Saimm 202305 may by SAIMM

VOLUME 123 NO. 5 MAY 2023

UNIVERSITY OF PRETORIA

DEPARTMENT OF MINING ENGINEERING

HARD ROCK PILLAR RESEARCH

Faculty of Engineering, Built Environment and Information Technology

Fakulteit Ingenieurswese, Bou-omgewing en Inligtingtegnologie / Lefapha la Boetšenere, Tikologo ya Kago le Theknolotši ya Tshedimošo

Make today matter www.up.ac.za

Educating a generation of imagineers The University of Pretoria’s Department of Mining Engineering strives to enable the mining industry to transition from being reactive and compliant to becoming resilient through well-structured and committed postgraduate education and research.

RESEARCH FOCUS AREAS

Mechanisation and automation

Management and leadership

Rock engineering

Extended reality (XR) technology

Faculty of Engineering, Built Environment and Information Technology

FOR MINERALS AND MINING ENGINEERING WORLDWIDE IN THE LATEST QS UNIVERSITY RANKINGS BY SUBJECT

Fakulteit Ingenieurswese, Bou-omgewing en Inligtingtegnologie / Lefapha la Boetšenere, Tikologo ya Kago le Theknolotši ya Tshedimošo

www.up.ac.za/mining-engineering Make today matter www.up.ac.za

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

Printed by Camera Press, Johannesburg

VOLUME 123 NO. 5 MAY 2023

Contents Journal Comment: Research on pillar strength by D.F. Malan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

President’s Corner: Giving YOU recognition by Z. Botha . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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PILLAR DESIGN EDITION Numerical simulation of large-scale pillar-layouts J.A.L. Napier and D.F. Malan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . In certain platinum mine layouts, pillars are designed to ‘crush’ in a stable manner as they become loaded in the panel back area. It is particularly necessary to understand the impact of the layout geometry on the effective regional ‘stiffness’ of the rock mass around each pillar. An important design strategy is to model relatively detailed layout configurations which include a precise representation of the local pillar layout geometry. This paper outlines an efficient numerical strategy that can be used to assess large-scale pillar layout performance while retaining the ability to modify individual pillar constitutive behaviour. Simulating pillar reinforcement using a displacement discontinuity boundary element code J.C. Esterhuyse and D.F. Malan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A novel numerical approach to model the effect of pillar reinforcement on pillar stability is presented. To date no clear methodology exists to select the type of support or to design the capacity of the support required. This has led to ongoing collapses in some mines. The model described correctly predicts that an increase in confinement will lead to a decrease in the extent of pillar failure. The effect of pillar confinement can now be studied on a mine-wide scale. Accurate calibration of the limit equilibrium model is, however, required.

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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.

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A study of backfill confinement to reinforce pillars in bord-and-pillar layouts D. Ile and D.F. Malan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . This study explores the use of backfill in hard rock bord-and-pillar mines to increase the pillar strength and extraction ratio at depth. The use of backfill will also minimize the requirement for tailings storage on surface. Numerical modelling of an actual platinum mine layout is used to illustrate the beneficial effect of backfill on pillar stability at greater depths. However, the magnitude of confinement exerted by the backfill on the pillar sidewalls needs to be quantified. A study of the effect of pillar shape on pillar strength J.A. Maritz and D.F. Malan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pillar strength is affected by pillar shape, but this has largely been ignored in past research studies and bord-and-pillar layouts are typically designed using empirical strength equations developed for square pillars. Numerical modelling was used in this study to investigate the effect of pillar shape on strength. An analytical limit equilibrium model of a square and a strip pillar also provided useful insights. The study found that the perimeter rule should not be used for irregularly shaped pillars. Displacement discontinuity modelling, using a limit equilibrium approach, is proposed as an alternative to determine the strength of these pillars. Bord-and-pillar design for the UG2 Reef containing weak alteration layers P.M. Couto and D.F. Malan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A layout design is proposed for the UG2 Reef in cases where weak geological alteration layers are present. These layers have been proven to substantially weaken the pillars. Underground investigations were conducted at Everest mine and numerical modelling undertaken using the TEXAN code and a limit equilibrium model. The modelling predicted that the barrier pillars appear to remain stable even in the case of large-scale collapses, provided their width exceeds 25 m. Main access routes into the mine can be protected by a double row of pillars at least 15 m wide. These conclusions are based on the model calibration, however, and this needs to be refined in future. Calibration of the limit equilibrium pillar failure model using physical models R.P. Els and D.F. Malan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The use of laboratory-scale physical models to calibrate the limit equilibrium model in order to simulate pillar failure was investigated. The models enabled a more precise calibration of the limit equilibrium model compared to previous attempts. Guidelines to assist with calibration of the model are given. The limit equilibrium model appears to be a useful approximation of the pillar failure as it could simulate the stress-strain behaviour of the laboratory models. A study of UG2 pillar strength using a new pillar database T.E. Oates and D.F. Malan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A recent experimental pillar extraction project at a UG2 bord-and-pillar mine presented a unique opportunity to compile a new UG2 pillar database consisting of 66 pillars, of which seven are classified as failed. This enabled a revised ‘first-order’ calibration of the K-value for the Hedley and Grant formula. The new estimated value for the UG2 is K = 75 MPa. This gives a pillar strength that is more conservative than the PlatMine formula. As the database was small, further work is required to determine whether the exponents in the formula are appropriate for UG2 pillars. A proposed method for optimizing coal pillar design using coalfield-specific uniaxial compressive strength F.J.N. Bruwer and T.R. Stacey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The research described in this paper considers whether the variability in coal material strength could be used to indicate the variability in coal pillar strength. The aim is to be able to use a distribution of UCS test results as input into the coal pillar strength calculation. The research considered actual UCS data from multiple mines in the Mpumalanga coalfields of South Africa, and has proved that the variability in material strength between coalfields could allow for some optimization using the proposed approach. Based on the data used, a 2.78% increase in extraction could be achieved. However, further research will be required to validate the results in an underground environment.

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Journ

Research on pillar strength

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his edition of the Journal is the first of a series of planned themed editions. The South African mining industry faces several engineering challenges and it is hoped that these themes will stimulate research and groundbreaking papers. The first of these challenges is to develop local pillar strength equations and pillar design methodologies for hard rock mines. The shallow chrome, platinum, and manganese mines in South Africa typically use mechanized bord-and-pillar mining layouts. The older operations are gradually increasing in depth and this adversely affects the extraction ratios. The available design methodologies and pillar strength formulae dictate an increase in pillar size and a decrease in extraction ratio with depth. As these mining operations are vital to the South African economy, it is critical to maximize the extraction ratios and to ensure that the orebodies are optimally exploited. For outsiders, it is therefore somewhat surprising to learn that the layout designs are still mostly based on the Hedley and Grant pillar strength formula, which was originally developed for Canadian uranium mines in the early 1970s. Since then, very little research has been conducted to develop reef-type specific pillar strength formulae for the hard rock mines in South Africa. Considering the importance of this aspect, it is remarkable that a dedicated research programme to address this issue was not established a long time ago. In contrast, extensive research into coal pillar strength was conducted in the aftermath of the Coalbrook disaster in 1960. The famous Salamon and Munro power-law strength formula was the result of this research effort. Interestingly, the selection of a power-law equation was inspired by laboratory and underground experiments that were conducted much earlier in the 1940s and 1950s. These studies indicated that the strengths of square pillars of the same height vary as the square root of their widths. The strengths of pillars of the same width also vary in inverse ratio to their height. This was generalized by Salamon in a power-law formula with the familiar exponents α and β. These exponents were subsequently calibrated using a database of failed and intact pillars. For the hard rock strength formula, Hedley and Grant used the same references from the 1940s and 1950s, as well as Salamon’s work, to motivate the use of a power-law equation. It is not clear, however, if the calibrated exponents apply to the reef types in the South African mines. Almost no collapses have been reported in the Bushveld Complex mines using this pillar formula, except where weak clay layers were present. This may indicate that the current designs are possibly too conservative. It also presents a difficult problem to researchers, as a database of failed and intact pillars for bord-and-pillar layouts cannot be compiled. The statistical approach followed by Salamon to calibrate an empirical strength equation for coal can therefore not be replicated for hard rock. Attempts have been made to use small UG2 and Merensky Reef crush pillars for such an analysis, but most of these crush pillars are at a similar mining height, they are irregular in size, and it is difficult to classify them as failed or intact based on visual observations. This special edition of the Journal is therefore a welcome addition to the available research literature on pillar strength and we thank the authors who contributed papers. The work includes interesting studies on the use of a limit equilibrium pillar model in a boundary element code, laboratory studies to calibrate these models, underground observations of pillar behaviour, the effect of confinement on pillar strength, and the effect of pillar shape. Professor John Napier made many of these studies possible with his TEXAN displacement discontinuity code, and the authors are deeply grateful for his contribution in this regard.

D.F. Malan

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s dent’

Presi

orner

Giving YOU recognition

n my own environment, it’s that time of the year again where we purposefully, and in detail, give recognition to our team members that have gone above and beyond the call of duty. In the SAIMM it’s also that time of year where the current President reflects on the year that has passed and plans a seamless handover to the next President. While I was busy with these reflections, I realized that it is always about the team, about the support the team members give each other and their work to create a safe space for innovation to flourish. It is therefore no surprise (for me, at least) that I dedicate this article to the people that make it happen. With this article, I want to encourage everyone, no matter where you are, to help build a culture of recognition, to share with everyone why recognition is so extremely important. Humans have a natural psychological need for respect; to this I want to add validation, extrinsic recognition, and the knowledge that they matter, that they are seen. The acknowledgement of efforts and a job well done creates a sense of fulfilment, achievement, and belonging (The Power of Employee Recognition, Ramin Edmond1). I think extrinsic recognition has the power to dictate our perception of who we are and what our value is.

Why is external recognition so important? Some of the data I found shows that, for example, among university students 15.6% of excellence award recipients originally wanted to withdraw their enrolment but were motivated to continue after recognition. Also, 92% of workers were inclined to repeat a specific action after receiving recognition for it (Bright Ewuru2). The data shows concepts like more job satisfaction, better performance, higher productivity, more engagement, reduced stress, and less absenteeism. There is also substantial evidence for the correlation between recognition and competition for talent. Close to a quarter of senior leaders say finding talent is one of the biggest challenges they’re faced with as managers (McKinsey and Company). High-recognition companies have ‘31% lower voluntary turnover than companies with poor recognition cultures’ (Deloitte Review, Issue 163).

Figure 1–Taken from Claire Hastwell, co-author of Women in the Workplace, Creating a Culture of Recognition (https://www.greatplacetowork.com/ resources/blog/creating-a-culture-of-recognition) 1

https://blog.gaggleamp.com/the-power-of-recognition https://www.awardforce.com/blog/articles/the-remarkable-power-of-recognition/ 3 https://www2.deloitte.com/us/en/insights/deloitte-review/issue-16/employee-engagement-strategies.html 2

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President’s Corner (continued) Quantifying the benefits The remarkable power of recognition lies in the plethora of benefits it offers. 1. Recognition creates greater employee engagement; 53% of employees will stay longer in a company if they feel appreciated, 53% will be more focused on their work, and 59% more engaged in their work. 2. Morale boost, improved performance and productivity. A genuine ‘thank you’ can ignite a 69% increase in the likelihood of employees bringing extra effort to their work. Compared to those who do not consistently feel recognized at work, people who do feel recognized are twice as likely to say that people [in their organization] are willing to go above and beyond. Companies with engaged employees are 21% more profitable because their employees are 17% more productive (Gallup). 3. Increased employee retention. A lack of employee recognition is the most common reason why people leave their jobs (Gallup). When people feel recognized and valued, they’re more likely to be happy with their jobs and stay with their organization. Just 37% of US workers say they’re happy with how much they get recognized and acknowledged at work, making it one of the most disappointing factors for workers (The Conference Board). 4. Innovation, innovation, innovation! Recognition spurs innovation. Compared to those who do not consistently feel recognized at work, people who do feel recognized are 2.2 times more likely to drive innovation and bring new ideas forward (Figure 2). 5. With a healthy recognition culture, team members are 2.6 times more likely to think that promotions are fair (Figure 2). During the Trust Index™ survey, when asked what makes their workplace ‘great’, employees who responded positively to survey questions (measuring recognition) said that they were ‘incredibly lucky’ that the company had ‘excellent integrity’ and an ‘uplifting environment’, and some mentioned their ‘career success’. Conversely, employees who didn’t feel recognized at work responded to the same question with phrases such as ‘plays favouritism’ and ‘popularity contest’. These benefits are summarized from work done by Bright Ewuru, 12 October 2022; The Power of Employee Recognition, Ramin Edmond, 28 November 2022; Creating a Culture of Recognition, Claire Hastwell, 2 March 2023; 5 ways to harness the power of recognition, by Michele McGovern, 21 April 2023; The Energy Project; and Harvard Business Review. They are also based on the Great Place To Work® Trust Index™ survey, Great Place To Work, which analysed 1.7 million employee survey responses gathered between 2018 and 2020 across small, mid-sized, and large companies.

Figure 2–Taken from Claire Hastwell, co-author of Women in the Workplace, Creating a Culture of Recognition (https://www.greatplacetowork.com/ resources/blog/creating-a-culture-of-recognition)

What should recognition look like? Here are a few best practices from the literature. 1. Define the goals of the employee recognition programme. Why do you want to implement a culture of recognition? Think about standards in your organization, promoting a culture of appreciation and respect, boosting employee retention or enhancing your brand.

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President’s Corner (continued) 2. Share the criteria. It’s essential to bring every team member on board. If the company leaders demonstrate enthusiasm for the programme and exhibit commendable behaviours, team members will follow. 3. Be very clear and specific about the criteria; be transparent about what you want to reward and how employees can achieve it. Clarifying the rules maintains the integrity of the employee reward programme and gives your team members a good idea of where they need to focus their efforts. Also, recognition is more meaningful when tied to a specific accomplishment or business objective. Refer to an exact action, behaviour, or idea and how it positively affected colleagues, a project, the company, etc. Try to cite the exact time and place it happened. Then focus heavily on the positive impact it will continue to have on the external factors. When being specific, attempt to connect to the bigger picture. 4. Determine frequency. According to a study conducted by Deloitte, 85% of professionals want to hear ‘thank you’ in daily interactions. The regular provision of rewards and praise fosters a culture of appreciation while increasing employees’ zeal and motivation. The key to having a positive impact is consistency and honesty. It’s critical for any manager to schedule time and resources to honour a culture of recognition. Also consider being timeous – recognition that arrives months after the fact isn’t nearly as meaningful as recognition received promptly. The longer it takes for managers to recognize employees, the less likely employees will see the affirmations as authentic. 5. If you’re running a multi-faceted programme or simply want to manage your recognition programme more effectively, consider employee recognition software. This can help you organize your programme, easily accept and judge nominations in one easy hub, and streamline your entire management process. AI, machine learning, and advanced analytics give us greater insight than we’ve ever had into employees’ diverse needs, interests, and behaviours. There are AI tools that can analyse keywords and emojis sent via office instant messaging platforms to get a feel for the team’s overall morale. Other tools can track a combination of real-time job performance, feedback from employees, and surveys to pinpoint which employees are deserving of recognition. The global hotel chain Hilton provides managers with an annual Recognition Calendar that features 365 no-cost and low-cost, easyto-implement ideas for thanking employees. The calendar includes reminders and tips for enterprise-wide brand, and department recognition programsmes, appreciation best practices, important dates like International Housekeeping Week, and recognition quotes to share with employees. It also allows users to add employee service anniversaries and local events. Users can download a print-friendly PDF or import an Outlook-friendly file into their personal calendars. 6. Recognition goes up, down, and sideways. By encouraging rewards and recognition throughout the organization you create and reinforce a culture of appreciation. It also increases the number of opportunities for employees to receive recognition by widening the pool of potential recognizers. Examples from the literature are the software company Atlassian with their Kudos programme, the law firm Alston & Bird LLP, which uses its quarterly newsletter to share the ways that team members are engaging with the surrounding community, and Ally Financial’s ‘I am an Ally’ award programme, which invites team members to nominate colleagues for their contributions and impact. 7. Operationalize and socialize recognition. Schedule a point on regular meeting agendas for employees to thank their colleagues. Or perhaps install a virtual bulletin board where employees can celebrate their co-workers’ successes. This also encourages internal communication. Let them know you want them to speak up and share ideas, then give them credit for when their ideas make an impact. Employees who feel their voices are heard are 4.6 times more likely to feel empowered and perform their best work (Salesforce). 8. Assess the programme’s effectiveness. After all is said and done, you should gauge the outcome of your employee recognition programme. The assessment process can measure such areas as employee retention, morale, engagement, and productivity. If there is a lack in any area, it will be revealed and necessary adjustments can then be made. There is considerable information on the power of recognition out there; therefore, my question is: what resources are your organization utilizing to encourage a culture of recognition? And then, something I am looking forward to immensely is our own two sessions where we would like to give recognition to everyone that makes the SAIMM great. Please join us for our TP Cocktail Evening and our SAIMM AGM. I look forward to recognizing everyone that makes the SAIMM a family!

Z. Botha President, SAIMM

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Numerical simulation of large-scale pillarlayouts J.A.L. Napier1 and D.F. Malan1

Afﬁliation: 1Department of Mining Engineering,

University of Pretoria, South Africa.

Correspondence to: D.F. Malan

Email: francois.malan@up.ac.za

Dates: Received: 13 Nov. 2022 Revised: 8 May 2023 Accepted: 30 May 2023 Published: May 2023

How to cite: Napier, J.A.L. and Malan, D.F. 2023 Numerical simulation of large-scale pillar-layouts. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 5. pp. 203–210 DOI ID: http://dx.doi.org/10.17159/24119717/2451/2023

Synopsis A number of shallow coal or hard rock mines employ pillar mining systems as a strategy for roof failure control. In certain platinum mine layouts, pillars are designed to ‘crush’ in a stable manner as they become loaded in the panel back area. The correct sizing of pillars demands some knowledge of the pillar strength and the overall layout stress distribution. It is particularly important to understand the impact of the layout geometry on the effective regional ‘stiffness’ of the rock mass around each pillar. An important design strategy is to model relatively detailed layout configurations which include a precise representation of the local pillar layout geometry and to analyse multiple mining scenarios and extraction sequences to select optimal pillar sizes and barrier pillar spacing. Although computational solution techniques are now impressive in terms of run time efficiency, a major difficulty is often encountered in assigning suitable material properties to the pillars and in devising an effective material description of the layered rock strata overlying the mine excavations. This paper outlines an efficient numerical strategy that can be used to assess large-scale pillar layout performance while retaining the ability to modify individual pillar constitutive behaviour. The proposed method is applied to selected layouts to compare estimated average pillar stress values against values determined by detailed modelling and against observed behaviour.

Keywords pillar layout, numerical simulation, pillar stress, extraction ratio.

