatial colour maps. The figures show contour plots of the measured longitudinal and transverse residual stress components on the outer wall faces indicated in Figure 2(a). The following observations were made: ➤ A maximum compressive stress of ~320 MPa and maximum tensile stress of ~240 MPa was observed. ➤ In all samples the stress variations along the x-direction (along the wall lengths) were qualitatively the same, having symmetrical trends about the wall mid-lengths and build heights. - Th ere was no difference in the stress magnitudes in the sample with respect to build height. This may be a result of all four samples being printed on the same baseplate and that the high energy input of the multiple prints 96

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induced a type of heat treatment and allowed the stresses to relax. - I n the case of the longitudinal stress components (x-direction), the stresses were close to zero at the corners and tensile at the wall mid-lengths. The maximum tensile stresses were located in the top 5 mm of the sample heights. In the 25 mm high samples, the stresses were predominantly compressive from the baseplate to a height of approximately 18 mm. - Th e transverse stresses were more complex, being tensile at the corners and generally compressive at the wall midlengths. - A long the z-direction (build direction), the stresses for the longitudinal component became more tensile with height, while the transverse stress values decreased (became less compressive) with height, as expected (Masubuchi, 2013). ➤ These two stress components thus had opposing trends with height above the baseplate. - The transverse stress components (z-direction) showed the development of significant tensile stresses at the corners. These stresses were approximately 200 MPa until about 50% of the wall height, thereafter the values decreased with increasing height. - Th e transverse components had significant compressive stresses at the mid-wall lengths that were largest closest to the baseplate and decreased with build height. ➤ Thus, significant tensile stresses existed along the longitudinal direction (x-direction) in the central sections of the top layers. This led to the development of tensile stresses along the transverse directions in the corners where the samples were attached to the baseplate. This would lead to delamination of the built structure from the baseplate if the yield stress of the material were exceeded. This maximum in the tensile transverse stress extended to most of the sample height. The baseplate was significantly bent towards the build planes. This indicated that the baseplate was being deformed plastically by the stresses associated with the additive manufactured parts. ➤ No significant differences were observed in the stress values and trends for the two corner shapes, sharp (S25E and S10W) and filleted (F25W and F10E). Since the closest measurement positions to the corners in the neutron investigations were 3 mm, it can be concluded that the influence of the corner shape did not extend further than 3 mm from the corners. Figure 6 indicates similar stress results along the walls of the samples with sharp (S25E and S10W) and filleted (F25W and F10E) corners, i.e., the corner geometries had no long-range effect on the residual stresses in the walls. Measurements at each position were done with the gauge volume centred on the wall thicknesses, and for the longitudinal and transverse orientations to correspond with Figure 3. The Journal of the Southern African Institute of Mining and Metallurgy

Material characteristics of Ti-6AL-4V samples additively manufactured using laser-based direct

Figure 5—Graphs of residual stress results

Simulations To ensure correlation between the simulated and measured stress results, a mesh size of 6.5 × 6.5 × 6.5 mm3 was set in the ANSYS Additive Suite simulations. The baseplate was assumed to be a rigid structure, i.e., without any deflection. The model was also set up for the case where each sample was built individually at the centre of its own baseplate. Stress values are given in the figures to provide a correlation between samples with different build heights. Taking account of the assumptions, only the qualitative trends are valid for the comparison with the stresses measured with neutron diffraction. For this mesh size, the simulations of the sharp corner and filleted corners did not lead to any stress differences. Figure 7 and Figure 8 respectively shows the spatial stress maps for the transverse component generated in the ANSYS simulations for the 10 mm and 25 mm samples. However, the influence of the corner geometries could not be resolved when using a 6.5 × 6.5 × 6.5 mm3 grid size. Furthermore, it was observed in the simulations that the 10 mm samples showed tensile stresses towards the lower wall corner edges and top midsection. Although compressive The Journal of the Southern African Institute of Mining and Metallurgy

stresses were identified, this was more prevalent from the bottom midsection to about half the sample height and the top corner edges (as shown in Figure 7). The 25 mm samples were generally compressive, in contrast to the 10 mm samples, with the lower wall edges showing some tensile stress, similar to the 10 mm samples. The top midsection of the 25 mm sample showed minimal tensile stress magnitude, however, the central region of the sample showed a significant compressive stress magnitude of approximately 300 MPa. Similar observations were made with the neutron diffraction experiments. Thus, it can be concluded that the experimental and simulation results compare well. Table I shows the difference in the stress magnitudes (purely for comparison to enable correlation between the different sample heights) for the 10 mm and the 25 mm high samples. In the simulations, the stress magnitudes increased along the print height. The maximum distortion shows longitudinal shrinkage along the laser track (x-direction) which increased as the build height increased. VOLUME 123

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Material characteristics of Ti-6AL-4V samples additively manufactured

Figure 6—Spatial colour maps of residual stress results

Figure 7—Spatial stress maps from ANSYS Additive Suite simulation results for the 10 mm sample 98

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The Journal of the Southern African Institute of Mining and Metallurgy

Material characteristics of Ti-6AL-4V samples additively manufactured using laser-based direct

Figure 8—Spatial stress maps from ANSYS Additive Suite simulation results for the 25 mm sample

Table I

R esults from residual stress magnitude ANSYS simulations and deformation predictions

Maximum deformation (mm) Maximum tensile stress (MPa) Maximum compressive stress (MPa)

10 mm high sample

25 mm high sample

0.56 1114.9 666.9

1.00 1355.3 810.9

Qualitative comparison between simulation and neutron diffraction stress results Stress components It should be realized that the ANSYS simulation results are spatial maps of the hydrostatic stresses that consists of all three stress components and the neutron diffraction results are resolved for each tri-axial component individually. Therefore, the ANSYS simulations are a combination of all three stress components, which is represented individually in the neutron diffraction and each component will contribute to a region's residual stresses formation. Using the ANSYS software, the principal stress vectors within the samples were determined and are shown qualitatively using red arrows (larger arrows have been added to ensure legibility). This is indicated for the 25 mm high sample with sharp corners at the bottom corner (attachment to the baseplate) in Figure 9, and at the top central surface in Figure 10. Figure 9 and Figure 10 show the longitudinal stress component acts in the x-direction and the transverse stress component in the z-direction. In Figure 9, the principal stresses at the bottom corners are represented by the red arrows and were in the z-direction, directly correlating with the transverse stress component results of neutron diffraction. Results at the central part of the top section, Figure 10, revealed that the principal stress shown by the red arrows were The Journal of the Southern African Institute of Mining and Metallurgy

Figure 9—Principal stress vectors at the bottom corner of the 25 mm sharp corner samples as predicted from the ANSYS analysis

Figure 10—Principal stress vectors along the central part of the top surface of the 25 mm sharp corner sample

in the x-direction, directly correlating with the longitudinal stress component results of neutron diffraction. Qualitatively similar results were predicted for the 10 mm samples. VOLUME 123

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Material characteristics of Ti-6AL-4V samples additively manufactured Microstructures Figure 11 shows an optical micrograph of the typical microstructure of the Ti6Al4V samples in the as-built condition. Figure 12 and Figure 13 illustrate the ANSYS simulation of the 10 mm high sample with the corresponding microstructures identified from experimental results. Figure 12 illustrates how the microstructure varies along the centre line of the sample based on the change in stress magnitude, while Figure 13 illustrates a similar change identified along the sample edge. By examining Figure 12 and Figure 13 it was evident that the amount of α-phase (darker phase) increased as the stress became more tensile. This was evident for all four samples. This suggests that the high stress regions (bright red regions) influenced the microstructural evolution since the regions identified from simulations and confirmed to be tensile stress regions showed an increased presence of α-phase (darker phase), while the regions from simulations that showed compressive stresses revealed less of the darker α-phase. This was analysed in the centreline and along the edge of the four samples and found to be consistent. Thus, the simulation and experimental results compare well.

Figure 11—Optical micrograph of Ti6Al4V showing α-phase (dark contrast) and β-phase (light contrast)

Hardness The grid where hardness measurements were taken is the same as used in the microstructure study shown in Figure 4. Figure 14 shows the hardness profile measured along the midsection of the build height of the 3D printed samples, while Figure 15 shows the average hardness values measured for each sample. It can be observed that the hardness was proportional to the residual stress magnitudes, particularly for the transverse component. The 10 mm samples reported higher average hardness values of 380 (F10E) and 379 HV0.3 (S10W) compared to the 25 mm samples, which reported

Figure 14—Hardness profile of the sample build height along the mid section

Figure 12—Correlation between simulated stresses and evolved microstructure from experiments along the sample centreline

Figure 15—Average hardness values of the various 3D printed samples

Figure 13—Correlation between simulated stresses and evolved microstructure from experiments along the sample edge 100

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361(F25W) and 358 HV0.3 (S25E). This was attributed to the effects of cooling rates due to size of samples (larger samples cool slower) and the material hardness of samples under slower cooling effects (slower cooling results in lower hardness) (Kalpakjian and Schmid, 2014). Also, it was postulated that the average hardness values were a result of the nature of the stresses, since the larger samples were generally compressive (25 mm reported lower hardness) and the smaller samples were more tensile (10 mm reported higher hardness), however this was inconclusive. The Journal of the Southern African Institute of Mining and Metallurgy

Material characteristics of Ti-6AL-4V samples additively manufactured using laser-based direct The hardness profiles seen in Figure 14 appeared to be proportional to the stress magnitudes, as the stress curve behaviour for the 10 mm samples of the transverse component showed similar behaviour to its corresponding hardness profile, while the 25 mm hardness profile also resembled its corresponding stress curve behaviour (see Figure 5). This was further confirmed through a similar peak in hardness observed at position three (sample centre) of samples F25W and S25E. This position corresponded to the region observed to display the highest compressive stress magnitude in both experimental and simulation results.

SEM The elemental distributions are shown in Table II for the samples with 10 mm and 25 mm heights. In general, the elemental compositions reported for the 3D printed parts satisfied ASTM standards (ASTM F136-13). However, no clear correlations to the stress type and magnitude were observed. Aluminium is known to be a very strong alpha-stabilizer, as reported by Callister and Rethwisch (2015), while Poondla et al. (2009) states that the stabilizing and strengthening effect of aluminium and oxygen trace amounts positively affects hardenability and enhances the alloy response towards heat treatment when alloyed with Ti. Vanadium, however, is known to be a very strong beta-stabilizer when alloyed with Ti (Arrazola et al., 2009; Peters et al., 2001), which results in an alloy that exhibits high strength and high toughness and is better suited for high temperature applications (Peters et al., 2001). Figure 16 is a SEM micrograph showing small pores within the 25 mm sample. Most of the micrographs showed some degree of porosity.

Table II

SEM-EDX elemental analysis of the 10 mm and 25 mm samples Elements

10 mm

25 mm

ASTM F136

Ti, wt.% Al, wt.% V, wt.%

89.8 6.4 3.82

89.4 6.68 3.88

Balance 5,5–6,5% 3,5–4,5%

investigations (Figure 6) to the simulated principle stress vectors (Figure 9 and Figure 10) the simulation spatial stress map is a combination of these two components. The top middle tensile region in the simulation was created by the longitudinal component associated with the longitudinal contraction along the laser path, and the tensile region in the bottom corners were derived from the transverse component which is a reactive stress to the longitudinal stresses at the top surface. The compressive region in the centre bottom was from the transverse component. Thus, very good qualitative agreement existed in the stress trends and origins, indicating that the software gave good qualitative predictions of the major stress concentrations and subsequent problem areas. Decreasing the mesh volume in the simulation software would greatly decrease the discretization error, which would greatly improve the spatial resolution and will greatly increase the accuracy of the simulated corner stresses.. Due to time constraints, the ANSYS model could not be refined. The following parameters need to be accounted with future modelling for the specific geometries of this study:

The tensile stress gave rise to a reactive tensile stress where the samples were attached to the baseplate. In extreme cases, these stresses can result in ‘tearing’ of the baseplate. The reactive stresses caused plastic deformation of the baseplate, which in turn caused a certain degree of stress relaxation.

➤ Baseplate being shared by the four samples, and thus not independent systems ➤ Deformation of the baseplate ➤ Reducing the size of the model mesh to account for the corner geometries ➤ Quantifying and considering the sample porosity ➤ Quantifying and considering inhomogeneous material compositions.

Simulations

Neutron diffraction

When comparing the residual stresses from the two independent stress components measured by the neutron diffraction

The neutron gauge volume should also be decreased to ensure a higher special resolution and would increase the testability of the stresses in the corner sections.

Discussion Stress relaxation

SEM The vanadium content was indirectly proportional to the fraction of β-phase present in the samples. This might be due to the higher aluminium content measured throughout the samples. The porosity can greatly affect the comparability between the actual stresses (neutron diffraction results) and that of the Ansys results (simulated results). The simulation assumed that the sample material was completely homogeneous and porosity free.