Introduction The displacement discontinuity boundary integral equation method has been applied successfully to the solution of tabular mine layout problems in South Africa for many decades (e.g. Plewman, Deist, and Ortlepp, 1969; Deist, Georgiadis, and Moris, 1972; Ryder and Napier, 1985). A particular class of applications relates to the solution of pillar layout problems which exhibit a number of multi-scale numerical features (Malan and Napier, 2006; Napier and Malan, 2021; Couto and Malan, 2022). Extensive mining operations can comprise thousands of individual pillars (Figure 1). The layout design demands an understanding of both the individual pillar deformations and failure mechanisms as well as assessment of the overall layout stability properties. which must be recognized to prevent large-scale pillar collapses. Individual pillar strength and failure response can be estimated using local fine-scale models of a single pillar employing either detailed displacement discontinuity simulations in which the pillar height effects are modelled indirectly, or finite element or finite difference models of the pillar height and a selected portion of the hangingwall and footwall in a limited volumetric region surrounding an individual pillar, (Esterhuizen, 2014; Li et al., 2021). In the latter case the main difficulty is that some explicit assumptions have to be made about the loading conditions on the selected volume-bounding surfaces. A crucial analysis step is then required to infer how the individual detailed response is incorporated into the overall layout configuration which addresses regional issues such as the positioning of barrier pillars and, in certain cases, multiple seam extraction sequences. The main advantage of the boundary element approach as opposed to finite element or finite difference analysis is the reduction of the numerical analysis space from three to two dimensions. However, even with this significant advantage it can be an arduous task to set up models of large-scale pillar layout problems comprising several thousand pillars and simultaneously requiring a sensitive response to individual pillar failure characteristics. For example, if a layout comprises 5000 pillars and if the allocated tributary unit cell area surrounding each pillar is tessellated using 20 × 20 = 400 elements, then the overall layout area is covered by two million elements. The use of finer grid sizes becomes progressively more prohibitive in total computational effort. In this paper we address this problem by proposing a numerical strategy to represent each pillar ‘cell’ as a single composite element equipped with an appropriate ‘effective stiffness’ constitutive

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Numerical simulation of large-scale pillar-layouts values have been described in detail by Napier and Malan (2007). For the special case of a rectangular displacement discontinuity element centred at the origin and having edge lengths 2a and 2b in the x and y directions respectively, it can be shown that the induced seam-normal traction component at a point R(x, y) in the plane is given by [2] where E is the rock mass Young's modulus, v is the Poisson's ratio, and is the assumed constant closure value. The influence function Iz (x, y, a, b)is defined by

[3] Figure 1—An illustration of the large number of pillars that can be found in bord-and-pillar layouts. The overall size of the layout shown here is approximately 500 m × 500 m

The self-effect stiffness modulus of the element is given by [4]

description. The composite element construction can allow the extraction ratio to be specified individually in each cell region, together with a specified pillar strength and residual strength which controls the pillar failure state. This approach yields a significant reduction in the problem specification detail by allowing the overall layout performance to be analysed in terms of the average load carried by each pillar and providing an indication of the overall pillar collapse potential. The detailed stress distribution and failure regions within individual pillars can be assessed by embedding submodels of selected local layout regions in a multi-scale simulation approach if required. This extension is not discussed in the present work.

Effective pillar stiffness model A large-scale pillar layout will generally assume a nominally regular rectangular mesh pattern, which may include the periodic use of barrier pillars to limit the potential for extensive pillar collapses. In this paper we assume that each pillar is located within a unit cell which includes both the intact pillar and an allocated surrounding mined area. The proposed numerical scheme seeks to approximate the response of the unit cell to reflect the average seam closure and the average load carried by the pillar. The layout is assumed to fall in an approximately horizontal x-y coordinate plane with the z-axis normal to the plane. The stope closure is represented by the z-component of the displacement discontinuity vector. Ride components are not considered in the present development. in each unit cell is determined The average stress component implicitly by the following relationship: [1] where is the average closure in the cell and is the cell element self-effect stiffness modulus. represents the sum of the average field stress at the centre of the unit cell and all ‘external’ stress values that are induced by the remaining layout cells and by other displacement discontinuity elements. The superscript C is used to distinguish quantities that are properties of each pillar cell region. The influence functions that are used to calculate the induced stress 204

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In the special case where the unit cell is a square with side length gc = 2a = 2b this expression becomes [5] The case of a plane strain geometry can be represented by taking the limit b¤∞ in Equation [4] and setting gc = 2a. In this case Equation [4] assumes the form [6] Let the unit cell area be Ac and assume that the intact pillar area within the cell is Ap. The unit cell extraction ratio ec is therefore given by [7] For the case of a plane strain geometry of parallel-sided panels separated by intervening strip pillars, define the unit cell width to be gc and let the pillar width be W. In this case Ac = gc and AP = W. If a particular unit cell average stress is , the average stress acting on the unmined pillar area within the cell must satisfy the stress balance relationship. [8] It is assumed further that the average unit cell stress is related to the average unit cell closure by a relationship of the form [9] where kc is defined to be the ‘effective stiffness modulus’ of the unit cell. The minus sign in Equation [9] reflects the assumption that The Journal of the Southern African Institute of Mining and Metallurgy

Numerical simulation of large-scale pillar-layouts [14]

compressive stress values are deemed to be negative. Substituting Equation [9] into Equation [1] allows the average cell closure to be expressed as

Calibration of effective pillar stiffness

[10] The effective stiffness modulus kc depends on the extraction ratio and on the local geometry of the intact pillar within the unit cell. The value of kc can be determined analytically for the special case of a regular, infinite train of strip pillars but must in general be ‘calibrated’ using a numerical sub-model of the detailed layout of each pillar cell. Once the effective cell stiffness values are established the overall pillar layout can be solved by recursively solving Equation [10] at each defined pillar cell element. It should be noted that this approximate scheme allows each pillar cell to have a unique extraction ratio ec and can be combined with elements that represent additional mining regions or fault structures. The computational saving that can be achieved relies on the assumption that an effective stiffness modulus can be determined for a few characteristic types of cell geometry and is controlled mainly by the unit cell extraction ratio. The case of a plane strain horizontal layout comprising an infinite sequence of pillars of width W with pillar centre spacing gc was solved by Salamon (1968). Using Salamon's solution it can be inferred (see Napier, 1991) that the average closure in each pillar cell is given by

In order to demonstrate the proposed calibration procedure, consider the case of a 5 × 5 pillar sub-layout in which each pillar cell has a side dimension of 17 m. The composite unit cell is illustrated for the central pillar and the associated mined region in Figure 2. The overall layout dimensions are 85.0 m × 85.0 m and the layout is assumed to be tessellated by a fine grid of square displacement discontinuity elements with grid size 1/3 m. In this case, each unit cell in the layout shown in Figure 2 has 51 × 51 square elements and the overall layout is covered by 65 025 square elements. This problem was analysed with five different intact pillar sizes having widths of 5, 7, 9, 11, and 13 m respectively. The corresponding cell extraction ratios and effective stiffness values are summarized in Table I. The assumed rock mass modulus was E = 7200 MPa and Poisson's ratio v = 0.2. The field stress Qz at the excavation horizon was assumed to be –9.0 MPa. It should be noted, however, that the calibration test run is not dependent on the explicit field stress value in the case where no failure of the intact pillar region occurs. The unit cell self-effect stiffness modulus given by Equation [5] is equal to 198.6 MPa/m for the assumed elastic parameters. The last column in Table I expresses the scaled effective stiffness values that are calculated using Equation [13].

[11] where Qz is the vertical field stress at the excavation horizon. (The field stress is negative for compressive stress values.) The average pillar cell stress in the case of an infinite sequence of similar pillars is equal to the vertical field stress and consequently = Qz. Employing Equations [9] and [11], the effective cell stiffness modulus is therefore deduced to be [12] It is useful to scale the effective stiffness modulus by the unit cell self-effect modulus and to define the scaled effective stiffness modulus by [13] Hence, combining Equations [6] and [12],

Figure 2—Test layout configuration to illustrate effective pillar cell stiffness estimation. The centre cell is used to calibrate the effective cell stiffness magnitude with different intact pillar dimensions

Table I

Numerical calibration results for the effective stiffness modulus in the central unit cell of the 5 × 5 pillar layout shown in Figure 2 Pillar width (m)

Extraction ratio ec

Effective stiffness modulus kc (MPa/m)

Scaled effective stiffness modulus

0.9135

121.48

0.612

0.8304

228.39

1.150

0.7197

425.86

2.144

0.5813

851.81

4.289

0.4155

2055.2

10.349

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Figure 3—Estimated pillar cell stiffness scaled by the pillar cell element selfeffect

Figure 5—Comparison of fine grid average pillar cell stress to coarse solution of 5 × 5 pillar cell elements with an extraction ratio of 0.7197 and using a corresponding effective stiffness value of 425.86 MPa/m. The fine grid solution comprises 65 025 elements with 2601 elements per pillar cell

The maximum allowed closure of the failed unit cell is therefore bounded according to [15]

Figure 4—Distribution of the test layout scaled cell stiffness values

Figure 3 shows a plot of the scaled pillar cell stiffness values, as a function of the extraction ratio ec together with the corresponding values that arise for the regular strip pillar layout given by Equation [14]. It should be noted that kc = 0 in the limiting case ec ¤1 as no intact pillar is present in the fully mined unit cell. The planar layout values reported in Table I and depicted in Figure 3 can be seen to follow a remarkably similar trend to the plane strain results of Equation [14] but are lower than the plane strain case when the extraction ratio exceeds 0.5. Figure 4 is a plot of the scaled effective stiffness modulus values that arise in each unit cell of the 5 × 5 pillar calibration layout when the extraction ratio is equal to 0.7197 (pillar width = 9.0 m). This indicates that the edge unit cells are somewhat stiffer than the central cells, which have nearly uniform values. The differential stiffness arises from the fact that no mining is included outside the 5 × 5 pillar cluster depicted in Figure 2. This suggests that the stiffness calibration should include a modest ‘pad’ region around a unit cell of specific interest. It should be noted that the extraction ratio ec is used in Equation [8] to determine the pillar average stress in the layout solution. If the average pillar stress exceeds a specified failure strength Smax, the pillar stress is assumed to fall to a specified residual stress level Sf. This assumption is conservative in the sense that no post-failure compression softening slope of the pillar is assumed in the current analysis. It is noted also that the post-failure pillar compression within the unit cell is ultimately limited by the failed pillar volume. 206

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where H is the pre-failure pillar height. If this closure restriction arises, the corresponding pillar cell stress is determined from Equation [1] in the iterative solution procedure with the imposed boundary condition . The overall iterative scheme includes a cell status flag indicating whether the pillar is ‘intact’ or ‘failed’. The status flags are revised at the end of each mining step cycle depending on the transition from ‘intact’ to ‘failed’ status that is determined for each cell. Experience to date suggests that updating each cell status at the end of each mining step cycle generally precludes the possibility of encountering pathological cyclic oscillations between cell intact/failed states. A final consistency test run of the 5 × 5 pillar calibration layout was carried out using the coarse unit cell layout having only 5 × 5 = 25 elements with element edge length 17.0 m and with each element assigned an effective stiffness value of 425.86 MPa/m corresponding to an extraction ratio of 0.7197 (see Table I). Figure 5 is a plot of the coarse cell layout average pillar stress values across the centreline y = 0, compared to the average values calculated in the fine scale layout simulation comprising 65 025 elements. The average pillar cell stress can be seen to compare favourably with the detailed layout results, indicating overall consistency of the results despite the massive reduction of the problem size to only 25 elements. In order to reduce grid size errors, it may be noted that the calibration could be carried out in two steps using element mesh grid sizes g1 and g2 = g1 /2 respectively and then using an extrapolative technique, such as outlined by Napier and Malan (2011) to estimate the asymptotic unit cell stiffness modulus values as g ¤ 0.

Large-scale layout simulations The use of the effective stiffness algorithm for a large-scale layout is illustrated by considering a hypothetical pillar layout comprising six mining panels separated by five barrier pillars as shown in Figure 6. The overall layout covers an area of 1615 m by 1275 m and comprises 95 × 75 = 7125 pillar cells with a cell grid size of 17.0 m. The test layout comprises six pillar panels separated by five barrier pillars. In the illustrative cases presented here it is assumed that the extraction ratio of the panel pillars is 0.7197 with an effective stiffness of 425.86 MPa/m (see Table I). The barrier pillars are simulated as pillar cells with an extraction ratio of 0.4155 and an The Journal of the Southern African Institute of Mining and Metallurgy

Numerical simulation of large-scale pillar-layouts effective cell stiffness of 2055.2 MPa/m. This ad hoc choice for the barrier pillar description can, however,- be amended. The initial effective width of the barrier pillar cell was set to one element (17.0 m) and the absolute field stress magnitude was assumed to be 9.0 MPa at the excavation horizon. The rock mass modulus and Poisson's ratio were chosen to be 7200 MPa and 0.2 respectively. Figure 7 illustrates the distribution of the calculated average absolute pillar stress values across the pillars centred on the layout centreline (y-coordinate = 637.5 m; see Figure 6). No failure is permitted to occur in this case and the peak panel pillar stress was approximately equal to 31.8 MPa. (The theoretical tributary area stress in this case is 32.11 MPa.) Assuming that the nominal pillar strength is 40.0 MPa, it was found that if the nominal barrier pillar width was equal to 17.0 m the entire layout would collapse if the centre element in panel 3 were to fail. Figure 8 shows the equivalent centreline plot to Figure 7 when the barrier pillar width was increased from 17.0 m to 51.0 m and when no pillar failure occurs. In this case the peak pillar stress decreases nominally to 31.68 MPa. Figure 9 shows the centreline pillar stress status if the centre pillar cell in panel 3 fails and using a nominal pillar strength of 40.0 MPa. It can be seen in this case that all the pillars in panel 3 collapse but the wider barrier pillars prevent this collapse from spreading to the adjacent panels. These hypothetical examples illustrate the potential use of the model to explore rapidly various layout configurations that comprise large numbers of pillars.

Figure 8—Average pillar stress for a barrier pillar width of 51.0 m (no failure)

Figure 9—Average pillar stress for a barrier pillar width of 51.0 m with inner panel failure (failure in panel 3)

Figure 6—Test pillar layout configuration

Figure 10—Section of a bord-and-pillar layout used for the case study

Case study to illustrate the application of the proposed model

Figure 7—Average pillar stress for a barrier pillar width of 17.0 m The Journal of the Southern African Institute of Mining and Metallurgy

The proposed model has been applied to the simulation of a platinum mine in the western Bushveld Complex. The mine uses a bord-and-pillar layout to exploit the Merensky Reef. A detailed portion of the mine layout is illustrated in Figure 10, showing the pillars that were established in a square grid pattern with a nominal pillar centre spacing of 12 m. The designed pillar size was 6 m × 6 m, yielding a nominal extraction ratio of 0.75. The average mining height is 2.3 m. The typical condition of the pillars is shown in Figure 11. VOLUME 123

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Figure 11—Typical condition of the pillars in the mine selected for the case study

A simplified diagram of the mine layout is illustrated in Figure 12, showing the 294 pillars that were established in a square grid pattern in the area of interest. A modelling exercise was undertaken initially to obtain an accurate estimate of the load carried by each individual pillar without using the effective stiffness model. The detailed model was constructed using triangular displacement discontinuity elements to facilitate the representation of local irregularities in the pillar shapes and the surrounding borders of the mined region. The model comprised 49 380 triangular elements. Only the pillars of interest were discretized. The dip of the reef is small in this area and it was simulated to be 0° to simplify the modelling. The depth of the area was approximately 637 m. The overburden density was estimated to be 3000 kg/m3 and the vertical virgin stress magnitude is therefore 19.11 MPa for the assumed depth. The modelling parameters are summarized in Table II. The total simulated layout area was 49 679 m2 and this included a total pillar area of 10 568 m2. It should be noted that these areas imply an overall extraction ratio for the simulated mine layout of approximately 0.7873. The average pillar stress values that were calculated for the highlighted row of pillars shown in Figure 12 are illustrated in Figure 13. The assumed field stress at the mining horizon of 19.11 MPa implies an overall layout tributary stress of 89.83 MPa for each pillar. The simulated pillar stress values for some of these pillars were higher than this tributary pillar stress as the pillar cutting is poor and some pillars are smaller than the dimensions specified for the layout design. It should be noted as well that two pillars (P167 and P179) adjacent to the abutments in the model have lower average stress values. The approximate pillar cell model using the effective stiffness concept was formulated utilizing the individual pillar areas from the detailed model to calculate each individual pillar cell extraction ratio ec as defined by Equation [7]. Using these values, the scaled effective stiffness values within each pillar cell can be inferred by using an empirical polynomial function to interpolate the square element point values shown in Figure 3 and in the last column of Table I. The interpolation function is given by [16] Equation [16] yields a value of = 0 when ec = 1 and provides a smooth representation of the stiffness values between each point reported in Table I and in Figure 3 when ec t 0.4. (This relationship should, however, not be used if ec 0.4.) The effective 208

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stiffness modulus of each cell is found by combining Equation [5] and Equation [13] to yield [17] Two effective stiffness models were constructed to simulate the detailed layout shown in Figure 12. In the first case a square element grid was solved with a pillar cell grid size of 12.0 m superimposed over the 294 pillars depicted in Figure 12. The individual pillar cell effective stiffness modulus was calculated from Equation [17] with gc = 12.0m and using the interpolated value of relevant to each pillar together with the elastic property values E = 70 000.0 MPa and v = 0.2. Figure 14 shows a comparison between the simulated average pillar stress values (square-shaped points) and the detailed fine grid results (diamond-shaped points). The approximate cell values can be seen to fall below the detailed model results but do follow the individual pillar stress fluctuations qualitatively. The underestimation of the approximate average pillar stress values evidently arises since the total area of the pillar cell elements is 294 × 144 = 42336 m2, which is significantly lower than the area of 49 679 m2 that is used in the detailed layout simulation. This discrepancy can be reconciled by allocating a nominal average area of 49679/294 (168.98 m2) to each pillar cell element. The approximate solution was re-computed by adjusting the extraction ratio in each pillar cell using the actual pillar areas and an amended cell area of 169.0 m2. The effective stiffness modulus values were re-computed using the adjusted pillar cell extraction ratios and using gc = 13.0 in Equation [17]. The simulation results are plotted in Figure 14 and show a remarkably good agreement between the approximate pillar cell average stress values (triangular point markers) and the detailed model average pillar stress values for the selected line of pillars. It should be re-iterated that the original problem comprising 49 380 elements has been reduced significantly to a problem comprising only 294 element cells (Figure 15). The effective pillar stiffness concept therefore appears to have considerable merit in providing a rapid means to assess the overall behaviour of largescale pillar layout problems. At the same time it must be emphasized that local mining regions can still be assessed in detail if necessary. In this case, the approximate pillar cell scheme can be adapted to provide an excellent approximation to the background stress values that are induced by the overall layout configuration within a local region of interest which can be modelled in finer detail. The Journal of the Southern African Institute of Mining and Metallurgy

Numerical simulation of large-scale pillar-layouts Table II

Modelling parameters for the pillar layout illustrated in Figure 12 Parameter

Value

Young’s modulus

70 GPa

k-ratio Average overburden density

1 3000 kg/m3

Poisson’s ratio

0.25

Depth

637 m

Dip of the reef Average element size

0° Approx. 0.83 m2

The reduction of the problem size also allows for the possibility of analysing multiple seam problems and the effective stiffness values can, in principle, be adjusted as well to simulate time-dependent pillar strength decay and pillar edge scaling behaviour.