Conclusions

Figure 16—Secondary electron SEM micrograph showing nominal porosity (black pores) within the 25 mm filleted sample The Journal of the Southern African Institute of Mining and Metallurgy

Four Ti-6Al-4V ELI 25 mm square sample tubes with 6 mm wall thicknesses were additively manufactured by the DED process and was printed on a shared Ti-6Al-4V baseplate to 10 mm and 25 mm heights. All samples were investigated whilst attached to the baseplate. Significant deformation of the baseplate was observed, without obvious delamination or distortion of the samples. The residual stress distributions along one wall of each of the four VOLUME 123

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Material characteristics of Ti-6AL-4V samples additively manufactured samples were investigated. FEM using a similar grid to the neutron study was performed with ANSYS assuming that each sample was manufactured on its own baseplate, and without distortion of the baseplate. There were good qualitative agreements between the stress measurements and FEM simulations. Large tensile stresses developed along the central length of the topmost layers due to longitudinal contraction. Modelling predicted that this would lead to distortion of the sample that would become more severe with build height. The gauge and grid volumes employed were not able to distinguish any influences of the corner geometries. By looking at the microstructures as the region's spatial stress map becomes more tensile, the hardness will decrease. The hardness is inversely proportional to that of the stress magnitudes. This corresponds well with literature and the hardness can be predicted with the help of the simulations/neutron diffraction spatial stress maps.

Recommendations for future studies ecrease the mesh volume with the ANSYS analyses to search D for possible influences by the corner geometries. Also, the complete sample geometry needs to be analysed, i.e., square tube geometry. ➤ The practical neutron gauge volume that can be used is limited. A synchrotron radiation study should be pursued where micron sized gauge volumes can be employed and thus render better spatial resolution, especially in the corner sections. ➤ Each sample should be printed on its own baseplate, to ensure that a sample is only subjected to its own heat input and not the subsequent prints heat inputs following it. ➤ Each sample should be printed on a thicker baseplate to ensure that no warpage of the baseplate can occur. ➤ Complete a full porosity analysis of the samples and investigate the effect of the porosity on the residual stresses. ➤

Acknowledgements SIR, NLC, Laser Enabled Manufacturing Group for the use C of their manufacturing facilities. ➤ Necsa SOC Ltd is acknowledged for the access and use of their neutron diffraction equipment. ➤ Mr SS Mahlalela, Lab Manager at the University of Pretoria’s Mineral Sciences Department, for all his assistance in the sample preparation. ➤

References ANSYS. 2020. Additive manufacturing simulation.https://www.ansys.com/products/ structures/additive-manufacturing [accessed 24 March 2020]. Arrazola, P.J., Garay, A., Iriarte, L.M., Armendia, M., Marya, S., and Le Maitre, F. 2009. Machinability of titanium alloys (Ti6Al4V and Ti555.3)., Journal of Materials Processing Technology, vol. 209. pp. 2223–2230. Arthur, N., Malabi, K., Baloyi, P., Moller, H., and Pityana, S. 2016. Influence of process parameters on layer build-up and microstructure of Ti6Al4V (ELI) alloy on the optomec LENS. Proceedings of the 17th Annual Conference of the Rapid Product Development Association of South Africa (RAPDASA). https:// researchspace.csir.co.za/dspace/bitstream/handle/10204/8992/Arthur_2016. pdf?sequence=1 Arthur, N.K. and Pityana, S. 2018. Microstructure and material properties of LENS fabricated Ti-6Al-4V components. R&D Journal, vol. 34. pp.33–36.

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ASTM International F136-13. 2013. Standard Specification for Wrought Titanium-6Aluminum-4Vanadium ELI (Extra Low Interstitial) Alloy for Surgical Implant Applications Callister Jr, W.D. and Rethwisch, D.G. 2015. Callister's Materials Science and Engineering. 9th edn. Wiley. pp. 451–453. Hu, Y.N., Wu, S.C., Wu, Z.K., Zhong, X.L., Ahmed, S., Karabal, S., Xiao, X.H., Zhang, H.O., and Withers, P.J. 2020. A new approach to correlate the defect population with the fatigue life of selective laser melted Ti-6Al-4V alloy. International Journal of Fatigue, vol. 136. p.105584. Kalpakjian, S. and Schmid, S.R. 2014. Manufacturing Engineering and Technology. Jurong, Singapore: Pearson Education South Asia Pte Ltd. Kumar, S. and Pityana, S. 2011. Laser-based additive manufacturing of metals. Advanced Materials Research, vol. 227. pp. 92–95. Liu, S. and Shin, Y. C. 2019. Additive Manufacturing of Ti6Al4V Alloy: A Review, Materials and Design, vol. 164. 107552. Liu, Yang, Yongqiang Yang, and Di Wang. 2016. A study on the residual stress during selective laser melting (SLM) of metallic powder. The International Journal of Advanced Manufacturing Technology, vol. 87, no. 4. p. 647. Masubuchi, K. 2013. Analysis of Welded Structures: Residual Stresses, Distortion, and their Consequences. 33nd edn. Elsevier/Oxford. Moletsane, M.G., Krakhmalev, P., Kazantseva, N., du Plessis, A., Yadroitsava, I., and Yadroitsev, I. 2016. Tensile properties and microstructure of direct metal laser-sintered Ti6Al4V (ELI) alloy. South African Journal of Industrial Engineering, vol. 27, no. 3. pp.110–121. Ngoveni, A.S., Arthur, N.K.K., and Pityana, S.L. 2019. Residual stress modelling and experimental analyses of Ti6Al4V ELI additive manufactured by laser engineered net shaping. Procedia Manufacturing, vol. 35. pp. 1001–1006. Optomec. 2016. LENS 850-R. https://optomec.com/wp-content/uploads/2014/04/ LENS_850-R_Datasheet_WEB_0816.pdf [accessed 19 March 2020]. Peters, M., Hemptenmacher, J., Kumpfert, J., and Leyens, C. 2001. Structure and properties of titanium and titanium alloys. Titanium and Titanium Alloys. Wiley-VCH, Weinheim, Germany. pp. 1–35. Poondla, N., Srivatsan, T.S., Patnaik, A., and Petraroli, M. 2009. A study of the microstructure and hardness of two titanium alloys: Commercially pure and Ti–6Al–4V. Journal of Alloys and Compounds, vol. 486, no. 2. pp. 162–167. Roy, S., Joshi, K.K., Sahoo, A.K., and Das, R.K. 2018 Machining of Ti-6Al-4V ELI alloy: A brief review. IOP Conference Series: Materials Science and Engineering, vol. 390, no. 1. p. 12112. Sibisi, P.N., Popoola, A.P.I., Arthur, N.K.K., Pityana, S.L., and Popoola, O.M. 2019. Morphological characterization of recycled powder and microstructures of Ti-6Al-4V components synthesized by LENS additive manufacturing. IOP Conference Series: Materials Science and Engineering, vol. 655, no. 1. p. 12019. Venter, A.M., van Heerden, P.R., Marais, D., and Raaths, J.C. 2018. MPISI: The neutron strain scanner materials probe for internal strain investigations at the SAFARI-1 research reactor. Physica B: Physics of Condensed Matter, vol. 551. pp. 417–421. Xu, M., David, J.M., and Kim, S.H. 2018. The fourth industrial revolution: Opportunities and challenges. International Journal of Financial Research, vol. 9, no. 2. pp. 90–95. Yumak, N. and Aslantas, K. 2020. A Review on Heat Treatment Efficiency in Metastable β Titanium Alloys: The Role of Treatment Process and Parameters. Journal of Materials Research and Technology, vol. 9, no. 6. pp. 15360–15380. Zhai, Y., Galarraga, H., and Lados, D.A. 2016. Microstructure, static properties, and fatigue crack growth mechanisms in Ti-6Al-4V fabricated by additive manufacturing: LENS and EBM. Engineering Failure Analysis, vol. 69. pp. 3–14. u

The Journal of the Southern African Institute of Mining and Metallurgy

Determination of the erosion level of a porphyry copper deposit using soil geochemistry by F. Moradpouri1, S.M.H. Ahmadi2, R. Ghaedrahmati1, and K. Barani1

Affiliation:

epartment of Mining D Engineering, Faculty of Engineering, Lorestan University, Khoramabad, Iran. 2 Statistics and Data Science Researcher, Massachusetts Institute of Technology, Massachusetts, USA. 1

Correspondence to: F. Moradpouri

Email:

moradpouri.fa@lu.ac.ir

Dates:

Received: 17 Feb. 2022 Revised: 12 Nov. 2022 Accepted: 24 Nov. 2022 Published: February 2023

Synopsis As exploration is time-consuming, costly, and risky, determination of the erosion surface of a metalliferous deposit before geophysical surveying and exploration drilling might be very helpful. Geochemical haloes can be used to determine whether the erosion surface is supra-ore or sub-ore and thus reduce the risk of exploration operations. The aim of this investigation is to determine the erosion surface of the North ROK porphyry deposit (NRPD) in northwestern British Columbia in Canada using linear productivity (LP), which is the content of an element deﬁning the halo multiplied by the width of the halo. A total of 2045 soil samples from the B horizon were analysed using ICP-MS for 36 elements, including Cu, Mo, Pb, Zn, Au, As, Ag, Ni, Co, Fe, and Mn. The data-set was snalysed to obtain the statistical parameters and the elements Cu, Mo, Pb, and Zn were chosen to calculate the linear productivity and the total linear productivity. These four elements were modelled using probability plots to identify and separate subpopulations in terms of anomalous haloes and background, including the threshold values of each subpopulation. The results of the probability plot modelling and thresholds values were then used to map the distribution of each element in a GIS to calculate the linear productivity. The total linear productivity indicated that the erosion surface is supra-ore. Finally, a 3D orebody model of the Cu, Mo, Pb, and Zn distributions was constructed using borehole data and used to validate the results.

Keywords porphyry deposit, surface erosion, probability plot modelling, linear productivity, 3D orebody modelling.

How to cite:

Moradpouri, F., Ahmadi, S.M.H., Ghaedrahmati, R., and Barani, K. 2023 Determination of the erosion level of a porphyry copper deposit using soil geochemistry. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 2, pp. 103–112

DOI ID:

http://dx.doi.org/10.17159/24119717/2029/2023

ORCID:

F. Moradpouri http://orcid.org/0000-0002-1654100X

Introduction Porphyry deposits are among the world’s major repositories of Cu, Au, and Mo, and thus are one of the main targets for the global mineral exploration industry (Holliday and Cooke, 2007; Chen, Huang, and Zhen, 2008; Cooke et al., 2014; Sillitoe, 2010). These deposits are usually eroded. In some cases the level of erosion is close to the Earth’s surface, but with deeper erosion it is possible for a part or even the whole deposit to become removed (Figure 1) (Carlson, Plummer, and Hammersley, 2011). Information about the status and depth of deposits considering the current level of the erosion surface is the most crucial factor in decreasing the exploration risk related to costs of drilling and the probability of detecting a deposit (Grigoryan, 1974). Geochemical methods can be used to estimate the depth of the probable reserve. Multivariate geochemical analysis and determination of axial zonality and linear productivity are among the useful methods. Through calculating the axial zonality or specific ratios of linear productivity, geoscientists might be able to determine the position of the deposits (Beus and Gregorian, 1977; Grigorian, 1992; Chen and Zhao, 1998). In the first steps of a prospecting project this can help to determine the probable existing anomaly rather than using alteration studies. Soil surveys along with alteration studies complete the analysis for future decision-making. Many researchers have used the concepts of axial zonality and linear productivity for different purposes through various statistical techniques such as multivariate analysis, machine learning, and prospectivity mapping (Chen and Liu, 2000; Chen, Huang, and Zhen, 2008; Wang et al., 2013; Li et al., 2016; An et al., 2020). The aim of this investigation is to determine the erosion surface using zonality and linear productivity.

Geochemical haloes and linear productivity The primary geochemical halo of a mineral deposit was deﬁned originally by Safronov (1936) as an environment enriched in ore-forming and associated elements which is formed by hydrothermal processes. Thus, research on primary haloes may form part of a mineral deposit model and various methods and scales of geochemical exploration have been developed based on the theory (Beus and Gregorian, 1977; Gundobin, 1984; Xie and Yin, 1993; Hannington et al., 2003; Distler et al., 2004).

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Determination of the erosion level of a porphyry copper deposit using soil geochemistry

Figure 1—Effect of erosion on an orebody (modified from Carlson, Plummer, and Hammersley, 2011)

In recent years, analysis of primary geochemical haloes has become increasingly important as a reliable exploration tool for revealing the presence of hidden or non-outcropping deposits (Eilu and Groves, 2001; Goldberg, Abranmson, and Los, 2003; Li et al., 2006; Schmid and Taylor, 2009). Primary geochemical characteristics of mineral deposits provide important information for predicting deep mineral resources, as they reflect the geochemical processes of metal precipitation and mineral formation. Many methods have been used to identify primary halo characteristics of mineral deposits, including vertical element zonation, element ratios vectoring towardsS ore zones, Pearce element ratios, and alteration indices. A major aspect of these methods is the determination of the spatial distributions of single elements and/or element associations (Distler et al., 2004; Gundobin, 1984; Ziaii, Carranza, and Ziaei, 2011; Goodell and Petersen, 1984; Jones, 1992; Pirajno and Smithies, 1992; Caranza and Sadeghi, 2012; Prendegast, 2007; Wang et al., 2021). In subvolcanic deposits including porphyry, massive sulphide, and vein-hosted deposits which the intrusive igneous rocks emplaced at medium to shallow depths within the crust, the primary geochemical haloes are symmetrical and are distributed vertically above the ore for up to 1 km. The zonation series of element-indicators for porphyry copper deposits from the surface to depth is in the order Ba, As, Sb, (Ag, Pb, Zn), Au, Bi (Cu, Mo) (Sn, Co, W, Be) (Ovchinnikov and Grigoryan, 1971). The elements in parentheses may replace each other, and for a specific case the variability gradient determines the right order of these elements. The primary geochemical haloes above the main ore deposit are called supra- (or above) ore haloes, whereas the (later) haloes below the main ore deposit are called sub- (or below) ore haloes (Levinson, 1974; Cameron et al., 2004; Carranza, 2008, 2011b; Carranza, Owusu, and Hale, 2009; Wang et al., 2013). A simple schematic image of haloes and their variety is shown in Figure 2. Linear productivity is one of the methods that use the concept of geochemical haloes. In a plane (e.g. a cross-section), the linear productivity of an element in an geochemical halo is the product of the average content of that element multiplied by the width of the halo in metres (Ovchinnikov and Grigorian, 1971). Thus, the linear productivity (LP) can be used as an indicator to recognize the current erosion surface. The linear productivity can be estimated using Equation [1] 104