Conclusions A simple pillar cell stiffness concept has been proposed to facilitate the assessment of the stability of large-scale pillar layout problems. The approximate scheme allows for individual variations of pillar extraction ratio within each pillar cell to be specified. The effective stiffness of a representative pillar cell can be established numerically for planar layout problems. Comparisons between the proposed scheme and detailed simulations of an actual pillar layout indicate encouraging agreement. It is noted that the overall mined area and overall extraction ratio should be represented accurately in order to obtain correctly scaled average pillar stress values.

Figure 12—Geometry simulated. The pillars numbered in red were studied in detail

Figure 13—Simulated average pillar stress (APS) for a number of pillars in the layout shown in Figure 12 The Journal of the Southern African Institute of Mining and Metallurgy

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Figure 14—Comparison between the effective stiffness model and the detailed pillar layout simulation for the selected line of pillars shown in Figure 12

(a) Fine mesh simulation

(b) Pillar cell model

Figure 15—The approach described in this paper has reduced the original problem comprising 49 380 elements (left) to a problem comprising only 294 element cells (right). An enlarged view of the elements used to represent pillar P104 is included on the left to indicate the size of the elements used

The effective cell stiffness scheme provides a tool for the rapid assessment of large-scale pillar layout performance with selected pillar extraction ratios. The new pillar cell feature can be combined with any existing layout configurations and can be incorporated as well in multi-scale simulations.

References Couto, P.M. and Malan, D.F. 2022. A limit equilibrium model to simulate the large-scale pillar collapse at the Everest Platinum Mine. Rock Mechanics and Rock Engineering, vol. 56. pp. 183–197. https://doi.org/10.1007/s00603-022-03088-z Deist, F.H., Georgiadis, E., and Moris, J.P.E. 1972. Computer applications in rock mechanics. Journal of the South African Institute of Mining and Metallurgy, vol. 72. pp. 265–272. Esterhuizen G.S. 2014. Extending empirical evidence through numerical modelling in rock engineering design. Journal of the Southern African Institute of Mining and Metallurgy, vol. 114. pp. 755–764. Li, C., Zhou, J., Armaghani, D.J., and Li, X. 2021. Stability analysis of underground mine hard rock pillars via combination of finite difference methods, neural networks, and Monte Carlo simulation techniques. Underground Space, vol. 6, no. 4. pp. 379–395. Malan D.F. and Napier J.A.L. 2006. Practical application of the TEXAN code to solve pillar design problems in tabular excavations. Proceedings of the SANIRE Symposium “Facing the Challenges”, Rustenburg. South African National Institute of Rock Engineering. pp. 55–74. 210

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Napier, J.A.L. and Malan, D.F. 2007. The computational analysis of shallow depth tabular mining problems. Journal of the Southern African Institute of Mining and Metallurgy, vol. 107. pp. 725–742. Napier, J.A.L. 1991. Energy changes in a rockmass containing multiple discontinuities. Journal of the South African Institute of Mining and Metallurgy. vol. 91. pp. 145–157. Napier, J.A.L. and Malan, D.F. 2011. Numerical computation of average pillar stress and implications for pillar design. Journal of the Southern African Institute of Mining and Metallurgy, vol. 111. pp. 837–846. Napier, J.A.L. and Malan D.F. 2021. A limit equilibrium model of tabular mine pillar failure. Rock Mechanics and Rock Engineering, vol. 54. pp. 71–89. Plewman, R.P., Deist, F.H., and Ortlepp, W.D. 1969. The development and application of a digital computer method for the solution of strata control problems. Journal of the South African Institute of Mining and Metallurgy, vol. 70. pp. 33–44. Ryder, J.A. and Napier, J.A.L. 1985. Error analysis and design of a large-scale tabular mining stress analyser. Proceedings of the 5th International Conference on Numerical Methods in Geomechanics, Nagoya, Japan. Balkema, Rotterdam. pp. 1549–1555. Salamon, M.D.G. 1968. Two-dimensional treatment of problems arising from mining tabular deposits in isotropic or transversely isotropic ground. International Journal of Rock Mechanics and Mining Sciences, vol. 5. pp. 159–185. The Journal of the Southern African Institute of Mining and Metallurgy

Simulating pillar reinforcement using a displacement discontinuity boundary element code J.C. Esterhuyse1 and D.F. Malan1

Afﬁliation: 1Department of Mining Engineering,

University of Pretoria, South Africa.

Correspondence to: D.F. Malan

Email: francois.malan@up.ac.za

Dates: Received: 12 Nov. 2022 Revised: 8 June 2023 Accepted: 9 June 2023 Published: May 2023

Synopsis In this study we explore the use of a novel numerical modelling approach to study the effect of pillar reinforcement on pillar stability. Case studies in the literature indicate that tendons, strapping of the pillars, and shotcrete or thin spray-on liners are commonly used to reinforce pillars. No clear methodology exists to select the type of support or to design the capacity of the support required, however. This has led to ongoing collapses in some mines in spite of heavy support being used to reinforce unstable pillars. A limit equilibrium model with confinement on the edge of the pillar was used to simulate the interaction of the support with the failing pillar. The model correctly predicts that an increase in confinement will lead to a decrease in the extent of pillar failure. As the displacement discontinuity boundary element method allows for the efficient solution of largescale bord-and-pillar layouts, the effect of pillar confinement can now be studied on a mine-wide scale. Accurate calibration of the limit equilibrium model is, however, required before this method can be used for the design of effective pillar support.

Keywords How to cite:

pillar reinforcment, limit equilibrium model, displacement discontinuity boundary element code.

Esterhuyse, J.C. and Malan, D.F. 2023 Simulating pillar reinforcement using a displacement discontinuity boundary element code. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 5. pp. 211–222 DOI ID: http://dx.doi.org/10.17159/24119717/2450/2023

Introduction As described by Alejano et al. (2017), partially failed pillars are occasionally encountered in bord-and-pillar layouts. Selective pillar reinforcement may assist in these cases to improve the overall stability of the layout. Tendons, strapping of the pillars, and shotcrete or thin spray-on liners (TSLs) have been used in the past to reinforce pillars. An example recently recorded by the authors in a Merensky Reef bord-and-pillar mine is given in Figure 1. Extensive spalling of the pillar sidewalls was observed and TSLs were successfully used to stabilize some of the pillars. As the TSL was only selectively applied to some pillars, the benefit was clearly discernible as the unsupported pillars adjacent to the pillars with TSL reinforcement were subjected to extensive spalling.

Figure 1—Application of a TSL stopped the Merensky pillar on the left from spalling. The pillar on the right was not reinforced and extensive spalling was observed

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Simulating pillar reinforcement using a displacement discontinuity boundary element code As discussed in the next section, pillar reinforcement has not been successful in all cases and large collapses have occurred in spite of the remedial work. A methodology to better quantify the effect of pillar reinforcement in large bord-and-pillar layouts, where localized pillar failure occurs, is required. As part of this methodology, a modelling approach is required to accurately simulate the irregular pillar sizes, the pillar stress, and the effect of the support. Simulating rock mass reinforcement is routinely done using finite difference or distinct element codes (e.g. Ghee, Zhu, and Wines, 2011; Najafi, 2021; Sinha and Walton, 2021). It is feasible to simulate a pillar which is reinforced with bolting and shotcrete using these codes. In the FLAC3D program, these structural elements can be cables or liners (Itasca, 2022). A cable may be anchored at a specific point in the grid, or grouted so that a force develops along its length. Cables may also be pretensioned. Liner elements are used to simulate thin liners for which both the normal compressive or tensile and shear frictional interaction with the rock are present. Examples such as tunnels lined with shotcrete can therefore be simulated. A major drawback of the finite difference codes is that it is very difficult to simulate large-scale tabular geometries with numerous irregular-shaped pillars. The modelling presented in the literature is typically for a single pillar only (e.g. York, 1998; Naidoo, Handley, and Leach, 2008; Jessu, Spearing, and Sharifzadeh, 2018). In contrast, displacement discontinuity boundary element codes, such as TEXAN, can easily simulate a very large numbers of irregular pillars in a bord-and-pillar layout (e.g. Malan and Napier, 2006; Napier and Malan, 2021). The drawback of the displacement discontinuity method (DDM) is that the excavations are simulated using a ‘slit’-type approximation where the excavation has a height of zero. Although this seems counterintuitive to simulate an open stope, it allows for very accurate simulations of average pillar stress (APS) and facilitates the computation of design criteria, such as energy release rate, used in the deep tabular gold mines. Although this approach works exceptionally well for simulating tabular excavations where the lateral extent of the excavations is very large, the detailed pillar failure mechanisms cannot be simulated. This is unfortunate as the edges of hard rock pillars are often fractured. One method to simulate pillar failure in the DDM codes is the socalled limit equilibrium model. For these models, it is assumed that the fractured edge of the pillar is in a state of equilibrium and that the vertical extent of this fracture zone is bounded by parting planes at the hangingwall and footwall contacts of the pillar. Based on these assumptions, it is possible to construct a differential force balance for the average reef-parallel and reef- normal tractions that obey the following relationship (see Napier and Malan, 2021):

In this paper we describe a simple extension of the limit equilibrium model to simulate the confining effect of pillar reinforcement. It was implemented in the TEXAN code by Professor John Napier. Although this approach cannot model the detailed support mechanisms available in the finite difference codes, it is still a useful method to simulate mine-scale layouts and the confining effect of pillar reinforcement, provided the necessary calibration can be done using underground observations. A case study from Santa Rosa mine in Spain is used as an example in this paper.

Examples of pillar reinforcement In South Africa, a number of hard rock pillar failure case studies have been conducted where attempts were made to reinforce the pillars. Figure 1 in the previous section illustrates an example where the TSL seem to have worked very well. Not all previous attempts to support the pillars were successful, however. Spencer (1999) describes the reinforcement of pillars traversed by thick clay layers using mesh and lacing with cables at the Wonderkop mine. The blocky and fractured nature of the pillars caused delays during the drilling and grouting of the support holes. Only about 70 pillars were supported. Spencer noted that the support assisted to keep the pillars together and prevented further spalling, but he speculated that the support did little to strengthen the overall pillar support system. Conditions deteriorated further and the mine was closed in 1998. The failure was partially attributed to the drilling process, which introduced additional water into the clay and probably weakened the pillars further. Couto and Malan (2023) reported another unsuccessful attempt to increase the pillar confinement using fibre-reinforced shotcrete at the Everest mine in the eastern Bushveld Complex. This attempt was also unsuccessful and a large part of the mine collapsed. Figure 2 illustrates the subsequent cracking of the shotcrete at the Everest mine as pillar failure progressed. A further example of pillar support in areas with a weak clay layer in a different mine is illustrated in Figure 3. It consisted of a layer of shotcrete, bolting, mesh, steel strapping, and a further layer of shotcrete. This support unfortunately did nothing to arrest the eventual collapse of the mine. Figure 4 illustrates the failure of the support as the pillars continued to deteriorate. Some manganese pillars in South Africa have also been supported with TSLs in areas where the joint spacing is small. This is illustrated in Figure 5. Some of the pillars reinforced using this method continue to deteriorate, however. Siwak (1984) reported failure in pillars in underground chalk quarries in northern France. The pillars were supported with a 6 mm thick layer of glass-fibre-reinforced resin, but the additional

[1] where H is the height of the fracture zone normal to the plane of the excavation, σs(P) is the gradient vector of the average reef parallel stress σs at point P in the pillar while σn is the reef-normal compressive stress at point P. The parameter μI is the friction coefficient at the upper and lower parting separating the fractured rock from the intact rock above and below the pillar. Of interest is that with the implementation of this model in the DDM codes, the parameter H is now introduced as a ‘pillar height’ parameter. A specific limit equilibrium strength relationship, σn = f(σs), also needs to be assumed. This model, implemented in the TEXAN code, has been extensively used to simulate pillar failure (e.g. Napier and Malan, 2021; Couto and Malan, 2023). 212

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Figure 2—Ongoing failure of a pillar reinforced with shotcrete at the Everest mine (after Malan and Napier, 2011) The Journal of the Southern African Institute of Mining and Metallurgy

Simulating pillar reinforcement using a displacement discontinuity boundary element code

Figure 3—Support of pillars in an area where weak clay layers resulted in pillar failure. The reinforcement consisted of two layers of shotcrete, mesh, and steel straps (after Alejano et al., 2017)

Figure 4—Failure of the pillar support illustrated in Figure 3. The photograph on the right illustrates the bolt pulling through the strap owing to the excessive dilation of the pillar (after Alejano et al., 2017)

confinement only delayed, and did not prevent, the eventual failure. In contrast, Esterhuizen, Dolinar, and Ellenberger (2011) reported the apparently successful use of rib pillar support, such as chain link mesh and bolts to prevent further deterioration of the pillars in underground stone mines in the USA. Wojtkoviak, Rai, and Bonvallet, (1985) conducted a study of the effectiveness of various approaches of pillar reinforcement based on laboratory test samples. These included mine fill, rockbolting, shotcrete or resin spraying,

and ‘steel banding’ (pillar strapping). The tests illustrated an increase in pillar strength using all these techniques, but unfortunately the study did not investigate the post-failure behaviour of pillars. A review of pillar reinforcement is also given in Alejano et al. (2017). In the Santa Rosa Mine in Spain, selected pillars were reinforced by using tensioned cables. This example is explored in more detail below. It should be noted that this proposed method will not be universally applicable as it will not prevent creep or extrusion phenomena. Andrews, Butcher, and Ekkerd (2020) reported on the reinforcement of the yield pillars in the destress cuts at the South Deep gold mine. The unsupported pillars deteriorated with time and were subsequently supported using bolts, mesh, and shotcrete. The support consists of dynamic friction bolts and 5.6 mm gauge weldmesh. The support was installed down the sidewalls of the pillars to 1.5 m from the footwall at a spacing of 1.4 m × 1.2 m. Shotcrete was later added to reduce pillar unravelling below the mesh line. The methodology used to design this reinforcement is not known. An earlier study at the same mine, based on visual observations by Sengani (2018), indicated that the bolt-reinforced in-stope pillars were subjected to extensive spalling and fracturing during seismic events, while bolt-reinforced and shotcreted pillars suffered only minor or no damage. Examination using a borehole camera showed that the pillar fractures were only minor when the pillar was supported using both bolt reinforcement and fibre shotcrete. Figure 6 shows typical pillar failure modes presented by Brady and Brown (2006). This is included to give some insight as to why pillar support may work in some cases and not in others. For pillars in massive rock where there are no weak contacts with the hangingwall and footwall, failure typically occurs by spalling from the pillar surfaces (see Figure 6a). This leads to a gradual reduction of the pillar width and will increase the stress on the pillar. For small width/height ratios, an inclined shear failure may develop in the pillar (Figure 6b). If there are weak contacts present between the pillar and the hangingwall and footwall, axial splitting of the pillar may occur (Figure 6c). If there is a joint set with a dip angle larger than the friction angle, the pillar can fail owing to slip on these joints (Figure 6d). In contrast, if the joints are sub-parallel to the loading axis, the pillar may fail by buckling of the slabs (Figure 6e). Alejano et al. (2017) hypothesized that for the first five case cases in Figure 6, cabling reinforcement will contribute to an increase in pillar stability. The deformation of the pillar will tension the cables, increasing the confining stress and, consequently, the pillar strength. This may work provided the lateral dilation and force exerted by the pillar is less than the capacity of the support. If there is a weak material forming intermediate layers or filling the discontinuities

Figure 5—Support of a manganese pillar using TSL, mesh, and cable strapping. In some cases it works well (example on the left), but in other cases the liner could not stop the ongoing deterioration of a pillar (right) The Journal of the Southern African Institute of Mining and Metallurgy

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Figure 6—Different modes of pillar failure (after Brady and Brown, 2006). The mode of failure shown in 6f may not be arrested with the cabling method

as shown in Figure 6f, the pillar support may prove ineffective, as was illustrated by the mine collapses in Southern Africa described above. To investigate the effectiveness of TSLs for reinforcing pillars, Qiao et al. (2014) conducted laboratory testing of TSL-coated rock samples. The results illustrated a significant increase in strength for the TSL-encapsulated specimens. The authors concluded that the reinforcement appears to be more effective for weaker rocks than for stronger rocks. Rock reinforcement using TSLs is effective in cases where the tensile strength of the TSL material is larger than that of the rock. A laboratory study was also conducted by Dondapati et al., (2022). They found that a 5 mm fibreglass-reinforced TSL could increase the peak strength of concrete samples by 30%, and of coal samples by nearly 50%. In summary, from the literature study it is clear that pillar reinforcement may work in some cases and may increase the strength of the pillars. A methodology to design the required support capacity and select the most appropriate support elements is not readily available, however. The next section explores a novel modelling approach that may assist in this regard.

A limit equilibrium model to simulate the effect of pillar confinement A detailed description of the limit equilibrium model and its implementation in the TEXAN code has been given in a number of

papers and it will not be repeated here (e.g. see Napier and Malan, 2014, 2021; Couto and Malan, 2022). The important extension to the model discussed in this paper is the application of a confinement stress on the pillar edge to simulate the effect of pillar reinforcement. The force equilibrium in the failed edge of a pillar is shown in Figure 7. The limit equilibrium model assumes that there is a frictional interface at the contacts between the pillar and the hangingwall and footwall. Note the confinement stress, σh, applied by the pillar reinforcement. As described above, an important extension of the model illustrated in Figure 7 is that a confining stress, σh, is applied on the skin of the pillar at x = 0 as a result of the pillar reinforcement. The seam-parallel stress component σs increases as x increases. It is assumed that the fractured rock between the dotted lines in Figure 7 is in equilibrium. From the balance of forces, it can be shown that the following differential equation applies if the width of the slice in equilibrium tends to zero: [2] The model assumes that there are frictional partings between the pillar and the hangingwall and footwall and the following slip condition applies: [3] where μI is the coefficient of friction at the interface of the pillar contacts and I is the friction angle on the interfaces. For the limit equilibrium model, a strength criterion for the failure zone needs to be adopted and it is assumed that σn is related to the seam- parallel stress component σs by the following relationship: [4] where σc and m are specified constants. In the TEXAN code, a model with two strength relationships is implemented. The failure relationship for the intact pillar material is given by the parameters m = mi and σc = σci. For the failed pillar material, the parameters m = mf and σc = σc f are adopted. When calibrating these parameters, the requirements of mi ≥ mf and σci ≥ σc f must be met.