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[1] where ca is the average of anomalies (i.e. values greater than a threshold), cb is average of the background (i.e. values less than or equal to a threshold), and d is the width of the anomalous halo (metres) in a cross-section. Levinson (1974) presented a diagram that is derived by comparing the results of linear productivity ratio for a known porphyry deposit, which can clarify the current surface (Figure 3). The total linear productivity is calculated using Equation [2], in which Pb and Zn are supra-ore elements and Cu and Mo are sub-ore elements. [2] where LPPb, LPZn, LPMo, LPCu represent the linear productivities for Pb, Zn, Mo, and Cu respectively, derived using Equation [1]. The current research is aimed at determining the erosion surface at the North ROK porphyry deposit (NRPD) in Canada by means of linear productivity, using 2045 soil samples, probability plot modelling, GIS mapping, and 3D orebody modelling for validation.

Location and geological setting of the study area The North ROK property deposits (NRPD) is located in the Stikine River area of northwestern British Columbia, or the northeast part of the Stikine Arch, within Stikine Terrane (‘Stikinia’) of the

Figure 2—Sub-ore, near-ore, and supra-ore haloes for a metalliferous deposit (Wang et al., 2013; Li et al., 2016) The Journal of the Southern African Institute of Mining and Metallurgy

Determination of the erosion level of a porphyry copper deposit using soil geochemistry

Figure 3—Ratio of linear productivities

Canadian Cordillera. The Stikine Arch is a structural domain known for hosting late Triassic-early Jurassic, quartz-deficient alkaline and sub-alkalic intrusive rocks with associated porphyry copper-gold mineralization and peripheral gold-silver-bearing quartz veins. The centre of the property is at about UTM coordinates 447000 East and 6409330 North (NAD 83, Zone 9) or 57°49’20” north latitude and 129°53’30” west longitude. The NRPD is considered to represent an alkalic porphyry deposit lacking free quartz (quartz-deficient), with a copper-gold metal signature (no significant molybdenum) and development of strong magnetiterich potassic and potentially calc-potassic alteration assemblages associated with copper-gold mineralization (Ash et al., 1977; Ash, MacDonald, and Friedman, 1997; Dawson and Norris; 2014). The study area is located in the west part of the NRPD, in the northeast part of the Eddontenajon Lake (Figure 4). The main mineral occurrences in this region are as follows.

The Edon copper-gold occurrence is located in the southern portion of the area, where a 1 km × 1.5 km gossan consisting of strong pyrite and quartz alteration occurs within a well-developed zone of propylitic alteration marked by chlorite, epidote, and pyrite. Chalcopyrite and molybdenite have been reported in the area (Ash, MacDonald, and Friedman, 1997; Mehner and Dunlop, 2010). In the north part of the area, the historical Mabon copper-gold occurrence was discovered by Chris Ash in 1997 on the northern flank of Ehahcezetle Mountain, south of Mabon Creek, where a sample of quartz-sericite-pyrite altered rock assayed 0.33% Cu and 0.42 g/t Au (Ash, MacDonald, and Friedman, 1997). It was demonstrated that the Mabon mineralized alteration zone (Mabon Zone) contains two principal types of porphyry copper-gold mineralization.

Methodology Lithogeochemical techniques are valuable exploration tools for many porphyry and massive sulphide deposits, particularly for deeply buried systems. The standard lithogeochemical techniques identify primary alteration zones directly associated with the formation of deposits, although they do not generally distinguish whether a dispersion halo anomaly is primary, secondary, or tertiary. However, like surficial methods, various extraction methods or differential thermal analysis can potentially discriminate between primary, secondary, and tertiary dispersion haloes. Regardless of the anomaly, the dispersion haloes are useful for deep exploration because they can extend well beyond any noticeable primary alteration system.

Figure 4—Location map and geological setting of the study area (Moradpouri and Hayati, 2021) The Journal of the Southern African Institute of Mining and Metallurgy

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Determination of the erosion level of a porphyry copper deposit using soil geochemistry An important point that should be considered in the interpretation of residual secondary geochemical haloes is the erosion level of a mineral deposit, since this affects the size and extent of anomalies in soil. This point has been conceptualized by different examples, variously known as the blind economic mineralization, outcropping economic mineralization, and dispersed mineralization zone models (Beus and Grigorian, 1977; Ovchinnikov and Grigorian, 1978; Solovov, 1987). Soil anomalies associated with outcropping economic mineralization would normally be stronger than those associated with blind mineralization, and they may be erroneously assumed to be more promising than others, unless the erosion levels are taken into account. Soil anomalies based on the dispersed mineralization zone model may well be similar in intensity to those associated with blind mineralization.

Soil samples The geochemical indices for evaluation of the newly discovered anomalies are derived through studies of the primary geochemical haloes of typical ore deposits. Residual secondary soil haloes in most cases are well correlated in composition and structure with the orebodies and primary haloes that have generated them. Their successful use is related to the landscape-geochemical conditions in the ore regions.

In the NRPD study area, geochemical sampling of residual secondary haloes (as the most correlated composition with primary haloes) was carried out using a mattock, shovel, or auger to reach an appropriate depth to obtain adequate soil samples from the ‘B’ horizon. Line spacing varied from 200 m to 100 m and 50 m from north to the south. The location map of the soil samples is shown in Figure 5.

Statistical analysis and probability plot modelling In geochemical prospecting, it is not always possible to solve a problem by studying only one element. It is common for a set of variables to interact and associate. In this case, it is necessary to study several elements together, or even other variables representative of geological or environmental phenomena. The soil samples in the current study were analysed for 36 elements by inductively coupled plasma mass spectrometry (ICP‐MS). Some major elements that are indicative of the general geochemical character of the deposits and which were incorporated into the statistical analysis included Cu, Pb, Mo, Zn, Au, Ag, As, Sb, Bi, Fe, Mn, Ni, Co, Sr, Cr, Ba, and V. These elements might have a relationship with the probable Cu-Mo (Au) porphyry mineralization. Cu, Mo, Pb, and Zn were used for calculating linear productivity. The statistical parameters for soil data are listed in Table I. The frequency distributions of the data for elements that

Figure 5—Location map of the soil, rock, and borehole samples in the study area 106

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The Journal of the Southern African Institute of Mining and Metallurgy

Determination of the erosion level of a porphyry copper deposit using soil geochemistry Table I

Summary of the statistical parameters for the measured elements in soil samples (ppm, except where indicated) Element

Number Mean Variance Std. dev. Coef. var. Skewness Minimum Median Maximum

1022 2.849 20.445 4.522 158.717 11.941 0.2 1.9 95.2

1022 72.795 17066.91 130.64 179.463 6.879 6.6 33.75 1894

1022 18.477 535.723 23.146 125.269 8.043 0.5 13 388.6

1022 108.521 13033.76 114.165 105.202 8.916 6 84 1795

1022 10.566 2133.337 46.188 437.149 12.538 0.5 2.5 935.7

1022 0.352 0.127 0.356 101.167 5.110 0.1 0.3 5

1022 17.061 1066.193 32.653 191.382 14.957 0.5 10.6 674.6

1022 0.477 0.072 0.269 56.412 2.678 0.1 0.4 2.5

1022 0.421 0.655 0.809 192.155 11.653 0.1 0.3 15.6

Element

Fe (%)

Number Mean Variance Std. dev. Coef. var. Skewness Minimum Median Maximum

1022 4.58 4.037 2.009 43.869 3.429 0.49 4.23 20.78

1022 850.898 758749.4 871.062 102.37 5.360 78 631.5 10000

1022 30.149 313.232 17.698 58.703 1.651 2.5 25.7 175.2

1022 14.535 107.827 10.384 71.441 4.570 2 12.2 120.3

1022 44.277 1941.699 44.065 99.521 4.737 6 31 524

1022 2.709 12.3 3.507 129.485 8.131 0.5 1.9 58.3

1022 70.203 13801.93 117.482 167.345 7.301 6.6 32.95 1982

1022 87.969 928.14 30.465 34.632 1.391 3 82.5 302

were used to calculate linear productivity are presented in Figure 6. As can be seen, the histograms show lognormal distributions and positive skewness for all four elements. In addition to the histogram, the cumulative frequency curve (probability plot) shows the number of data-points (or, much more commonly, the percentage of the total) fallìng below a certain value, plotted against that value. Reimann, Filzmoser, and Garrett (2005) reported that one of the best graphical methods of displaying geochemical distribution is the cumulative probability plot, originally introduced to geochemists by Tennant and White (1959), Sinclaìr (1974), and , Hawkes, and Webb (1979). It is used for background and halo separation and to calculate thresholds in the geochemical data (Moradpouri and Ghavami-Riabi, 2019; Moradpouri and Hayati, 2021). Also, for the calculation of the erosion surface this could be done as halo and background separation. For this purpose, the NRPD soil data in Figure 5 was used to identify the probable anomalous halo, mixture of anomalous halo and background, and background subpopulations using probability plot modelling software by Sinclair 1974) and Sinclair and Blackwell (2004). The probability plot models for Cu, Mo, Pb, and Zn are shown in Figure 7. It is obvious that the distribution is polymodal and the separation characteristics need to be applied to each subpopulation for further details on anomaly haloes and backgrounds. The observed distribution may be described as a mixture of four subpopulations for Cu and Mo and three subpopulations for Pb and Zn. The descriptive statistics of the anomalous subpopulations thus identified are listed in Table II. For example, for Cu the four sub-populations include 3.5, 11.5, 55, and 30% of the data with maximum thresholds of 1.3825, 2.0606, 2.4425, and 3.1097 for each subpopulation respectively. Therefore, the first probability plot model is the point-based arrangement. The probability plots represented by straight lines are generated for each subpopulation and the recombination of these modelled populations yields the curve that approximates the line joining the original points (see Table II for more details on each subpopulation). The final step is revision of the first estimation by optimization steps to maximize the correspondence between points The Journal of the Southern African Institute of Mining and Metallurgy

and curve with the threshold values in the lower parts of Table II. This was implemented through least-squares optimization.

Evaluation of the erosion surface and 3D orebody modelling Information from probability plot modelling on anomalous haloes, backgrounds, and their related threshold values for each element is used to generate the anomaly map, which is a crucial step in calculating the linear productivity. The anomaly maps for Cu, Mo, Pb, and Zn are shown in Figure 8. These were compiled using the Esri ArcGIS 10.5 GIS software, which was also used to determine the width and element content of each anomaly for linear productivity calculation by Equation [2]. The ‘widths’ were calculated using an add-on tool in ArcGIS 10.5. that can calculate the width of the halo based on the content values in the direction that show the compatible transversal zonality pattern. Here, the criterion for calculating width was the results of probability plot modelling in Table II. The details on the width, average content of each elements, and the linear productivity of them are presented in Table III. Finally, the linear productivity ratio (Equation [2]) was calculated, which has the value of 9.27 (see Table III). It presents the current erosion surface that matches the upper side of the orebody as a supra-ore halo. Finally, the classification of the deposit as a supra-orebody was validated using borehole information; the locations of the holes are shown in Figure 9. Based on the borehole data a 3D orebody model was constructed for the variables Cu, Mo, Pb, and Zn, which can be seen in Figure 10. These models show the different anomalies of the NRPD based on 4715 samples taken from 34 boreholes from 300 m to 600 m depth. As can be seen, the 3D models indicate good compatibility that validates the results of probability plot modelling and erosion surface calculation.

Summary and conclusions The current research was conducted to delineate the erosion surface for the North ROK porphyry copper deposit (NRPD) in British Columbia, Canada. This was achieved using linear productivity as an indicator to identify the current erosion surface: VOLUME 123

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Determination of the erosion level of a porphyry copper deposit using soil geochemistry

600.

160.

300.

(b)

Frequency

240.

400.

800. 1200. Cu (ppm)

1600.

80.

0. 0.

2000. (bb)

Histogram North ROK Porphyry Deposit

400.

900.

300.

600.

40.

Mo (ppm)

0. -3.

120.

80.

Histogram North ROK Porphyry Deposit

300. Frequency

600.

Frequency

400.

900.

300.

200. 100.

100.

200. Pb (ppm)

300.

Histogram North ROK Porphyry Deposit

0. -3.

400. (dd)

3. LN (Pb) (ppm) Histogram North ROK Porphyry Deposit

500.

800.

400. Frequency

600. 400. 200. 0. 0.

3. 0. LN (Mo) (ppm)

(cc)

Histogram North ROK Porphyry Deposit

(d)

100.

0. 0.

LN (Cu) (ppm)

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300.

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Histogram North ROK Porphyry Deposit

1200.

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900.

0. 0.

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Histogram North ROK Porphyry Deposit

(aa)

Histogram North ROK Porphyry Deposit

(a)

300. 200. 100.