Figure 7—An illustration of the force equilibrium in the failed portion of a pillar. The confining stress applied by the pillar reinforcement, is included in this extension of the classical model 214

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Simulating pillar reinforcement using a displacement discontinuity boundary element code Substituting Equations [4] and [3] into Equation [2] and integrating gives the following solution: [5] where A is the integration constant. The effect of the pillar reinforcement is now taken into account and the constant A is derived from Equation [5] by applying the boundary condition σs = σh when x = 0. This gives: [6] This can be inserted into Equation [5] and simplified to give [7] and furthermore [8] From Equation [8], the solution of the reef-parallel stress is derived as [9] From Equations [9] and (4), the solution for σn is given as: [10] Equation [10] implies that on the skin of the pillar when x = 0: [11] This equation is of a similar shape to that of Equation [4] but now includes the confining stress σh. Interestingly, the slope parameter m is in this equation and the model will predict large normal stresses on the edge of the pillar for high values of m and large confining stresses. This is illustrated in Figure 8. Note the rapid increase in normal stress for m = 3 and σh = 0.5 MPa. Also note the characteristic exponential increase in normal stress in the failed zone of the pillar as predicted by the limit equilibrium model. It should be noted that the model derived above has some limitations and these should be carefully considered when using this approach in a numerical model. Tendons will apply point loads, whereas the derivation above assumes a uniform load, σh, being applied on the edges of the pillar. The use of stiff strapping and liners between the bolts may result in a more uniform application of the tendon load. This limitation of the limit equilibrium model nevertheless always needs to be considered for different pillar reinforcement methods and the resulting distribution of confinement load on the pillar. One possibility would be to downgrade the value of σh when only tendons without load spreaders are used as support, but some experimentation and measurements will be required to determine realistic downgrade factors. As future work, pillar failure with and without tendon support should be simulated in a code such as FLAC3D and this should be compared to the confinement approach in the limit equilibrium model. Furthermore, the model above assumes that the support is ‘active’ and that it applies an immediate confinement to the pillar. This may be applicable if the tendons are prestressed, The Journal of the Southern African Institute of Mining and Metallurgy

Figure 8—An illustration of the effect of the confining stress on the normal pillar stress predicted by the limit equilibrium model. (a) is for a confinement of 0 MPa and (b) is for a confinement of 0.5 MPa. The graphs were plotted using the following parameters: σ = 1 MPa, φ = 30°, and H = 2 m

for example, but the numerical model needs to be extended in future to simulate the pillar dilation and the stiffness of the pillar support. This will enable the simulation of the gradual build-up of confinement as the pillar fails and dilates. As a final comment, it should be noted that these limitations are the result of the nature of displacement discontinuity boundary element codes, where the tabular excavations are simulated as a ‘slit’ without a finite height. The limit equilibrium model is simply an elegant method to introduce pillar failure in this modelling approach and its benefit is that it can simulate a large number of irregularly shaped pillars on a mine-wide scale. For a completely failed pillar, Equation [10] can be used as an illustration of the effect of confinement on the residual strength of the crushed pillar. Assume the width of the pillar is as illustrated in Figure 7 and the failure on the pillar edge and the normal stress profile illustrated in Figure 8 will be symmetrical for both sides of the pillar. As the pillar is completely failed, wc = 0, and therefore w = 2L (see Figure 7). The residual APS can then be computed by integrating Equation [10] over the width of the fracture zone pillar: [12] VOLUME 123

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Simulating pillar reinforcement using a displacement discontinuity boundary element code By considering that for the completely failed pillar, L = w⁄ 2, it follows from Equation [12] that: [13] This equation assumes that the pillar support does not fail and that it is capable of supplying the specified confinement, regardless of the amount of pillar dilation and unravelling. Equation [13] is plotted in Figure 9 for the parameters given in the caption. It is clear that increasing confinement will increase the residual strength of the pillar and a higher slope angle for the strength envelope of the failure criterion will result in a larger residual strength. As the model seems to be useful to simulate pillar confinement, the next section explores an actual case study of pillar confinement in the Santa Rosa mine.

A numerical modelling study of pillar failure and reinforcement at the Santa Rosa mine Alejano et al. (2017) describe a case study of a room-and-pillar layout in the Santa Rosa mine. The mine exploits a haematite seam that varies in thickness from 2 m to 10 m. The layout of the area of interest is shown in Figure 10. The depth of mining was 190 m. The small pillars, labelled a and b, collapsed during February 2012. In 2012 and 2013, pillars c, d, and f were strapped using cables. The

Figure 9—Effect of increasing confinement on the residual strength of a completely failed pillar. This was calculated for Vc = 4 MPa, H = 3.6 m , w = 2.45 m and I = 15o

strapping of the pillars is shown in Figure 11. Alejano et al. (2017) estimated the factor of safety (FOS) on the pillars using Hedley and Grant (1972) for the pillar strength and tributary area theory (TAT) to estimate the pillar stress. This information is given in Table I. Pillars h and i were part of a single pillar before it was split and which is still included as a single pillar in the table. The pillar height varied from 3.5 m to 4.5 m. An average height of 3.6 m was therefore used for the numerical modelling described in the section below. The calculated FOS values for pillars a and b are close to unity and this therefore correctly predicted that these two pillars were at risk of collapsing. In terms of the mechanism of pillar failure, a horizontal parting is visible for the pillar in Figure 10. The material also appears to be highly jointed and it seems as if the horizontal parting is facilitating the unravelling of discontinuous material. This most likely occured in a time- dependent fashion, but no data is available in this regard and it will therefore not be considered in this study. The case study above was selected for modelling as the cable strapping seemed to arrest the deterioration of the pillars. Pillar f in Figure 11 was supported during June 2013. The extensive spalling of the pillar can be seen in the figure when comparing the width of the strapped portion to the original size of the pillar visible in the upper portion of the photograph. No further deterioration was noted after the strapping, and observations made three years later during January 2016 confirmed the stability of the pillar. The TEXAN code used in this study is a displacement discontinuity boundary element code that was specifically developed to simulate a large number of small pillars in tabular layouts (Malan and Napier, 2006). It allows for the use of triangular

Figure 11—Example of reinforcement of a pillar using cables and mesh in the Santa Rosa mine. This is pillar f in Figure 10 (after Alejano et al., 2017)

Figure 10—Layout of the area used in the case study simulated below (after Alejano et al., 2017). The photograph on the right illustrates the condition of pillar b before it collapsed 216

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Simulating pillar reinforcement using a displacement discontinuity boundary element code Table I

Calculation of the FOS for the pillars shown in Figure 10 (after Alejano et al., 2017). The symbol e refers to the extraction ratio and weff is the effective width (Wagner, 1974) of an equivalent square pillar Pillar area m2

Supported area m2

e %

Depth m

weff m

H m

Pillar stress MPa

Pillar strength MPa

FOS

w/H

13.08

73.54

190

3.06

3.5

29.90

34.00

1.14

0.87

19.50

96.00

190

3.97

4.5

26.20

32.10

1.22

0.88

34.65

92.06

190

4.84

3.5

14.30

42.80

3.03

1.38

29.66

89.07

190

4.41

3.5

16.00

40.90

2.56

1.26

63.01

132.40

190

6.93

3.5

11.18

51.17

4.58

1.98

42.01

123.59

190

5.63

3.5

15.65

46.15

2.95

1.61

107.90

204.98

190

8.89

3.5

10.11

58.00

5.74

2.54

h-i

139.86

216.01

190

9.32

3.5

8.22

59.40

7.23

2.66

Pillar

boundary elements, which circumvents the problem of ‘partially mined’ elements encountered using square element shapes. The simplified ‘two-dimensional’ limit equilibrium model described above had to be extended for use in the TEXAN code to simulate the actual irregular pillar shapes in three dimensions (see Napier and Malan, 2021). A useful feature of the TEXAN code is that it can simulate pillar failure behaviour on a stope-wide scale by using the limit equilibrium model. Details of the use of this constitutive model can be found in du Plessis, Malan, and Napier (2011) and Napier and Malan (2012, 2014, 2018). A drawback of the model is that the failure is restricted to the plane of the reef. It is nevertheless an elegant method to simulate failure on the reef horizon in a large mine-wide model. The geometry simulated in TEXAN is illustrated in Figure 12. This layout represents the 2012 geometry prior to the collapse of pillars a and b. The pillars had to be covered with a triangular mesh to enable the calculation of the APS. Figure 13 illustrates the mesh for pillar c. The mesh used for the pillars and mined areas had to be small to ensure an accurate calculation of the APS values (see Napier and Malan, 2011) and also that the limit equilibrium model provides an accurate simulation of the extent of failure in the pillars (Malan and Napier, 2018). The element sizes used for this study were therefore small, approximately 0.09 m2 on average.

Numerical modelling using rigid pillars As a first modelling step, the pillars were not allowed to fail and were simulated as ‘rigid’ pillars that were not allowed to deform. This enabled an accurate calculation of the average pillar stresses. Figure 14 illustrates the simulated APS values for the pillars. Table II illustrates the pillar sizes and compares the simulated APS values with those given by Alejandro et al. (2017). Although there is rough agreement between the values, the numerically simulated values are more accurate as the effect of the abutments is taken into account. Tributary area theory is a crude assumption for a geometry with such a small overall span.

Simulating pillar failure using a limit equilibrium model The limit equilibrium model currently implemented in TEXAN requires a large number of parameters to be calibrated, and these are listed in Table III. The values in Table III are only crude approximations for the Santa Rosa mine as they were derived from values calibrated by the authors for a different hard-rock mine The Journal of the Southern African Institute of Mining and Metallurgy

Figure 12—The layout that was simulated using the TEXAN code. Small triangular displacement discontinuity elements were used to represent the geometry. The pillars were also covered by the mesh, but it is not shown in this figure

where pillar failure occurred. The rigid pillar simulation described above was repeated using this limit equilibrium failure model. No confining stress was applied to the pillars for the first simulation. The simulated APS values are illustrated in Figure 15. These can be compared to Figure 14. For the pillars that completely failed (shown in Figure 16), the stress decreased to a residual value slightly above 4 MPa. These residual strength values are determined by the residual strength and slope parameter values (see Table III). The pillars that did not fail (e, g, h, and i) illustrate an increase in stress as they carry some of the additional load originating from the failed pillars (a, b, c, d, f). In the subsequent simulations, the effect of pillar confinement was modelled by gradually increasing the confinement, σh. The amount of confinement applied by the various types of support needs to be quantified in future, so these preliminary runs were done simply to provide a qualitative illustration of the effect of VOLUME 123

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Simulating pillar reinforcement using a displacement discontinuity boundary element code Table II

A comparison of the simulated APS values and those calculated by Alejandro et al., (2017) using TAT Pillar

Figure 13—Example of the mesh generated for pillar c

Size (m2) in model

APS (TAT) (MPa)

APS (TEXAN) (MPa)

6.54

29.9

22.17

9.28

26.2

18.98

18.43

14.3

15.86

14.51

17.34

28.08

11.18

14.23

15.23

15.65

17.11

33.98

10.11

12.42

84.72

26.4

8.22

10.76 12.59

Table III

Parameters used for the limit equilibrium model Parameter

Value

Intact strength intercept, σci

25.0 MPa

Intact strength slope, mi

2.0

Residual strength intercept, σc

4.0 MPa

Residual strength slope, m

2.0

Effective seam height, H

3.6 m

Intact rock Young’s modulus, E

148 000. MPa

Intact rock Poisson’s ratio, ν

0.24

Fracture zone interface friction angle,φI

15°

Seam stiffness

41 111 MPa/m

Figure 14—Simulated APS values for the pillars

Figure 15—Simulated APS values when using a limit equilibrium model and no pillar confinement is applied

confinement. Figures 16, 17, and 18 illustrate the decrease in failure in the pillars for increasing confinement. This is an encouraging result and the approach described in this paper therefore seems to be a useful method to simulate the effect of pillar confinement using displacement discontinuity codes. Of interest is that the 0.02 MPa 218

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Figure 16—Illustration of the simulated pillar failure for a confinement of zero MPa. The yellow portions of the pillars are intact and the orange colour indicates failure

confinement is of the same order as the value of 0.05 MPa measured by Galvin and Wagner (1982) at their experimental site where ash fill was used to reinforce coal pillars. The Journal of the Southern African Institute of Mining and Metallurgy

Simulating pillar reinforcement using a displacement discontinuity boundary element code

Figure 19—The failed pillar area for different pillars as a function of confinement Figure 17—Illustration of the simulated pillar failure for a confinement of 0.02 MPa. The yellow portions of the pillars are intact and the orange colour indicates failure. Substantially less pillar failure is noted for this small amount of confinement

The decrease in the extent of failure is also more gradual for this pillar with increasing confinement at the greater depth of 220 m. In summary, these simulations indicate that the design of pillar confinement to prevent pillar spalling will be dependent on the pillar size, the strength of the pillar material, and depth of the excavation (the stress acting on the pillar). Simplified design rules for pillar reinforcement will therefore be difficult to provide and every case should be assessed on its own merits. Numerical modelling will have to be conducted to determine the various parameters. For the approach described in this paper, the pillar strength will have to be assessed to calibrate the limit equilibrium model. Furthermore, the confinement that can be supplied by the various pillar support systems needs to be known.

Conclusions

Figure 18—Illustration of the simulated pillar failure for a confinement of 0.7 MPa. The yellow portions of the pillars are intact and the orange colour indicates failure. For this value of confinement, only the corners of pillars a and d showed signs of spalling (barely visible in the diagram)

Figure 19 illustrates the decrease in pillar failure for increasing confinement. As expected, the smallest pillar (pillar a) requires a higher value of confinement to reduce the extent of failure compared to pillars b and d. The stress acting on pillar a is higher owing to its small size (Figure 14 and Table II) and a higher confinement is therefore required. Also interesting is that for the selected limit equilibrium parameters, the small pillars, and the selected depth, there is a ‘threshold’ value of confinement that causes a sudden, significant decrease in the extent of failure. To illustrate the difficulty of designing appropriate pillar confinement, the layout was also simulated at a greater depth of 220 m using the same limit equilibrium parameters for the rock material. The increase in confinement required at this greater depth to stabilize the pillars are shown in Figures 20, 21, and 22. Pillar h is larger and requires less confinement. The Journal of the Southern African Institute of Mining and Metallurgy

Tendons, strapping of the pillars and shotcrete or thin spray-on liners are occasionally used to reinforce pillars in bord-and-pillar layouts. A trial-and-error approach is mostly followed in industry to design this type of support. In some cases, the reinforcement does not work and ongoing pillar deterioration occurs. A methodology therefore needs to be developed to determine the capacity of the required support and in which of the cases pillar reinforcement will work. A limit equilibrium model, with the option to apply confinement on the edge of the fracture zone, was investigated as a modelling methodology to study pillar confinement. The model correctly predicted that an increase in confinement leads to a decrease in the extent of pillar failure and therefore a more stable layout. As the displacement discontinuity boundary element method allows for the efficient solution of large-scale bord-andpillar layouts, the effect of pillar confinement can now be studied in the context of real pillar layouts. The appropriate support capacity of the pillar reinforcement can be determined using a quantitative approach. In its current form the model is useful to simulate the effect of pillar confinement and to select the required support capacity of the pillar reinforcement, provided an accurate calibration of the model can be done. This may be difficult, however, and further work is needed in this regard. Selecting an appropriate value for the confinement, σh, applied by the support may be particularly VOLUME 123

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Simulating pillar reinforcement using a displacement discontinuity boundary element code of the gradual build-up of confinement as the pillar fails and dilates. Further work also needs to be done to obtain more accurate calibrations of the limit equilibrium model for different pillar types. The confinement applied by various types of support systems, comprising bolts, strapping, and liners needs to be determined.

Acknowledgements This work forms part of the PhD study of Johann Esterhuyse at the University of Pretoria. The authors would like to thank Professor John Napier for his kind assistance and the original implementation of the confinement model in the TEXAN code.

References Figure 20—The failed pillar area for pillar a as a function of confinement at two different depths

Andrews, P.G., Butcher, R.J., and Ekkerd, J. 2020. The geotechnical evolution of deep-level mechanized destress mining at South Deep mine. Journal of the Southern African Institute of Mining and Metallurgy, vol. 120. pp. 33–40. Alejano, L.R., Arzúa, J., Castro-filgueira, U., and Malan, F. 2017. Strapping of pillars with cables to enhance pillar stability. Journal of the Southern African Institute of Mining and Metallurgy, vol. 117, no. 6. pp. 527–540. Brady, B.H.G. and Brown, E.T. 2006. Rock Mechanics for Underground Mining. 3rd edn. Springer. Couto, P.M. and Malan, D.F. 2023. A limit equilibrium model to simulate the large-scale pillar collapse at the Everest Platinum Mine, Rock Mechanics and Rock Engineering, vol. 56. pp. 183–197. Dondapati, G.P., Deb, D., Porter, I., and Karekal, S. 2022. Improvement of Strength-Deformability Behaviour of Rock-Like Materials and Coal Using Fibre-Reinforced Thin Spray-on Liner (FR-TSL). Rock Mechanics and Rock Engineering, vol. 55. pp. 3997–4013. Du Plessis, M., Malan, D.F., and Napier, J.A.L. 2011. Evaluation of a limit equilibrium model to simulate crush pillar behaviour. Journal of the Southern African Institute of Mining and Metallurgy, vol. 111. pp. 875–885.

Figure 21—The failed pillar area for pillar d as a function of confinement at two different depths

Esterhuizen, G.S., Dolinar, D.R., and Ellenberger, J.L. 2011. Pillar strength in underground stone mines in the United States. International Journal of Rock Mechanics and Mining Sciences, vol. 48, no. 1. pp. 42–50. Galvin, J.M. and Wagner, H. 1982. Use of ash to improve strata control in bord and pillar workings. Proceedings of the Symposium on Strata Mechanics, Newcastleupon-Tyne, 5-7 April 1982. Farmer, I.W. (ed.). Elsevier, Amsterdam. Ghee, E.H., Zhu, B.T., and Wines, D.R. 2011. Analysis of twin road tunnels using numerical modelling techniques. Proceedings of the 14th Australasian Tunnelling Conference: Development of Underground Space. Ausyralasian Institute of Mining and Metallurgy, Melbourne. pp. 443–454. Hedley, D.G.F. and Grant, F. 1972. Stope-and-pillar design for the Elliot Lake Uranium Mines. Bulletin of the Canadian Institute of Mining and Metallurgy, vol. 65. pp. 37–44. Itasca Consulting Group, Inc. 2022. FLAC3D Documentation,Minneapolis, MN. Jessu, K.V., Spearing A.J.S, and Sharifzadeh, M. 2018. A parametric study of blast damage on hard rock pillar strength. Energies, vol. 11. 1901.

Figure 22—The failed pillar area for pillar h as a function of confinement at two different depths

challenging. Furthermore, the work presented in this paper assumes that the support is ‘active’ and it applies an immediate confinement to the pillar. This needs to be extended to simulate the pillar dilation and the stiffness of the pillar support. This will enable the simulation 220

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Malan D.F. and Napier J.A.L. 2006. Practical application of the Texan code to solve pillar design problems in tabular excavations. Proceedings of the SANIRE Symposium “Facing the challenges”, Rustenburg, South African National Institute of Rock Engineering. pp. 55–74. Malan, D.F. and Napier, J.A.L. 2011. The design of stable pillars in the Bushveld mines: A problem solved? Journal of the Southern African Institute of Mining and Metallurgy, vol. 111. pp. 821–836. Malan, D.F. and Napier, J.A.L. 2018. Reassessing continuous stope closure data using a limit equilibrium displacement discontinuity model. Journal of the Southern African Institute of Mining and Metallurgy, vol. 118, no. 3. pp. 227–234. The Journal of the Southern African Institute of Mining and Metallurgy

Simulating pillar reinforcement using a displacement discontinuity boundary element code Motamedi, M.H. and Najafi, M. 2021. A numerical simulation of bolt grouting reinforcement for reducing the optimum dimensions of jointed hard rock pillars in Faryab chromite mine (Iran). Geotechnical and Geological Engineering, vol 39. pp. 4747–4763. Naidoo, K., Handley, M.F., and Leach, A.P. 2008. Applying numerical modelling to pillar design in South African mines — An initial study. SHIRMS 2008: Proceedings of the First Southern Hemisphere International Rock Mechanics Symposium. Potvin, Y., Carter, J., Dyskin, A., and Jeffrey, R. (eds.). Australian Centre for Geomechanics, Perth. pp. 379–390. Napier, J.A.L. and Malan, D.F. 2011. Numerical computation of average pillar stress and implications for pillar design. Journal of the Southern African Institute of Mining and Metallurgy, vol. 111. pp. 837–846.

Sengani, F. 2018. The performance of bolt-reinforced and shotcreted in-stope pillar in rockburst-prone areas. International Journal of Mining and Geo-Engineering, vol. 52, no. 2. pp. 105–117. Sinha, S. and Walton, G. 2021. Modelling the behaviour of a coal pillar rib using Bonded Block Models with emphasis on ground-support interaction. International Journal of Rock Mechanics and Mining Sciences, vol. 148. doi: 10.1016/j.ijrmms.2021.104965 Siwak J.M. 1984. Carrieres de craie du Nord de la France. Comportement des piliers et confortation par gunitage. [Shale quarries in northern France. Pillar behaviour and shotcrete support]. PhD thesis. Université des Sciences et Techniques de Lille [in French].

Napier, J.A.L. and Malan, D.F. 2012. Simulation of time-dependent crush pillar behaviour in tabular platinum mines. Journal of the Southern African Institute of Mining and Metallurgy, vol. 112. pp. 711–719.

Spencer, D. 1999. A case study of a pillar system failure at shallow depth in a chrome mine. Proceedings of SARES99, 2nd Southern African Rock Engineering Symposium. Hagan, T.O. (ed.). South African National Institute of Rock Engineering. pp. 53–59.

Napier, J.A.L. and Malan, D.F. 2014. A simplified model of local fracture processes to investigate the structural stability and design of large-scale tabular mine layouts. Proceedings of the 48th US Rock Mechanics / Geomechanics Symposium, Minneapolis, MN. American Rock Mechanics Association, Alexandria, VA.

Wagner, H. 1974. Determination of the complete load-deformation characteristics of coal pillars. Proceedings of the 3rd ISRM Conference, Denver, CO. Vol IIB, Advances in Rock Mechanics, International Society for Rock Mechanics and Rock Engineering, Lisbon. pp. 1076–1081.

Napier, J.A.L. and Malan D.F. 2018. Simulation of tabular mine face advance rates using a simplified fracture zone model. International Journal of Rock Mechanics and Mining Sciences, vol. 109. pp. 105–114.

Wojtkoviak, F., Rai, M.A., and Bonvallet, J. 1985. Études expérimentales en laboratoire de différentes méthodes de renforcement des petits piliers de mine [Experimental studies in laboratory of different reinforcement methods to be applied on small mining pillars]. Bulletin of the International Association of Engineering Geology, vol. 32. pp. 131–138.

Napier, J.A.L. and Malan D.F. 2021. A limit equilibrium model of tabular mine pillar failure. Rock Mechanics and Rock Engineering, vol. 54. pp. 71–89. Qiao, Q., Nemcik, J., Porter, I., and Baafi, E. 2014. Laboratory investigation of support mechanism of thin spray-on liner for pillar reinforcement. Geotechnique Letters, vol. 4. pp. 317–321.

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York, G. 1998. Numerical modelling of the yielding of a stabilizing pillar/foundation system and a new design consideration for stabilizing pillar foundations, Journal of the Southern African Institute of Mining and Metallurgy, vol. 98, pp. 281–298.

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he Southern African Pyrometallurgy Conference ĮÐīðÐĮ ìĮ ÆďŒÐīÐÌ īĊæÐ ďå ĴìÐĉÐĮ ĮðĊÆÐ ĴìÐ ťīĮĴ edition in 2006. The Southern African Pyrometallurgy 2024 International Conference will structure a programme which covers crucial aspects of this continually evolving ĊÌ ÐŘÆðĴðĊæ ťÐăÌ ĴďœīÌĮ ĮķĮĴðĊÅăÐ ĨřīďĉÐĴăăķīæřȘ AĴ ðĮ envisaged as an international conference on pyrometallurgy œðĴì wďķĴìÐīĊ åīðÆĊ ŦŒďķīȘ

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A study of backﬁll conﬁnement to reinforce pillars in bord-and-pillar layouts D. Ile1 and D.F. Malan1

Afﬁliation: 1Department of Mining Engineering,

University of Pretoria, South Africa.

Correspondence to: D.F. Malan

Email: francois.malan@up.ac.za

Dates: Received: 13 Nov. 2022 Revised: 4 Apr. 2023 Accepted: 30 May 2023 Published: May 2023

Synopsis This study explores the use of backfill in hard rock bord-and-pillar mines to increase the pillar strength and extraction ratio at depth. The use of backfill will also minimize the requirement for tailings storage on surface and the risk of environmental damage. A literature survey indicated that backfill is extensively used in coal mines, but rarely in hard rock bord-and-pillar mines. To simulate the effect of backfill confinement on pillar strength, an extension of the limit equilibrium model is proposed. Numerical modelling of an actual platinum mine layout is used to illustrate the beneficial effect of backfill on pillar stability at greater depths. The magnitude of confinement exerted by the backfill on the pillar sidewalls is unknown, however, and this needs to be quantified using experimental backfill mining sections equipped with suitable instrumentation.

Keywords backfill, bord-and-pillar, pillar strength, limit equilibrium model.

How to cite: Ile, D. and Malan, D.F. 2023 A study of backﬁll conﬁnement to reinforce pillars in bord-and-pillar layouts. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 5. pp. 223–234 DOI ID: http://dx.doi.org/10.17159/24119717/2452/2023

Introduction There is still uncertainty regarding the strength of the pillars in the shallow tabular excavations of the Bushveld Complex (e.g. Malan and Napier, 2011; Couto and Malan, 2022). The Hedley and Grant (1972) empirical formula is typically used to estimate pillar strength. Historically, one-third of the laboratory uniaxial compressive strength value of the pillar material was used for the K-value in the formula for South African mines. Stacey and Page (1986) suggested the use of the DRMS (design rock mass strength; Laubscher, 1990) as the K-value. Many stable layouts have been designed using these formulae. The lack of precise knowledge regarding pillar strength nevertheless causes a conservative approach to be adopted in many cases. This, in conjunction with the adoption of a factor of safety of 1.6, as used in the coal mining industry (Ryder and Jager, 2002), possibly resulted in oversized pillars. As the mining depths increase, the pillar sizes will increase further. This will be detrimental to the extraction ratio and the profitability of the mines in future. The placement of backfill in underground stopes presents an opportunity to minimize the damage that mining causes to the environment (Zhang et al., 2019). Tailings production is inherent to minerals processing. The International Council on Mining and Metals (ICMM, 2022) recently published a Tailings Reduction Roadmap. The motivation for this study was the catastrophic tailings dam failures at Mount Polley in Canada (2014), Samarco in Brazil (2015), and Brumadinho in Brazil (2019). South Africa is not immune to this type of failure, as illustrated by the Merriespruit disaster (1994) and the more recent failure of the tailings dam at the Jagersfontein mine. The ICMM investigated technologies that can minimize tailings production. Their proposals focused on the following aspects. ³ Precision geology: Geological techniques are needed to better characterize the orebody to maximize ore production and minimize the mining of waste rock. This will reduce the amount of tailings generated. ³ Precision mining: This also aims to reduce the mining of waste rock and the amount of tailings generated. ³ Precision segregation: This focuses on better segregation technology to optimize mineral recovery and produce more benign tailings. ³ In-situ recovery: Leaching techniques can possibly be used to optimize mineral recovery and eliminate the production of waste rock. ³ Tailings enhancement: This requires the creation of value from tailings to minimise the requirements for tailings storage.

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Figure 1—Different systems useed to place backfill in coal mines. (a) Pumped slurry, (b) pneumatic filling, (c) grout injection (after Palarski, 1993)

[3] where σs is the pillar strength. This can be rearranged as: [4] Equation [4] can be inserted in Equation [2] to give: [5] As described above, a power-law strength formula is typically used to determine the pillar strength in South African mines. The general form of the power-law can be written as (Malan and Napier, 2011):

Figure 2—A regular bord-and-pillar layout used to define the extraction ratio, e

The use of tailings to reinforce pillars and enable pillar sizes to be reduced is part of the last aspect, which is explored in this paper. The increased profitability of the mine when using smaller pillars may offset the additional infrastructure and maintenance required for using backfill in underground workings. Figure 1 illustrates some of the systems used in coal mines to place the backfill. These methods are beyond the scope of this paper and the focus will be on the effect of backfill confinement on pillar strength.

[1] where ρ = density of the rock g = gravitational acceleration e = extraction ratio H = depth of mining Equation [1] can be rearranged to give the extraction ratio as: [2] To prevent failure of the pillars, a factor of safety (SF) is adopted for the design, and this is given by: VOLUME 123

[7]

[8]

As an illustration of the detrimental effect of depth on the extraction ratio in bord-and-pillar workings, consider the layout shown in Figure 2. A similar approach was described by Malan and Esterhuyse (2021), but a more general equation is derived below. The dip of the layout is considered to be 0° and the extent of mining in the two lateral directions is considered to be very large. Tributary area theory (TAT) can therefore be used as a good approximation to calculate the stresses acting on the pillars (Ryder and Jager, 2002). The average pillar stress (APS) for the layout in Figure 2 is given by Ryder and Jager (2002) as:

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where K is the strength of the rock material in the pillar, w is the pillar width, and h is the pillar height. The values for the exponents α and β must be determined for the particular pillar type. Equation [6] can be inserted in Equation [5] to give:

where

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[6]

From Equation [7], the extraction ratio e is therefore a simple decreasing linear function of the depth, H, and the rate of decrease is dependent on the parameter γ. This parameter is a function of the assumed pillar strength, the overburden density, and the factor of safety and should preferably be as small as possible. From Equation [8], there are not many options to increase the extraction ratio. For example, the mining height can be reduced, but this is not always feasible owing to the reef width or the minimum height limitations imposed by the equipment used. A further subtle aspect of Equations [7] and [8] is that the extraction ratio can be increased by increasing the pillar width (increasing the pillar strength), which will enable the bord spans to be increased. However, this is not always feasible. The decrease in extraction ratio predicted by Equation [7] is illustrated in Figure 3 for a typical bord-and-pillar mine in the Bushveld Complex. The factor of safety for the pillars is maintained at a value of 1.6 g = 9.81 m/s2, the overburden density is 3000 kg m3, the mining height is assumed to be 2 m, and the pillar width is maintained at 7 m. The Hedley and Grant pillar strength formula is assumed and therefore α = 0.5 and β = 0.75. If the UCS of the laboratory samples is 100 MPa, when adopting the classical rule for the strength of the pillar material it follows that K = ⅓UCS = 33 MPa. The Journal of the Southern African Institute of Mining and Metallurgy

A study of backﬁll conﬁnement to reinforce pillars in bord-and-pillar layouts

Figure 3—Relationship between mining depth and extraction ratio

From Figure 3 it follows that an extraction ratio of 1.6 can be maintained only up to a depth of 280 m. This is problematic for mines planning to implement mechanized bord-and-pillar operations at greater depths. Research is currently being conducted to determine better estimates of pillar strength so as to investigate if higher extraction ratios can be maintained at greater depths and with pillars containing weak material (Watson et al., 2022, Couto and Malan, 2022). An alternative is to use methods to artificially increase the pillar strength. This paper describes a study of using backfill to reinforce the pillars. Smaller pillars could then possibly be used at greater depths and the extraction ratio increased.

Examples of the use of backfill to reinforce or extract pillars Backfill is commonly used as mine support. For example, in South Africa it is used for regional and local support in deep gold mine stopes. It is also used in shallow operations to enable multi-reef extraction (see e.g. Squelch, 1993; Ryder and Jager, 1999). There is a vast amount of literature available on backfill and the types of backfill, but the objective of this paper is not to summarize these studies. The focus is on exploring the use of backfill to increase pillar strength for bord-and-pillar mining layouts. From a literature study on this narrow aspect, it appears that the use of backfill to reinforce pillars and minimize environmental damage is mostly confined to the coal mining sector. Extensive use is made of this method in the Chinese coal mines, as described by Zhang et al. (2019). It appears the backfill is mostly used in conjunction with high extraction mining methods such as longwalling, with the backfill being placed in the goaf area. Apart from the environmental

aspects, the use of backfill is mainly for control of surface subsidence. The Polish coal mining industry also uses backfilling in their longwalls, as described by Palarski (1994). Tailings backfill was introduced as early as 1893 in these mines. The main reasons for backfilling are to support the roof, to prevent movement of the rock mass, and to eliminate the fire hazard in old mine workings. The backfill methods described above are employed to increase the stability of longwall stopes and prevent or minimize subsidence. Only a few studies of using backfill to enhance pillar strength could be found. For South African coal mines, backfilling was studied as a method to stabilizing under-designed bord and pillar layouts and to achieve higher recoveries by increasing pillar height in thick seam conditions (Galvin and Wagner, 1982; Buddery, 1985). This work is described in more detail later. Salamon and Oravecz (1976) describe the benefits of ash, sand, or waste filling in coal mines. Practical experience indicated that filling can arrest the gradual deterioration of pillar areas. As the backfill is typically not in contact with the roof, the fill will not transmit any pressure between the roof and floor. The load on the pillars is therefore not reduced. The benefit of the fill is the lateral pressure it exerts on the pillar sidewalls, which can increase the strength of the pillars. The more important benefit arises when the pillars are failing and undergoing significant lateral expansion. The effectiveness of the fill will depend on the compaction of the material and the height of the fill in relation to pillar height. Hydraulically transported material may therefore be more effective than fill introduced in a dry state. In terms of fill height, the dilation of pillars is typically the greatest at mid-height and the fill height must be greater than this. Salamon and Oravecz (1976) recommended that the fill height should extend to at least twothirds of the mining height. Donovan (1999) studied the effects of backfilling in coal mining and derived revised pillar strengths that arose from the confining effect of backfill. An increase in extraction from 3% to 32% was predicted. Zhang et al. (2017) proposed a method to extract coal pillars using backfill support (Figure 4). Two rows of pillars are mined incrementally. The backfill is transported to the area using a belt conveyer and placed in the goaf using a so-called ‘high-speed power material thrower’. A bulldozer is used to compact the backfill. It is not clear if this method was successfully implemented in practice. Kostecki and Spearing (2015) used FLAC3D modelling to investigate the effect of various fill heights on pillar strength. The study indicated a 40% increase in pillar strength when a cohesive backfill material is used and 75% of the mining height is filled. Shen et al. (2017) conducted FLAC3D modelling of coal pillars to study

Figure 4—Method proposed by Zhang et al. (2017) for mining coal pillars using backfill support The Journal of the Southern African Institute of Mining and Metallurgy

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Figure 5—Pillar extraction at the Buick Mine using cemented rock fill. Part of the fill fence is shown on the right. Note the large height of the pillars (after Tesarik. Seymour, and Yanske, 2009

the effect of backfill consisting of non-cohesive fly ash grout in a typical bord-and-pillar mine. A single pillar with various fill heights was simulated. The stress/strain behaviour of the pillar changed from strain softening at low fill percentages to strain hardening at fill percentages above approximately 70%. Mo et al. (2018) used FLAC2D modelling to quantify the effect of backfilling on pillar strength in highwall mining. The simulated behaviour of pillars was found to vary with the type and percentage of backfill placed as well as the pillar width to height ratio. For cohesive backfill, 75% backfilling resulted in a significant increase in peak pillar strength, especially for pillars with lower width to height ratios. For noncohesive backfill, the effect of the backfill was less pronounced. An example of successful pillar extraction in a hard rock mine using backfill is given by Tesarik. Seymour, and Yanske (2009). Figure 5 illustrates the test area, with a size of approximately 107 m × 69 m, in the Buick Mine, St Louis, Missouri. The pillar heights were 14 m to 19 m and the widths were approximately 9 m. The pillars were slender with a width to height ratio of less than 1. These pillar dimensions are therefore not comparable to the pillar sizes in the bord-and-pillar operations in the Bushveld Complex. Prior to extraction, a fill fence was constructed around the pillars (Figure 5). Cemented rock fill was used and the numbered pillars were successfully mined. The so-called ‘trapped pillars’ were excavated using an access drift in the footwall. This is not deemed a feasible method for the mines in the Bushveld Complex, however, as the

Figure 6—A backfill paddock in a deep tabular gold mine. The stope closure compressed the backfill and the lateral dilation broke the elongates used to construct the paddock 226

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pillar volumes are much smaller and building the fill fence may be problematic for a large area. The trapped pillars can also not be accessed via footwall development. In the South African hard rock mining industry, backfill is typically only used in the deep gold mines to reduce stope closure and the associated energy release rates, and to minimize the risk of rockbursts (Jager and Ryder, 1999). A typical backfill paddock in one of these tabular stopes is illustrated in Figure 6. Most historical studies of backfill in the tabular gold mine stopes focused on the reef-normal closure (to reduce the energy release rates) and the stress generated in this direction. For the application of backfill to strengthen the pillars in a bordand-pillar layout, the horizontal stress component is important. The convergence in these layouts is very small and therefore almost no vertical stress will be generated in the backfill apart from the gravitational component owing to the weight of the material. The panel deformation will also occur before the backfill is placed and therefore it can be assumed that no closure will act on the backfill. This negates the need for tight filling and backfill contact with the hangingwall is not required. Salamon and Oravecz (1976) noted that the beneficial effect of backfill in bord-and-pillar layouts is due to the pressure that it exerts on the pillar sidewalls, thereby increasing the strength of the pillars. Figure 7 illustrates measurements conducted inside backfill in a gold mine. The instrumentation recorded the vertical stress as well as the lateral stress in the dip and strike directions. An example of typical backfill load cell instrumentation is shown in Figure 8. The stress in the lateral directions became meaningful only if the strain in the vertical direction exceeded approximately 0.1. This implies that for a bord-and-pillar layout with a mining height of 2.5 m, at least 250 mm of closure needs to be recorded after the backfill is placed. This is not observed for the hard rock bord-and-pillar layouts in the Bushveld Complex, except for the rare cases where large-scale pillar collapses occur (Couto and Malan, 2022). In an experimental pillar mining set-up where some of the pillars failed and the spans were substantially increased (see Napier and Malan, 2021), the maximum recorded closure was in the order of 12 mm. The mining height was 2.5 m and the strain on the backfill was therefore only be 5 millistrains. A further problem with backfill in flat-dipping tabular stopes is that good contact with the hangingwall cannot be achieved. The Journal of the Southern African Institute of Mining and Metallurgy

A study of backﬁll conﬁnement to reinforce pillars in bord-and-pillar layouts Estimating the pillar confinement exerted by backfill

Figure 7—Stress recorded in backfill for increasing strain (after Piper, Gürtunca, and Maritz, 1993)

The historical measurements of horizontal stress in backfill in the South African gold mines were not sensitive enough to determine the magnitude of the stress at small strains. Some estimation of the horizontal stress therefore needs to be made for the numerical modelling described in the next section. For coal pillars and ash filling, Buddery (1985) estimated that the strain in the ash fill would be 1.7 × 10-3 and this translated to a confinement stress of 0.05 MPa when assuming a modulus of 27 Mpa, and 0.51 MPa for a modulus of 300 MPa. As a crude estimate of the increase in pillar strength, Buddery assumed a ‘Coulomb failure criterion’ for these pillars and demonstrated that a 13.6% increase in pillar strength is possible for the higher modulus and confining stress. The application of this failure criterion and the associated assumptions are highly uncertain, however. Galvin and Wagner (1982) studied the use of ash filling to improve strata control in coal bord-and-pillar workings. For the notation shown in Figure 9, the fill reaction stress (pillar confinement stress), σF, is given by: [9] where εF is lateral fill strain, EF is the fill modulus, and the fill stiffness, kF (MN/m3) is given by: [10]

Figure 8—Example of load cells installed in a backfill paddock to record the stresses generated in different directions

Blight and Clarke (1983) investigated the relationship between the lateral and vertical stress for soft and stiff fills. The ratio of lateral to vertical stress was found to vary from 0.1 to 0.45 for stiff fills and 0.4 to 0.7 for soft fills. They noted that backfill can therefore support pillars, but conceded that significant vertical strains are necessary to develop the lateral stress. As the vertical strains are very low in shallow bord-and-pillar operations, a different approach will have to be used to estimate the lateral confinement exerted by the backfill on the pillars. Rankine theory is useful as a first approximation, and is discussed in the next section.