400.

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2000.

0. 0.

6. LN (Zn) (ppm)

Figure 6—Histograms of the Cu, Mo, Pb, and Zn concentrations (in ppm) from 2045 B horizon soil samples. (a, aa) Cu and log (Cu), (b, bb) Mo and log (Mo), (c, cc) Pb and log (Pb), (d, dd) Zn and log (Zn)

➤ Analysis of different subsets of the lithogeochemical data reveals several multi-element associations describing the mineralization and geochemical haloes present in the NRPD. ➤ Coexisting superimposed supra- and sub-ore elements in soil haloes indicate good potential for orebodies at greater depths. Calculated and interpolated values of linear productivity based on soil halo zoning indicate the existence of Cu porphyry resources at depth and that erosion did not remove the deposits, which was conﬁrmed by drilling. ➤ Compared with the fresh porphyry rocks in this district, the mineralized rocks are enriched in Cu, Au, Ag, Mo, Pb, Zn, W, As, and Sb. Certain elements show clear anomalies, such as Zn, Ag, Cu, Au, W, and Mo. These can be regarded as pathfinders for prospecting new orebodies at depth. 108

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➤ The main porphyry mineralization is generally described by a Cu-Mo-Au association. Supra- and/or near-ore haloes in mineralized altered rocks are generally characterized by an AsSb-Ag-Pb-Zn association, whereas sub-ore haloes in altered rocks around Cu -mineralization are generally characterized by Au-Cu-Mo-W-Co. ➤ The ratios of indexes such as (Pb-Zn) / (Cu-Mo) decrease with depth. The values are greater in the upper levels toward the middle portion, while in the lower levels of the orebody the value is small. The analysis of soil geochemical haloes linked with mineralization indicates its effectiveness as an exploration tool for revealing the presence (or absence) of the deposit type of interest at depth. The Journal of the Southern African Institute of Mining and Metallurgy

Determination of the erosion level of a porphyry copper deposit using soil geochemistry

Figure 7—Results of the probability plot modelling, subpopulation estimation. and revision of the first estimation for variables. (a) Cu, (b) Mo, (c) Pb, and (d) Zn. Note that the vertical axis is scaled logarithmically

We recommend the use of fractal methods, along with probability plot modelling, for similar exercises in background and anomaly separation. This may lead to more accurate results.

Declarations The authors have no conflicts of interest to declare that are relevant to the content of this article.

References

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logratio-transformed stream sediment data with censored values. Journal of Geochemical Exploration, vol. 110. pp. 167–185. Carranza, E.J.M. 2008. Geochemical Anomaly and Mineral Prospectivity Mapping in GIS. Elsevier, Amsterdam. 368 pp. Carranza, E.J.M., Owusu, E.A., and Hale, M. 2009. Mapping of prospectivity and estimation of number of undiscovered prospects for lode gold, southwestern Ashanti Belt, Ghana. Mineralium Deposita, vol. 44. pp. 915–938. Chen Y., Huang. J., and Zhen L. 2008. Geochemical characteristics and zonation of primary halos of Pulang porphyry copper deposit, northwestern Yunnan Province, southwestern China. Journal of China University of Geosciences, vol. 19, no. 4. pp. 371–377. Chen, Y. and Zhao, P. 1998. Zonation in primary halos and geochemical prospecting pattern for the Guilaizhuang gold deposit, eastern China. Nonrenewable Resources, vol. 7, no. 1. pp. 37–44. Chen, Y.Q. and Liu, H.G. 2000. Delineation of potential mineral resources region based on geo-anomaly unit. Journal of China University of Geosciences, vol. 11. pp. 158–163. Cooke, D.R., Hollings, P., Wilkinson, J.J., and Tosdal, R.M. 2014. Geochemistry of porphyry deposits. Treatise on Geochemistry. 2nd edn. Holland, H.D. and Turekian, K.K. (eds). Elsevier. pp. 357–381. Dawson, J.G and Norris, J. 2014. Geological, geochemical, geophysical and diamond drilling report on the North ROK property. Colorado Resources Ltd., Vancouver, BC. Distler, V.M., Yudovskaya, M.A., Mitrofanov, G.L., Prokof'ev, V.Y., and Lishnevskii, E.N. 2004. Geology, composition, and genesis of the Sukhoi Log noble metals deposit, Russia. Ore Geology Reviews, vol. 24. pp. 7–44. Eilu, P. and Groves, D.I. 2001. Primary alteration and geochemical dispersion haloes of Archaean orogenic gold deposits in the Yilgarn Craton: The preweathering scenario. Geochemistry: Exploration, Environment, Analysis, vol. 1. pp. 183–200. Goldberg, I.S., Abranmson, G.Y.A., and Los, V.L. 2003. Depletion and enrichment of primary haloes: their importance in the genesis of and exploration for mineral deposits. Geochemistry: Exploration, Environment, Analysis, vol. 3. pp. 281–293. VOLUME 123

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Determination of the erosion level of a porphyry copper deposit using soil geochemistry Table II

Results of the probability plot modelling, including the details for each subpopulation and the threshold values Logarithmic values

Logarithmic values

Variable : Cu Unit: ppm N: 2045 N CI:34

Variable : Mo Unit: ppm N: 2045 N CI:34

Populations

Pop.

Mean

Std.dev.

Pop.

Mean

Std.dev.

1 2 3 4

1.1848 1.6395 2.2380 2.6688

0.0988 0.2105 0.1022 0.2204

30.0 55.0 11.5 3.5

1 2 3 4

0.1733 0.5438 0.9060 1.3418

0.1527 0.0967 0.0923 0.2252

70.0 23.0 5.5 1.5

Pop.

1 2 3 4

Thresholds

0.9871 1.2184 2.0336 2.2280

1.3825 2.0606 2.4425 3.1097

Pop.

1 2 3 4

Thresholds

-0.1317 0.3505 0.7215 0.8914

Logarithmic values

0.4791 0.7372 1.0905 1.7921

Logarithmic values

Variable : Pb Unit: ppm N: 2045 N CI:34

Variable : Zn Unit: ppm N: 2045 N CI:34

Populations

Pop.

Mean

Std.Dev.

Pop.

Mean

Std.Dev.

1 2 3

0.5481 1.0912 1.6377

0.2672 0.1366 0.2379

3.0 82 15

1 2 3

1.3614 1.9386 2.5451

0.2271 0.1576 0.1857

2.0 93 5.0

Pop.

1 2 3

Thresholds

0.0138 0.8179 1.1619

1.0824 1.3644 2.1135

Goodell, P.C. and Petersen, U. 1984. Julcani mining district, Peru: A study of metal ratios. Economic Geology, vol. 69, no. 3. pp. 347–361. Grigoryan, S.V. 1974. Prospecting and exploration of hydrothermal deposits. International Geology Review, vol. 16, no. 1. pp. 12–25. doi:10.1080/00206817409471901 Gundobin, G.M. 1984. Peculiarities in the zoning of primary halos. Journal of Geochemical Exploration, vol. 21, no. 1-3. pp. 193–200. Hannington, M.D., Santaguida, F., Kjarsgaard, I.M., and Cathles, L.M. 2003. Regional-scale hydrothermal alteration in the central Blake River group, western Abitibi subprovince, Canada: Implications for VMS prospectivity. Mineralium Deposita, vol. 38. pp. 393–422. Holliday, J.R. and Cooke, D.R. 2007. Advances in geological models and exploration methods for copper ± gold porphyry deposits. Ore Deposits and Exploration Technology, vol. 53. pp. 791–809. Jones, B.K. 1992. Application of metal zoning to gold exploration in porphyry copper systems. Journal of Geochemical Exploration, vol. 43, no. 2. pp. 127–155. Li, H., Zhang, G.Y., and Yu, B. 2006. Tectonic primary halo model and the prospecting effect during deep buried ore prospecting in gold deposits. Geological Publishing House, Beijing. 146 pp. [in Chinese]. Li, Y., Zhang, D., Dai, L., Wan, G., and Hou, B. 2016. Characteristics of structurally superimposed geochemical haloes at the polymetallic Xiasai silver-lead-zinc ore deposit in Sichuan Province, SW China. Journal of Geochemical Exploration, vol. 169. pp. 100–122. Mehner, D. and Dunlop, D. 2010. Prospecting, silt, and rock sampling on the North ROK property, 2010. British Columbia Ministry of Energy, Mines and Petroleum Resources, Assessment. 110

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Pop.

1 2 3

0.9071 1.6234 2.1738

Thresholds

1.8156 2.2539 2.9165

Moradpouri, F. and Ghavami-Riabi, R. 2020. A multivariate geochemical investigation of borehole samples for gold deposits exploration. Geochemistry International, vol. 58, no. 1. pp. 40–48. Moradpouri, F. and Hayati, M. 2021. A copper porphyry promising zones mapping based on the exploratory data, multivariate geochemical analysis and GIS integration. Applied Geochemistry, no. 132, 105051. https://doi. org/10.1016/j.apgeochem.2021.105051 Ovchinnikov, L.N. and Grigoryan, S.V. 1978. Geochemical prospecting for ore deposits. International Geology Review, vol. 20, no. 12. pp. 1413–1425. Ovchinnikov, L.N. 1971. Prognostic evaluation of world reserves of metals in land deposits. Doklady RAS, no. 3. pp. 683–686. Ovchinnikov, L.N. and Grigorian, S.V. 1971. Primary halos in prospecting for sulphide deposits. Geochemical Exploration, vol. 11. pp. 375–380. Pirajno, F. and Smithies, R. H. 1992. The FeO/(FeO+MgO) ratio of tourmaline: A useful indicator of spatial variations in granite related hydrothermal mineral deposits. Journal of Geochemical Exploration, vol. 42, no. 2-3. pp. 371–381. Prendergast, K. 2007. Application of lithogeochemistry to gold exploration in the St Ives Goldﬁeld, Western Australia. Geochemistry: Exploration, Environment, Analysis, vol. 7. pp. 99–108. Reimann, C, Filzmoser, P., and Garrett, R. 2005. Background and threshold: critical comparison of methods of determination. Science of the Total Environment, no. 346. pp. 1–16. Rose, A.W., Hawkes, H.E., and Webb, J.S. 1979. Geochemistry in Mineral Exploration. 2nd edn. Academic Press, London. 658 pp. Safronov, N.I. 1936. Dispersion haloes of ore deposits and their use in exploration. Problemy Sovetskoy geologii, vol. 4. pp. 41–53. The Journal of the Southern African Institute of Mining and Metallurgy

Determination of the erosion level of a porphyry copper deposit using soil geochemistry

Figure 8—Distribution anomaly maps generated using GIS software to calculate the average content and width of each element. (a) Cu, (b) Mo, (c) Pb, (d) Zn

Cambridge University Press. doi:10.1007/s13398-014-0173-7.2

Table III

Sinclair, A.J. 1974. Selection of threshold values in geochemical data using probability graphs. Journal of Geochemical Exploration, vol. 3, no. 2. pp. 129–149.

A verage content, width of the halo, and linear and total productivity Variable

Cu Mo Pb Zn

Average content (ppm)

Width (m)

Linear productivity

1141 55.1 608.5 1177

211 217 405

240751 11956.7 246442.5 92108284

LPtotal

9.27

Schmid, S. and Taylor, W.R. 2009. Signiﬁcance of carbonaceous shales and vanadium geochemical haloes in the exploration for rock phosphate deposits in the southern Georgina Basin, central Australia. Journal of Geochemical Exploration, vol. 101. pp. 91–92. Sillitoe, R.H. 2010. Porphyry copper systems. Economic Geology, vol. 105, no. 1. pp. 3–41. Sinclair, A.J. and Blackwell, G.H. 2004. Applied Mineral Inventory Estimation. The Journal of the Southern African Institute of Mining and Metallurgy

Solovov, A.P. 1987. Geochemical Prospecting for Mineral Deposits. Mir, Moscow. 288 pp. [trans. Kuznetsov, V.V.]. Tennant, C.B. and White, M.L. 1959. Study of the distribution of some geochemical data. Economic Geology, vol. 54. pp. 1281–1290. Wang, C., Carranza, E.J.M., Zhang, S., Zhang, J., Liu, X., Zhang, D., Sun, X., and Duan, C. 2013. Characterization of primary geochemical haloes for gold exploration at the Huanxiangwa gold deposit, China. Journal of Geochemical Exploration, vol. 124. pp. 40–58. doi: 10.1016/j.gexplo.2012.07.011 Wang, L., Percival, J., Hedenquist, J.W., Hattori, K., and Qin, K.Z. 2021. Alteration mineralogy of the Zhengguang Au-Zn deposit, Northeast China: Interpretation of shortwave infrared analyses during mineral exploration and assessment. Economic Geology, vol. 116, no. 2. pp. 389–406. Xie, X.J. and Yin, B. 1993. Geochemical pattern from local to global. Journal of Geochemical Exploration, vol. 47. pp. 109–129. Ziaii, M., Carranza, E.J.M., and Ziaei, M. 2011. Application of geochemical zonality coeﬃcients in mineral prospectivity mapping. Computational Geosciences, vol. 37, no. 12, pp. 1935–1945. u VOLUME 123

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Determination of the erosion level of a porphyry copper deposit using soil geochemistry

Figure 10—3D ore-body models from borehole data for (a) Cu, (b) Mo, (c) Pb, (c) Zn

Figure 9—Location map of the boreholes (modified from Jacobe, 2013) 112

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