From Equation [9] it follows that a large pillar confinement stress can be achieved only if the fill stiffness is high. From Equation [10], this stiffness is proportional to the fill modulus, EF, and inversely proportional to the bord width. The authors note that the dilation of failing pillars is greatest at mid-height and therefore the fill depth must be more than the half the pillar height, and preferably two-thirds of this height. Galvin and Wagner (1982) describe an underground experiment where ash filling was used. The original factor of safety of the pillars was 1.3. Top-coal mining was done to decrease the width to height ratio of the pillars and ash fill was placed. The upper 3 m portions of the pillars were not covered by the fill. Although the final factor of safety decreased to 0.6, the area remained stable. The upper, uncovered parts of the pillars underwent only minimal slabbing. The lateral stress in the ash fill was measured at 0.05 MPa. Interestingly, this is similar to the stress estimated by Buddery (1985) for a fill modulus of 27 MPa. An alternative estimate of the pillar confinement stress can be made using calculations of lateral earth pressure (e.g., Rankine, 1856; Pantelidis, 2019). Lateral earth pressure is the pressure that

Figure 9—Ash filling in a coal mine (after Galvin and Wagner, 1982) The Journal of the Southern African Institute of Mining and Metallurgy

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[15]

[16] If the friction angle of the backfill is assumed to be 30°, then by using Equation [14], the at rest lateral earth pressure coefficient is calculated to be K0 = 0.5. Furthermore, as a simplification, if the force P (from Equation [13]) acts along a pillar of height h, the average confinement stress along the pillar face is

Figure 10—Stress distribution on a wall retaining a mass of soil (after Shamsabadi, Dasmeh, and Taciroglu, 2017)

[17]

soil exerts in the horizontal direction. This pressure is important for the design of geotechnical engineering structures such as retaining walls. The coefficient of lateral earth pressure, K, is defined as [11

[11]

where σh is the horizontal or lateral stress and σv is the vertical stress. As the vertical stress in soil is given by σv = γh where γ is the density of the soil and h is the depth of the soil, Equation [11] can be written as [12] Equation [12] results in the pressure distribution shown in Figure 10. The vertical stress (and therefore the horizontal stress) gradually increases with soil depth. At the surface of the soil, the stress will be zero, increasing linearly to a maximum value at the bottom of the retaining wall. The equivalent lateral earth force, shown in Figure 10 as P, which acts one-third of the height up the wall, can be obtained by integrating Equation [12] along h: [13] There are three different values for K, namely: ³ K0 = ‘At rest’ lateral earth pressure coefficient. This is for the in-situ lateral pressure of soil. ³ Ka = ‘Active’ lateral earth pressure coefficient. This is for soil at the point of shear failure owing to unloading in the lateral direction. This is when the retaining wall, for example, moves away from the soil mass. ³ Kp = ‘Passive’ lateral earth pressure coefficient. This is for a soil mass that is externally forced inward. The soil mass is therefore at the point of incipient shear failure owing to loading in the lateral direction. The applicability of this theory for backfill against a pillar is not clear and it is hypothesised that the K0 parameter will be important in cases where there is little or no pillar dilation. For extensive pillar failure and dilation, the Kp parameter may be more important. This is speculation, however, and underground measurements in backfill will be required to determine the actual lateral confinement exerted by the backfill. The three coefficients mentioned above can be calculated using the following equations (Pantelidis, 2019): 228

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Note that this equation is a simplification as it assumes the original graded distribution of horizontal stress in Figure 10 is now a constant average value along the edge of the pillar. This approximation may not be correct and needs to be verified by underground measurements in actual backfill placed against a pillar. If the density of backfill is 1750 kg/m3 (relative density 1.75, Jager and Ryder, 1999), and the pillar height is assumed to be 2.5 m, it follows from Equation [17] that σB = 11 kPa (0.011 MPa). If there is significant pillar dilation after failure, the passive lateral earth pressure coefficient Kp may possibly apply, but this needs verification as indicated above. From Equation [16], Kp = 3 for the assumed friction angle. From Equation [17] it then follows that σB = 66 kPa (0.066 MPa). Incidentally, this value is of the same order as the lateral stress value measured by Galvin and Wagner (1982) in the ash fill experiment. In the absence of any better-calibrated values, a value of 0.05 MPa is therefore used as a first estimate of the confinement that will be exerted by backfill. It should be noted that Cai (1983) argued that cemented fill has self-supporting characteristics and that the stress is evenly distributed along the full height of the pillar. The approximation given in Equation [17] also assumes that the stress is evenly distributed against the pillar sidewall.

A limit equilibrium model including the effect of backfill confinement The limit equilibrium model used to simulate pillar failure in boundary element codes and its implementation in the TEXAN code has been discussed in a number of papers (du Plessis, Malan, and Napier, 2011; Napier and Malan, 2014, 2018, 2021; Couto and Malan, 2022). Additional detailed information on the TEXAN code can be found in Napier and Malan (2007). The basic limit equilibrium model used in these earlier references assumed there was no confinement on the pillar edge. An extension of this basic model was used in this study to include the effect of backfill confinement. The force equilibrium of a thin slice of rock in the failed edge of the pillar is shown in Figure 11. This illustrates the mined bord on the left, which was subsequently filled with backfill, and part of the pillar on the right. The model assumes that there is an interface at both the hangingwall and footwall pillar contacts. The edge of the pillar will fail if the applied stress exceeds the strength and the remainder of the pillar may remain intact depending on the selection of parameters. If weak material properties and high stress are simulated, the entire pillar can fail. At x = 0, the edge of the pillar, a confining stress σh is applied as a result of the backfill placement. The seam-parallel stress component The Journal of the Southern African Institute of Mining and Metallurgy

A study of backﬁll conﬁnement to reinforce pillars in bord-and-pillar layouts

Figure 11—A limit equilibrium model illustrating the force equilibrium of a slice of rock in the failed zone. The confining stress applied by the backfill is included in this model

σs increases as x increases. The thin slice of rock between the dotted lines in Figure 11 is in equilibrium. This requires that [18]

[27] and

Equation [18] can be written in the form of a differential equation if the width of the slice tends to zero:

[28] The solution of the seam-parallel stress is given by [19] [29]

To solve Equation [19], a relationship between τ and σs needs to be assumed. If there is friction on the interfaces between the pillar and the hangingwall and footwall, τ is related to the normal stress, σn, by [20] where μI is the coefficient of friction and ϕ is the friction angle. We also assume that σn is related to the seam-parallel stress component σs by a failure relationship of the form [21] where σc and m are constants. Once failure occurs, σc can be considered as the strength of the failed pillar material and m is a slope parameter. Substituting Equations [20] and [21] into Equation [19] gives the a differential equation of the form [22] Equation [22] can be integrated if the variables are separated: [23] This equation has the following solution with the integration constant A: [24] To include the effect of the backfill confinement, constant A is obtained from Equation [24] by applying the boundary condition σs = σh when x = 0. This gives the value of A as: [25] This can be inserted into Equation [24] to give [26] This can be simplified as The Journal of the Southern African Institute of Mining and Metallurgy

From Equations [29] and [21], it follows that [30] Equation [21] defines the pillar material strength. In the TEXAN code, an extended model is implemented where the failure relationship for the intact pillar material is given by [31] For the failed pillar material, the following parameters are adopted: [32] The requirements of must be met when selecting these parameters. To illustrate the behaviour of the model, Equation [30] is plotted in Figure 12 for different values of confining stress. Note how the normal stress in the failed zone of the pillar increases substantially for an increase in confining stress.

A numerical modelling study to simulate pillar slabbing at increasing depths The TEXAN code used in this study is a displacement discontinuity boundary element code that was speciﬁcally developed to simulate a large number of small pillars in tabular layouts (Malan and Napier, 2006). It allows for the use of triangular boundary elements, thus circumventing the problem of ‘partially mined’ elements encountered using square element shapes. The ‘two-dimensional’ limit equilibrium model illustrated above had to be extended for use with actual irregular bord and pillar layouts (see Napier and Malan, 2021). The geometry simulated in TEXAN is illustrated in Figure 13. This area was selected due to minor pillar spalling being observed. Backfilling is currently not used in the bord-and-pillar layouts of the Bushveld Complex and the modelling was therefore a theoretical study to investigate the potential benefits of backfill. To simplify VOLUME 123

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A study of backﬁll conﬁnement to reinforce pillars in bord-and-pillar layouts 2014). This is typically not observed in shallow platinum mines and this effect was therefore ignored for this study. The selected parameters resulted in no spalling of the pillar edges for a simulation at a depth of 290 m, and this agrees with the observations made in this area. To investigate the stability of the revised pillar design at increasing depths, the layout shown in Figure 14 was also simulated at depths of 400, 600, and 800 m. Backfill was

Figure 12—An illustration of the effect of the backfill confining stress on the normal pillar stress predicted by the limit equilibrium model. The graph was plotted using the following parameters: m = 2, σc = 1 MPa, ϕ = 25°, and H = 2 m

the digitizing of the outlines and the meshing procedure, the pillar outlines were approximated with straight line segments as illustrated in Figure 14. The pillar numbers used in the study are given in this figure. The size of the area simulated was 225 m × 150 m. Although the mine observed limited spalling in this area, the pillars were rehabilitated with shotcrete and they appeared to be in a good condition (see Figure 15). For the modelling, the mined area was covered using a triangular mesh. The pillars also had to be meshed to enable the calculation of the average pillar stress (APS). The mesh used for the pillars had to be small enough to ensure an accurate simulation when using the limit equilibrium failure model. The average element size was 0.68 m2 in the mined area, and as an example of the pillars, it was 0.36 m2 for pillar 73. The density of the rock was assumed to be 3100 kg/m3 and the k-ratio was assumed to be unity in both horizontal directions. The depth below surface was approximately 290 m. Although there are slight variations in depth in the area of interest, the excavation was assumed to be horizontal to simplify the model. The limit equilibrium model as described above requires a large number of parameters to calibrate it and these are listed in Table I. The values selected were obtained from a back-analysis of a pillar mining experiment at this particular mine (see Napier and Malan, 2021). An extension of the model, not discussed in this paper, can allow for the time-dependent failure of the pillar material (Napier and Malan,

Figure 13—The area selected for numerical modelling. This area was of interest as the mine noted some minor pillar spalling

Figure 14—Simplified outlines of the pillars and the mining area. This also illustrates the pillar numbers used in this paper

Figure 15—Condition of a rehabilitated pillar in the area of interest (left). Only a few pillars were covered with shotcrete. The photograph on the right illustrates the general condition of the pillars in this area 230

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The Journal of the Southern African Institute of Mining and Metallurgy

A study of backﬁll conﬁnement to reinforce pillars in bord-and-pillar layouts Table I

140

Parameters used for the limit equilibrium model 120

Parameter

Value

Intact strength intercept, σci

60.0 MPa 7.0

Intact strength slope, mi

100 80

Residual strength intercept, σc

4.0 MPa

Residual strength slope, m

7.0

Effective seam height, H

2.5 m

Intact rock Young’s modulus, E

90 000.0 MPa

Intact rock Poisson’s ratio, ν

0.2

Fracture zone interface friction angle φI,

30°

Seam stiffness

36 000 MPa/m

100

150

200

Figure 17—Predicted pillar spalling at 600 m depth. The red color indicate the areas of spalling

140

140 120

120

100

20 0

100

150

200

Figure 16—Predicted pillar spalling at 400 m depth. The red color indicate the areas of apalling

not included for these initial simulations. The limit equilibrium parameters that predicted no pillar failure at 290 m depth (Table I) were used for these simulations. The results are shown in Figures 16, 17, and 18. Note that the pillar spalling increases with depth until significant failure is observed at 800 m depth. The cores of the pillars are nevertheless still intact at this depth. This deterioration in pillar condition with depth agrees qualitatively with the decrease in extraction ratio with depth that can be sustained if a reasonable pillar factor of safety needs to be maintained (Figure 2).

A numerical modelling study to simulate the effect of backfill confinement To simulate the effect of backfill, the extended limit equilibrium model, as described previously, was used. The same geometry as that simulated above was used and all simulations were conducted at a hypothetical depth of 800 m. As there is uncertainty regarding the amount of confinement that the backfill will exert, simulations with σh values of = 0.05, 0.5, 1, and 2 MPa were conducted. The fraction of the pillars that failed decreased with increasing confinement. The failure for 2 MPa confinement is illustrated in Figure 19. The same simulation without backfill confinement is shown in Figure 18. The benefit of confinement is also illustrated in Figure 20, where the fraction of the pillar that failed is shown for a few pillars. The fraction that failed is the number of elements that failed divided by the total elements for the particular pillar. Note that the failure The Journal of the Southern African Institute of Mining and Metallurgy

100

150

200

Figure 18—Predicted pillar spalling at 800 m depth. The red color indicate the areas of spalling

140 120 100 80 60 40 20 0

100

150

200

Figure 19—Predicted pillar spalling at 800 m depth if backfill is present with a confining stress of 2 MPa. The red color indicate the areas of pillar failure

decreases for increasing confinement, with a substantial reduction for a 2 MPa value. It is doubtful if such a magnitude of stress will be exerted by the backfill, unless there is substantial pillar dilation. These results illustrate the value of the backfill confinement model in studies of the effect of backfill on pillar strength. The confinement exerted by backfill is not known, however, VOLUME 123

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Figure 20—Fraction of the pillars that failed at increasing backfill confinement

and therefore trial backfill sections in the mine, with sensitive instrumentation, will be required to obtain calibrated values for the model. The scope of this initial study was to test a modelling approach that could be used to simulate the effect of backfill on pillar strength. This tool can now be used to simulate aspects such as the timing of backfill placement and partial backfill placement in selected areas. As part of future work, a thorough study of the sequence of backfill placement needs to be done. Preliminary work not reported in this paper (Ile, 2023) has indicated that simultaneous mining and backfilling is preferred to ensure that the pillars are confined before extensive failure occurs. This may not be practical in actual mines and a rigorous study needs to be conducted in terms of sequencing. A further extension of the model in TEXAN is also required that will allow the coupling of the backfill lateral strain and resulting stress with pillar dilation. A novel scheme to compute the lateral dilation in the pillar has already been implemented in the TEXAN code by Professor John Napier. The next step will be to include the effect of the placed backfill and the interaction with pillar dilation.

Conclusions The current pillar design methodology for bord-and-pillar layouts in the Bushveld Complex will result in a substantial decrease in extraction ratio at increasing depths. The extraction ratio is a simple decreasing linear function of the depth, H, and a gradient parameter. Backfill will increase the pillar strength, enabling increased extraction ratios. The use of backfill will also minimize the requirement for tailings storage on surface and the risk of environmental damage. The literature survey indicated that backfill is extensively used in coal mines. This is done mostly for environmental considerations and to minimize the damage caused by subsidence, but also to increase the extraction ratio. In contrast, it seems as if backfill is rarely used in hard rock bord-and-pillar mines. Placement of backfill in sections of the mine may be challenging as containment barriers will have to be built between adjacent pillars. The sequence 232

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and timing of mining a section and placing the backfill will have to be carefully managed. This is a challenging aspect that requires additional research. An extension of the limit equilibrium model in the TEXAN code proved to be useful for simulating the effect of backfill confinement on pillar strength. The amount of spalling at depth is substantially decreased if a moderate confinement is applied to the pillars. The confinement that will be induced by backfill in actual mining layouts is unknown and this needs to be quantified in future by installing sensitive instrumentation in backfill trial sections. Previous workers measured a lateral stress of 0.05 MPa in ash fill in a coal mine. Areas where the pillar strength is reduced by weak layers may gain significant benefit from the placement of backfill. In some cases this may be the only method that will prevent large-scale collapses, and it requires further study.

Acknowledgements This work forms part of the MEng study of Divine Ile at the University of Pretoria. The authors would like to thank Professor John Napier for his kind assistance with the backfill confinement model in TEXAN.

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A study of backﬁll conﬁnement to reinforce pillars in bord-and-pillar layouts Couto, P.M. and Malan, D.F. 2022. A limit equilibrium model to simulate the large-scale pillar collapse at the Everest Platinum Mine. Rock Mechanics and Rock Engineering. https://doi.org/10.1007/s00603-022-03088-z Donovan, J.G. 1999. The effects of backfilling on ground control and recovery in thin-seam coal mining. MSc dissertation, Virginia Polytechnic Institute and State University. Du Plessis, M., Malan, D.F., and Napier, J.A.L. 2011. Evaluation of a limit equilibrium model to simulate crush pillar behaviour. Journal of the Southern African Institute of Mining and Metallurgy, vol. 111. pp 875–885. Esterhuyse, J.C. and Malan, D.F. 2018. Some rock engineering aspects of multireef pillar extraction on the Ventersdorp Contact Reef. Journal of the Southern African Institute of Mining and Metallurgy, vol. 118, no. 12. pp. 1285–1296. Galvin, J.M and Wagner, H. 1982. Use of ash to improve strata control in bord and pillar workings. Proceedings of the International Symposium on Strata Mechanics, Newcastle-upon-Tyne, 5-7 April 1982. Farmer, I.W. (ed.). Elsevier. pp. 264–270. Hedley, D.G.F. and Grant, F. 1972. Stope-and-pillar design for the Elliot Lake Uranium Mines. CIM Bulletin, vol. 65. pp. 37–44. ICMM. 2022. Tailings reduction roadmap. London. Ile, D. 2023. An investigation into the use of backfill to reinforce pillars in hard rock bord and pillar layouts. Draft MEng dissertation, University of Pretoria. Jager, A.J. and Ryder, J.A. 1999. A Handbook on Rock Engineering Practice for Tabular Hard Rock Mines. Safety in Mines Research Advisory Committee, Johannesburg. Kostecki, T. and Spearing, A.J.S., 2015. Influence of backfill on coal pillar strength and floor bearing capacity in weak floor conditions in the Illinois Basin. International Journal of Rock Mechanics and Mining Sciences, vol. 76, no. 3. pp. 55–67. Laubscher, D.H. 1990. A geomechanics classification system for the rating of rock mass in mine design. Journal of the South African Institute of Mining and Metallurgy, vol. 90. pp 257–273. Malan D.F. and Napier J.A.L. 2006. Practical application of the Texan code to solve pillar design problems in tabular excavations. Proceedings of the SANIRE Symposium “Facing the challenges”, Rustenburg. South African National Institute of Rock Engineers. pp. 55–74. Malan, D.F. and Napier, J.A.L. 2011. The design of stable pillars in the Bushveld mines: A problem solved? Journal of the Southern African Institute of Mining and Metallurgy, vol. 111. pp. 821–836. Malan, D.F. and Esterhuyse, J.C. 2021. Work Package 4.3.1: Rock Engineering Criteria for Mechanised Mining. SAMERDI final report. Mandela Mining Precinct, Johannesburg. Mo S., Canbulat I., Zhang C., Oh J., Shen B., and Hagan P. 2018. Numerical investigation into the effect of backfilling on coal pillar strength in highwall mining. International Journal of Mining Science and Technology, vol. 28. pp. 281–286. Napier, J.A.L and Malan, D.F. 2007. The computational analysis of shallow depth tabular mining problems. Journal of the Southern African Institute of Mining and Metallurgy, vol. 107. pp. 725–742. Napier, J.A.L. and Malan, D.F. 2014. A simplified model of local fracture processes to investigate the structural stability and design of large-scale tabular mine

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layouts. Proceedings of the 48th US Rock Mechanics / Geomechanics Symposium, Minneapolis. American Society for Rock Mechanics, Alexandria, VA. Napier, J.A.L. and Malan D.F. 2018. Simulation of tabular mine face advance rates using a simplified fracture zone model. International Journal of Rock Mechanics and Mining Sciences, vol. 109. pp. 105–114. Napier, J.A.L. and Malan D.F. 2021. A limit equilibrium model of tabular mine pillar failure. Rock Mechanics and Rock Engineering, vol. 54. pp. 71–89. Palarski, J. 1993.The use of fly ash, tailings, rock and binding agents as consolidated backfill for coal mines. Proceedings of Minefill 93, Johannesburg. Southern African Institute of Mining and Metallurgy, Johannesburg. pp. 403–408. Palarski, J. 1994. Design of backfill as support in Polish coal mines. Journal of the SouthAfrican Institute of Mining and Metallurgy, vol. 94, no. 8. pp. 218–226. Pantelidis, L. 2019. The generalized coefficients of earth pressure: A unified approach. Applied Sciences, vol. 9. 5291. doi: 10.3390/app9245291 Piper, P.S., Gürtunca, R.G., and Maritz, R.J. 1993. Instrumentation to quantify the in-situ stress–strain behaviour of mine backfill. Journal of the South African Institute of Mining and Metallurgy, vol. 93. pp. 109–120. Rankine, W. 1856. On the stability of loose earth. Philosophical Transactions of the Royal Society of London, vol. 147. Ryder, J.A. and Jager, A.J. 2002. A Textbook on Rock Mechanics for Tabular Hard Rock Mines. Safety in Mines Research Advisory Committee, Johannesburg. Salamon, M.D.G. and Oravecz, K.I. 1976. Rock Mechanics in Coal Mining. Chamber of Mines of South Africa, Johannesburg. Shamsabadi, A., Dasmeh, A., and Taciroglu, E. 2017. Guidelines for analysis and LRFD-based design of earth retaining structures. University of California, Los Angeles. Shen, B., Poulsen, B., Luo, X., Qin, J., Thiruvenkatachari, R., and Duan, Y. 2017. Remediation and monitoring of abandoned mines. International Journal of Mining Science and Technology, vol. 27, no. 5. pp. 803–811. Squelch, A.P. 1993. A methodology for the selection of backfill as local support for tabular stopes in South African gold mines. Journal of the South African Institute of Mining and Metallurgy, vol. 93. pp. 9–15. Stacey, T.R. and Page, C.H. 1986. Practical Handbook for Underground Rock Mechanics. Trans Tech Publications. Tesarik, D.R., Seymour, J.B., and Yanske, T.R. 2009. Long-term stability of a backfilled room-and-pillar test section at the Buick Mine Missouri, USA. International Journal of Rock Mechanics and Mining Sciences, vol. 46. pp. 1182–1196. Watson, B.P., Theron, W., Fernandes, N., Kekana, W.O., Mahlangu, M.P., Betz, G., and Carpede, A. 2021 UG2 pillar strength: Verification of the PlatMine formula. Journal of the Southern African Institute of Mining and Metallurgy, vol. 121, no. 8. pp. 449–456. Zhang, J-X., Huang, P., Zhang, Q., Li, M., and Chen, Z-W. 2017. Stability and control of room mining coal pillars—taking room mining coal pillars of solid backfill recovery as an example. Journal of Central South University, vol. 24, no. 5. pp. 1121−1132. Zhang, J., Li, M., Taheri, A., Zhang, W., Wu, Z., and Song, W. 2019. Properties and application of backfill materials in coal mines in China. Minerals, vol. 9. https://doi.org/10.3390/min9010053

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A study of the eﬀect of pillar shape on pillar strength J.A. Maritz1 and D.F. Malan1

Afﬁliation: 1Department of Mining Engineering,

University of Pretoria, South Africa.

Correspondence to: D.F. Malan

Email: francois.malan@up.ac.za

Dates: Received: 26 Nov. 2022 Revised: 20 May 2023 Accepted: 23 May 2023 Published: May 2023

Synopsis Pillar strength is affected by pillar shape, but this has largely been ignored in past research studies. Bord-and-pillar layouts are typically designed using empirical strength equations developed for square pillars. Owing to the poor quality of pillar cutting, many hard-rock pillars have an irregular shape and it is not clear how this affects pillar strength. Furthermore, the strength of rectangular pillars in comparison with square pillars is also difficult to quantify. The ‘perimeter rule’ is widely adopted for rectangular pillars, but its applicability for pillars with irregular shapes has never been tested. We used numerical modelling in this study to investigate the effect of pillar shape on strength. An analytical limit equilibrium model of a square and a strip pillar also provided useful insights. For slender pillars, the strength of a long rib pillar is essentially similar to that of a square pillar. In contrast, for rib pillars with a large width to height ratio, there is a substantial increase in strength. The study found that the perimeter rule should not be used for irregularly shaped pillars. Displacement discontinuity modelling, using a limit equilibrium approach, is proposed as an alternative to determine the strength of these pillars.

Keywords How to cite: Maritz, J.A. and Malan, D.F. 2023 A study of the effect of pillar shape on pillar strength. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 5. pp. 235–244 DOI ID: http://dx.doi.org/10.17159/24119717/2473/2023 ORCID: J.A. Maritz http://orcid.org/0000-0002-4176-8919

pillar shape, pillar strength, displacement discontinuity modelling, bord-and-pillar layout.

Introduction Pillar shape is one of the factors affecting pillar strength (Wagner, 1974; Maritz, 2017; Du et al., 2019), but no clear design methodology exists to account for different pillar shapes. The strength of irregularly shaped pillars is particularly difficult to estimate. Van der Merwe and Madden (2010) provide a methodology to determine the strength of pillars with a parallelogram shape, but this is for only one particular class of pillar shape. Their method is based on correcting for the actual width of the pillar and it does not consider possible premature failure of the corners of pillars with acute angles. Figure 1 illustrates a typical underground layout in the Bushveld Complex of South Africa, showing the variety of pillar shapes that can be found in these layouts. It is not clear what the strengths of these various pillars are, and this highlights the importance of conducting research on this particular problem.

Figure 1—A variety of irregular pillar shapes found in an underground layout in the Bushveld Complex

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A study of the eﬀect of pillar shape on pillar strength Salamon (1967) described the database used to derive the famous Salamon and Munro (1967) equation for coal pillar strength. He noted that most collieries used pillars with a square cross-section and therefore ‘oblong pillars’ were excluded from the database. He also stated that ‘Actual mine pillars vary in shape and size. Hence, the actual and nominal mining dimensions are likely to differ in practice’. He argued that the adopted factor of safety will largely consider the errors arising from this source. In contrast, when Hedley and Grant (1972) derived their power-law strength formula for hardrock pillars, the layout geometry and failed pillars they used were elongated rib pillars. They nevertheless only considered the smallest lateral dimension of these pillars in their database. Their argument was: ‘This equation refers to square pillars, whereas those in the uranium mines are usually long and narrow. However, it is considered that the strength of such a pillar will not be very much greater than that of a square pillar of width equalling the minimum width of a long pillar.’ They may have been influenced by Holland and Gaddy (1957), who stated that only the minimum lateral dimension affects the strength of a pillar, while the other dimension has no effect. In summary, the most popular strength equations for pillars used in South African bord-and-pillar layouts was developed for square pillars only. To consider the strengthening effect of elongated pillars, Wagner (1974) proposed the concept of an ‘effective width’, which can be calculated from the area and perimeter of a pillar as follows: [1] where A = cross-sectional area of the pillar C = perimeter of the pillar w = minimum lateral dimension of the pillar L = maximum lateral dimension of the pillar. Equation [1] became known as the ‘perimeter rule’ and it is widely used in the South African mining industry. It correctly predicts that weff = w if w = L for a square pillar. Wagner’s justification for the adoption of Equation [1] is: ‘The work described in this paper indicates that the strength of the circumferential portions of a pillar is virtually independent of the width-to-height ratio whereas the strength of its centre increases with increasing ratio.’ Wagner also noted that Equation [1] predicts that weff approaches a finite value of 2w for very long and narrow pillars. This was also highlighted by Maritz and Malan (2020). To investigate the implication as regards strength for an infinitely long pillar, consider the general form of the power-law strength equation and the effective pillar width, weff:

[2] where σp is the strength of the pillar, K is the strength of the rock material in the pillar, h is the height of the pillar, and the exponents α and β need to be calibrated for the particular rock type. If weff =2w for an infinitely long pillar, it follows that: [3] For the Hedley and Grant (1972) formula, α = 0.5 and β = 0.75. From Equation [3], for an infinitely long pillar, the pillar strength can be given as: [4] It is not clear if the perimeter rule given in Equation [1] is correct as no experimental work was conducted to verify this approximation. Ryder and Ozbay (1990) suggested a shape strengthening factor of the form f = 1.0/1.1/1.2/1.3 for pillars having L⁄w ratios of 1/2/4/f. The value 1.3 is slightly less than that predicted by Wagner’s perimeter rule for infinitely long pillars (Equation [4]) and was probably adopted as a more conservative approach. Equation [1] is possibly abused in the mining industry as it is also used for pillars with an irregular shape. For example, it is tempting to use the perimeter rule to estimate the strength of the various pillars shown in Figure 1. Its applicability needs to be carefully assessed, however, and this is explored in this paper. As it is difficult to examine the effect of pillar shape on strength in underground workings, researchers have studied different pillar shapes in the laboratory. A laboratory investigation of a small number of specimens of different shapes was conducted by Maritz Table I

Dimensions of the specimens tested by Maritz (2017), and weff values obtained. The height of all specimens was 204 mm Specimen shape

Contact area (mm2)

Perimeter (mm)

Weff (mm)

Square

10 404

408

102

Triangular

10 404

493

Cylinder

10 404

362

115

Hexagon

10 404

380

110

Figure 2—Concrete specimens of different sizes tested by Maritz (2017). The results of one set of tests are shown on the right. Surprisingly, the cylinder had the lowest strength in all three tests, although its weff was the highest value 236

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A study of the eﬀect of pillar shape on pillar strength

Figure 3—Specimens tested and the peak stress for different specimen shapes (after Du et al., 2019)

(2017). Concrete was used as an artificial rock material to cast different shapes (Figure 2). The sizes of the specimens were carefully selected to ensure that the cross-sectional loading surfaces had similar areas. The w:h ratio was small at 1:2 and the slender nature of the specimens probably affected the results. Even though the cross-sectional areas were constant, the perimeters varied and this resulted in different values of weff (Table I). According to Equation [2], a difference in strength would therefore be expected. Three sets of tests were conducted, and the results of one of the sets are illustrated in Figure 2. The cylinder was expected to be the strongest shape according to the weff value, but this was not reflected by the test results. No clear link between the weff parameter and the specimen strength could be established from this limited number of tests. The small number of tests, the variability of the concrete strength, and the w:h ratio of 1:2 could have affected the results. Additional laboratory work therefore needs to be conducted in the future. Du et al., (2019) studied the uniaxial strength of circular, square, and rectangular laboratory specimens (Figure 3). Four different height to width/diameter ratios were also tested. They found that the pillars with a lower height to width ratio (r) had a higher bearing capacity (Figure 3). Although it would not be practical, the authors noted that the best shape for mine pillars is cylindrical as this shape has the highest strength (Figure 3). Of particular significance is that the effect of specimen shape is apparent only for the lower height to width ratios (or higher width to height ratios). For the three shapes, it follows from the dimensions given in the figure that: circle weff = 50 mm; square weff = 50 mm; and rectangle weff = 33 mm. This would imply that the circle and square configurations are of equal strength according to Equations [1] and [2], but this is only the case at greater height/width ratios. These laboratory experiments provide some evidence that the perimeter rule should be used with caution. The width to height ratio of the specimens seems to play a prominent role, and for slender pillars the minimum lateral dimension should possibly be used in Equation [2], and not weff. In contrast, Durmeková et al., (2022) drew no firm conclusions regarding the effect of specimen shape on strength. They tested cylindric specimens (diameters of 20 mm, 35 mm, 50 mm, 70 mm) and cubic and prismatic specimens with a base length of 50 mm. Height to diameter ratios of 1:1 and 1:2 were tested. Four different rock types were also tested. The strength results were highly variable, even for the same rock type. To summarize, the available laboratory studies do not give conclusive evidence regarding the effect of shape on pillar strength and additional work needs to be conducted. Furthermore, the use of small laboratory samples to infer pillar strengths in mines is also The Journal of the Southern African Institute of Mining and Metallurgy

Figure 4—Numerical modelling of a room-andpillar layout with different pillar shapes and sizes (after Walter and Konietzky, 2008)

problematic owing to the size effect of rock strength (see e.g. Hoek and Brown, 1980). As an alternative to laboratory testing, numerical modelling can be used to study the strength of pillars with different shapes. Figure 4 illustrates the numerical modelling of a room-andpillar layout. The drawback of finite element or finite different modelling is that it is difficult to build the modelling meshes with irregular pillar shapes. This can be seen in Figure 4 as the pillars are still represented using relatively few straight edges. Most of the modelling done with these codes to study pillar strength considers only a single pillar, often only in two dimensions (e.g. Esterhuizen, 2014). In contrast, displacement discontinuity modelling allows irregular pillar shapes to be simulated, as illustrated in Napier and Malan (2021). This approach is explored further in this paper. In summary, historical studies do not give clear evidence regarding the effect of pillar shape on strength, and additional research is required. It seems that the width to height ratio of the pillars also play a role and this is not considered by the perimeter rule. This paper describes a numerical modelling and analytical study, using a limit equilibrium model, to investigate the effect of pillar shape.

Insights from an analytic limit equilibrium solution of pillar strength Napier and Malan (2021) derived an analytic model of pillar failure for a long strip pillar and a square pillar (Figure 5). VOLUME 123

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A study of the eﬀect of pillar shape on pillar strength

Figure 5—(a) Section view through a strip pillar and the pillar stress profile. (b) Plan view of a square pillar with the intact core shown (after Napier and Malan, 2021)

A limit equilibrium model is assumed for the two pillar shapes shown in Figure 5. The width of the square pillar and the minimum width dimension of the strip pillar is w=2a. The fracture zones on the edges of the pillars are in a state of equilibrium and the vertical extent of the fracture zone is bounded by parting planes at the hangingwall and footwall contacts. Using these assumptions and a failure model for the seam material, the scaled average pillar stresses A*strip and A*square for the two pillars are given by Equations [5] and [6]. Note that these equations are valid at the point when the intact core becomes completely fractured and, depending on the parameters selected, do not necessarily indicate the peak strength of the pillars (see Napier and Malan, 2021). They are nevertheless still useful to compare the relative strengths of the two pillar shapes. For a strip pillar: [5] Figure 6—The increase in strength of a strip pillar, normalized to the strength of a square pillar, as a function of the w/h ratio. This was plotted for a friction angle of 40°

For a square pillar: [6] where [7] and [8] For Equations [7] and [8], μI is the friction coefficient at the interface of the fractured seam and the host rock, m is the slope in the residual limit equilibrium strength envelope, is the intact rock uniaxial strength, and σc is the residual strength after failure. Note that the parameters γ and Q are dimensionless and therefore A*strip and A*square are also dimensionless. Additional information can be found in Napier and Malan (2021). To gain insight into the increase in strength for the strip pillar in relation to the square pillar for the same width of w, divide Equation [5] by Equation [6]. This gives: [9] The assumption in the previous section of adopting a perimeter rule and the Hedley and Grant power-law in Equation [4] indicated 238

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that an infinitely long strip pillar will be 1.414 times stronger than a square pillar of the same width. Equation [9], based on a limit equilibrium model, indicates a more complex scenario where the increase in strength for the rib pillar compared to the square pillar will also be based on the w⁄h ratio (included in the γ parameter in Equation [7]). The coefficient of friction μI and the slope parameter m in the strength envelope for the failed pillar material also play a role. Equation [9] is plotted in Figure 6 as a function of the w⁄h ratio. Figure 6 indicates that the increase in strength for the infinitely long strip pillar in relation to the square pillar is a function of the w⁄h ratio and not simply a constant as given by Equation [4]. Interestingly, the model predicts at a small width to height ratio, w⁄h<1, (or a large height to width ratio) that (A*strip/A*square) ≈ 1. There is therefore no increase in strength for an infinitely long strip pillar compared to a square pillar of the same width as the minimum dimension of this strip pillar. This is in qualitative agreement with the results in Figure 3, where there is no difference in the tested strength for slender pillars, regardless of pillar shape. Based on these results, care should be exercised when attempting to use the perimeter rule for slender pillars. Dolinar and Esterhuizen (2007) also noted that there is little or no increase in strength for an increase in pillar length for slender pillars. They conducted FLAC3D modelling on limestone pillars of different lengths and heights and developed equations to describe the modelled strength behaviour. The Journal of the Southern African Institute of Mining and Metallurgy

A study of the eﬀect of pillar shape on pillar strength They found that for w⁄h<0.66, there is little or no increase in strength with increasing pillar length. Only for the more ‘squat’ pillars is there a significant increase in strength with pillar length.

Numerical simulation of the effect of pillar shape on pillar strength The complex pillar shapes illustrated in Figure 1 and the effect of the width to height ratio discussed in the previous section highlight potential difficulties associated with using the perimeter rule. This was explored further by the use of numerical modelling.

Overview of the TEXAN code and the limit equilibrium model To simulate the effect of pillar shape on pillar strength, a novel approach using a displacement discontinuity boundary element code, TEXAN, was explored (Napier and Malan, 2007). Displacement discontinuity codes cannot simulate the failure of the pillars, but the inclusion of a limit equilibrium constitutive model in TEXAN allows for the modelling of on-seam failure. The model will not be described here and the reader is referred to the numerous papers already published on this topic (e.g. Napier and Malan, 2018, 2021; Couto and Malan, 2022). The host rock is assumed to be an isotropic, homogeneous, elastic medium. TEXAN is particularly well suited to simulate the shallow bord-and-pillar layouts in the Bushveld Complex in South Africa as it was designed to represent irregular pillar shapes. Regarding the limit equilibrium model TEXAN assumes that the pillar is bound by frictional parting planes at the contacts with the hangingwall and footwall. By considering the force equilibrium of a slice of rock in the fractured edge of the pillar, it is possible to construct a differential force balance for the average seamparallel and seam-normal tractions. The solution of the governing differential equation indicates that the tractions increase in an exponential fashion towards the intact core of the pillar. For a tabular layout problem, with irregular pillar shapes discretized using triangular elements, a ‘fast marching solution’ to determine the seam-parallel stress is used. A number of assumptions are made Table II

Parameters used for the limit equilibrium model. Additional information regarding these parameters can be found in Napier and Malan (2021) Parameter

Value

Intact strength intercept, σci

12.0 MPa

Intact strength slope, mi

6.0

Residual strength intercept, σc

2.8 MPa

Residual strength slope, m

2.0

Effective seam height, H

2.0 m

in the TEXAN program; for example it is assumed that the seamparallel stress gradient direction is perpendicular to the adjacent element edge at the excavation boundary. Napier and Malan (2021) provide a detailed description of this solution scheme. Table II lists the values of the limit equilibrium model parameters used for the modelling described in this paper. Additional information regarding these parameters can be found in Napier and Malan (2021) The model parameters given in Table II were selected arbitrarily as the objective was to investigate the effect of shape on strength and the only requirement was that the progressive failure of the pillar, from limited failure at the edges of the pillar to complete failure of the core, could be simulated for the imposed incremental loads. The same parameters were used to simulate the different pillar shapes. Of interest is that the limit equilibrium model implemented in TEXAN can predict both a softening and a hardening response after failure, depending on the choice of parameter values (Napier and Malan, 2021). The condition for immediate softening after the onset of failure for a square pillar is given by: [10] where parameters γ and Q were already defined in Equations [7] and [8], and [11] The parameters H,m,mi,σc, are defined in Table II where w is the pillar width of a square pillar and μI = tanϕI. Furthermore, the condition that the final average pillar stress for a completely failed pillar is greater than the average pillar stress at the onset of failure is given by (Napier and Malan, 2021): [12] For the parameters given in Table II, The condition given by Equation [10] is therefore not met and the parameters will not give immediate softening after failure. Furthermore, γ2 ⁄ [2(eγ - γ - 1)] = 0.1981 < 0.2333 = Q. The condition in Equation [12] is met and therefore the final average pillar stress for a completely failed pillar will be greater than the average pillar stress at the onset of failure. The load-deformation curves for the pillars presented later correctly reflect these conditions (see for example the curve for weff = 16.7 in Figure 14). The specimen continues to strain harden after the initial failure and the final strength value is greater than at this initial point of failure. Although similar model parameters were used for the results in Figure 13, the loading increments used for the model were too large Table III

Intact rock Young’s modulus, E

70 000 MPa

Intact rock Poisson’s ratio, ν

0.2

Various pillar shapes simulated. The dimensions were selected to give a constant value for Weff

Fracture zone interface friction angle, φI

20°

Pillar shape

Seam stiffness

2 000 MPa/m

Cross sectional area (m2)

Perimeter (m)

Weff (m)

Pillar width – square pillar W

10 m

Square

100.0

40.0

Parameter ϐ (Equation [7])

3.6397

Trapezoid

117.0

46.8

Parameter M (Equation [11])

0.3333

Circular (radius 5 m)

78.5

31.4

Parameter Q (Equation [8])

0.2333

Triangular

133.3

53.3

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A study of the eﬀect of pillar shape on pillar strength

Figure 7—An illustration of the simulated pillar shapes. The dimensions were selected to ensure a constant value for weff

and the point of initial failure is not indicated correctly – it should be lower. The method of applying the load increments in the model is described in the next section.

Numerical modelling geometries As a first experiment, the numerical model was used to determine whether different shapes with similar weff values could have similar peak strengths. Four pillar shapes were generated with the dimensions given in Table III. The pillar shapes are shown in Figure 7. The weff parameter was calculated using Equation [1]. Interestingly, the triangular pillar has a substantially larger area than the other specimens to meet the required weff value. The pillar height was 2 m as indicated in Table II. This gives a w:h ratio of 5 for the square pillar. These specimens can therefore be considered as ‘squat’ pillars and it is expected that the pillar shape will make a difference in terms of strength when considering the information discussed above. Various pillar shapes were simulated. The dimensions were selected to give a constant value for weff . The geometries were discretized using triangular elements of a size approximately 0.08 m2. The mesh for the triangular pillar is shown in Figure 8. As this was simulated using a displacement discontinuity code, the pillars had to be positioned in a ‘mined stope’ and an arbitrary size of 50 m × 50 m was selected. As a crude method to gradually increase the stress on the pillars, the depth of

Figure 9—The geometries used to investigate the increase in strength for increasing length of rectangular pillars. Although shown together in the figure, these pillar shapes were simulated individually

Figure 10—The typical pillar geometries (marked with a ‘P’) created if pillar holings are not completed

Figure 8—The triangular mesh elements used to simulate the triangular pillar shape 240

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the excavation was increased in successive runs and this enabled a stress-strain curve of the pillars to be generated. The effect of elongation of the square pillar was studied in a second set of simulations. The geometries are shown in Figure 9. The third pillar geometry simulated is the one frequently encountered underground in bord-and-pillar layouts where pillar holings were not completed. This is illustrated in Figure 10 for an actual layout. As a simplification for the modelling, a 10 m × 30 m pillar, which is incrementally mined in the centre holing, was simulated (Figure 11). The face advance was 2.5 m increments until the pillar was split into two 10 m × 10 m pillars. Note how the weff parameter decreases during this pillar splitting process. Table IV summarizes the change in pillar parameters for the various steps. The Journal of the Southern African Institute of Mining and Metallurgy

A study of the eﬀect of pillar shape on pillar strength

Figure 11—Simulated geometries typically encountered when mining a pillar holing

Table IV

Parameters for the pillar geometries illustrated in Figure 11 Parameter

10 m × 30 m

2.5 m cut

5.0 m cut

7.5 m cut

10 m × 10 m

Pillar area (m2)

300

275

250

225

100

Perimeter (m)

Weff (m)

12.9

11.1

9.5

Numerical modelling results The first results are for the different pillar shapes with a similar weff (see Figure 7). Figure 12 illustrates the failed sections of the various pillar shapes. Interestingly, the intact core for each pillar assumed the original outline shape of the pillar. The load-deformation curve for these four pillars are given in Figure 13. The circular pillar is stronger (similar to that observed by Du et al., 2019), but the peak strengths of the other three pillars are almost identical. According

to Equations [1] and [2], this should have been expected as the weff values of the three pillars are identical. The circular pillar is stronger, however, in spite of a similar weff, possibly because the absence of sharp corners delays the onset of fracturing and hence imparts a greater load-bearing capacity. In contrast to the constant weff simulated in Figure 12, the increase in length of a rectangular pillar resulted in an increase in weff. The results of simulating the geometry in Figure 9 are presented

Figure 12—Failed portions of the various pillar shapes at peak stress. The orange colour denotes the failed elements and the grey colour the intact elements The Journal of the Southern African Institute of Mining and Metallurgy

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A study of the eﬀect of pillar shape on pillar strength

Figure 13—Simulated pillar strength for the various pillar shapes. This is for a constant weff = 10 m

Figure 14—Simulated pillar strength for rectangular pillars of various lengths

in Figure 14. As expected the peak strength increases with an increase in value for weff. This is an important finding as the limit equilibrium model indicates the expected increase in strength for the rectangular pillars. The analytical model in Figure 6 also indicated this increase in strength for an infinitely long strip pillar versus a square of the same width for large w/h ratio pillars. For the parameters used, the modelling predicts an increase of peak strength from 19.4 MPa for the square pillar to 38.9 MPa for the 50 m long pillar. This is an increase in strength of approximately 2 for the rectangular pillar – higher than the 1.414 predicted by the perimeter rule for an infinitely long pillar. 242

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The third set of simulations investigated the effect of the holing of the pillar illustrated in Figure 11. The simulated stress profiles are illustrated in Figure 15. Note how the simulated peak strength of the pillar decreases as the weff decreases during the holing process. As the cut progressed to a depth of 5 m, the ‘bridge’ between the remaining two future square pillars became completely fractured (see Figure 16), and therefore the peak strengths for the pillar at cut distances of 5 m and 7.5 m are identical. This is not correctly predicted by the different weff values for these two geometries. The use of the weff value as a parameter to calculate pillar strength for irregular pillars similar to the scenario depicted in Figure 11 The Journal of the Southern African Institute of Mining and Metallurgy

A study of the eﬀect of pillar shape on pillar strength

Figure 15—Simulated load-deformation curves and pillar strengths for the various geometries shown in Figure 11

Figure 16—Failed portions of the pillar for holing cut lengths of 2.5 m and 5 m. Note that the central portion of the pillar is already failed in the diagram on the right. The orange colour denotes the failed elements and the grey colour the intact elements

is therefore questionable. Numerical modelling seems to be an attractive alternative, provided an accurate calibration of the limit equilibrium model can be done for the conditions encountered in different geotechnical areas.

Conclusions This paper is a preliminary study of the effect of pillar shape on pillar strength. A literature survey indicated that little is known about this topic and it has mostly been ignored in past research studies. The perimeter rule is widely adopted for non-square pillars, but its applicability for arbitrary pillar shapes has never been tested. An analytical limit equilibrium failure model of a square and a strip pillar indicated that for slender pillars (small width to height ratios), the strength of a long rib pillar is essentially similar to that of a square pillar (for geometries where the width of the The Journal of the Southern African Institute of Mining and Metallurgy

square pillar is identical to the smallest lateral dimension of the rib pillar). In contrast, the solutions indicate that long rib pillars with a large width to height ratio show a substantial increase in strength compared to the square pillar. This is confirmed by laboratory studies which indicated that for slender pillars, the pillar shape has almost no effect. The study indicated that the displacement discontinuity modelling approach, using a limit equilibrium failure model, is well suited to simulate the effect of pillar shape. It can, for example, predict the increase in strength for elongated rectangular pillars, and the results qualitatively agree with the increase in strength predicted by the perimeter rule for the relatively ‘squat’ pillars modelled. This study highlighted, however, that the perimeter rule should not be used for pillars with a complex or irregular shape. One such example is ‘elongated’ pillars where the holing between adjacent VOLUME 123

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A study of the eﬀect of pillar shape on pillar strength square pillars was not completed. Sections of these pillars may be fractured through completely and not carry load. On the mine plans, these failed sections are still indicated and this will affect the area and perimeter calculations used for the perimeter rule. The limit equilibrium constitutive model is a valuable addition to displacement discontinuity modelling. This can be used to simulate the effect of shape on pillar strength, but careful calibration of the model is required. Assigning material properties to the failed rock on the pillar edges is particularly challenging. Additional laboratory studies of the effect of pillar shape are required to confirm the results obtained from numerical modelling approaches.

Acknowledgements This work forms part of the PhD study of Jannie Maritz at the University of Pretoria.

References Couto, P.M. and Malan, D.F. 2022. A limit equilibrium model to simulate the large-scale pillar collapse at the Everest Platinum Mine. Rock Mechanics and Rock Engineering, vol. 56. pp. 183–197. https://doi.org/10.1007/s00603-02203088-z Dolinar, D.R. and Esterhuizen, G.S. 2007. Evaluation of the effect of length on the strength of slender pillars in limestone mines using numerical modeling. Proceedings of the 26th International Conference on Ground Control in Mining, Morgantown, WV: West Virginia University. pp. 304–313. Du, K., Su, R., Tao, M.,Yang, C., Momeni, A., and Wang, S. 2019. Specimen shape and cross-section effects on the mechanical properties of rocks under uniaxial compressive stress. Bulletin of Engineering Geology and the Environment, vol. 78. pp. 6061–6074. Durmeková, T., Bednarik, M., Dikejová, P., and Adamcova, R. 2022. Influence of specimen size and shape on the uniaxial compressive strength values of selected Western Carpathians rocks. Environmental Earth Sciences, vol. 81. p. 247. doi: 10.1007/s12665-022-10373-1 Esterhuizen G.S. 2014. Extending empirical evidence through numerical modelling in rock engineering design. Journal of the Southern African Institute of Mining and Metallurgy, vol. 114. pp. 755–764. Hedley, D.G.F. and Grant, F. 1972. Stope-and-pillar design for the Elliot Lake Uranium Mines. CIM Bulletin. vol. 65. pp. 37-44.

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Hoek, E. and Brown, E.T. 1980. Underground Excavations in Rock. Institution of Mining and Metallurgy, London. Holland, C.T. and Gaddy, F.L. 1957. Some aspects of permanent support of overburden on coal beds. Proceedings of the West Virginia Coal Mining Institute. pp. 43–65. Maritz, J. 2017. Preliminary investigation of the effect of areal shape on pillar strength. Proceedings of ISRM AfriRock - Rock Mechanics for Africa. Paper no. ISRM-AFRIROCK-2017-012 International Society for Rock Mechanics, Lisbon. Maritz, J.A. and Malan, D.F. 2020. Numerical assessment of the perimeter rule for pillar strength calculations. Proceedings of the ISRM International Symposium EUROCK 2020. International Society for Rock Mechanics and Rock Engineering , Lisbon. Napier, J.A.L. and Malan, D.F. 2007. The computational analysis of shallow depth tabular mining problems. Journal of the Southern African Institute of Mining and Metallurgy, vol. 107. pp. 725–742. Napier, J.A.L. and Malan D.F. 2018. Simulation of tabular mine face advance rates using a simplified fracture zone model. International Journal of Rock Mechanics and Mining Sciences, vol. 109. pp 105–114. Napier, J.A.L. and Malan D.F. 2021. A limit equilibrium model of tabular mine pillar failure. Rock Mechanics and Rock Engineering, vol. 54. pp. 71–89. Ryder, J A and Ozbay, M U. 1990. A methodology for designing pillar layouts for shallow mining. Proceedings of the International Symposium on Static and Dynamic Considerations in Rock Engineering, Swaziland. International Society for Rock Mechanics and Rock Engineering, Lisbon. Salamon, M.D.G. 1967. A method of designing bord and pillar layouts. Journal of the South African Institute of Mining and Metallurgy, vol. 68. pp. 68–78. Salamon, M.D.G. and Munro, A.H. 1967. A study of the strength of coal pillars. Journal of the South African Institute of Mining and Metallurgy, vol. 68. pp. 55–67. Van der Merwe, J.N. and Madden, B.J. 2010. Rock Engineering for Underground Coal Mining. Special Publications Series no, 8. Southern African Institute of Mining and Metallurgy, Johannesburg. Wagner, H. 1974. Determination of the complete load-deformation characteristics of coal pillars. Proceedings of the 3rd ISRM Conference, Vol IIB, Advances in Rock Mechanics. International Society for Rock Mechanics and Rock Engineering , Lisbon. pp. 1076–1081. Walter, K. and Konietzky, H. 2008. Room pillar dimensioning for gypsum and anhydrite mines in Germany. Proceedings of the Conference on Advances in Mining and Tunneling 2008, Hanoi, Vietnam. Publishing House for Science and Technology, Hanoi. pp. 349–362.

The Journal of the Southern African Institute of Mining and Metallurgy

Bord-and-pillar design for the UG2 Reef containing weak alteration layers P.M. Couto1 and D.F. Malan2

Afﬁliation: 1Cartledge Mining and Geotechnics,

Queensland, Australia. 2Department of Mining Engineering, University of Pretoria, South Africa.

Correspondence to: D.F. Malan

Email: franscois.malan@up.ac.za

Dates: Received: 26 Nov. 2022 Revised: 13 Feb. 2023 Accepted: 30 May 2023 Published: May 2023

Synopsis We propose a layout design for the UG2 Reef where weak geological alteration layers are present. The collapse of the Everest platinum mine in South Africa indicated that these layers substantially weaken the pillars. The popular Hedley and Grant pillar strength formula cannot be used where these alteration layers are present. Underground investigations at Everest mine and numerical modelling of the layout were conducted using the TEXAN code and a limit equilibrium model. Simulations of a collapsed area and an intact area allowed for a preliminary calibration of the model. This was subsequently used to explore modified layouts for these ground conditions. An alternative is to compartmentalize the blocks of ore using barrier pillars. The numerical modelling predicted that the barrier pillars appear to remain stable even in the case of large-scale collapses, provided their width exceeds 25 m. Main access routes into the mine can be protected by a double row of pillars at least 15 m wide to provide a safe travelling way. As a cautionary note, these conclusions are based on the model calibration and this needs to be refined in future. Calibration of the limit equilibrium model remains a challenge owing to the large number of parameters involved.

Keywords UG2 Reef, bord and pillar. Layout design, limit equilibrium model, TEXAN code.

How to cite: Couto, P.M. and Malan, D.F. 2023 Bord-and-pillar design for the UG2 Reef containing weak alteration layers. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 5. pp. 245–252 DOI ID: http://dx.doi.org/10.17159/24119717/2482/2023

Introduction The strength of hard rock pillars has been studied extensively and a large number of publications are available on this topic (e.g. Martin and Maybee, 2000; Malan and Napier, 2011). Pillar design in the Southern African hard rock industry is mostly based on the Hedley and Grant (1972) pillar strength formula. In comparison, extensive research on pillar strength in the coal industry, following the Coalbrook colliery disaster (van der Merwe, 2006), has resulted in a much-improved understanding of coal pillar strength. Research on stable layouts and pillar strength for the manganese, chrome, and platinum mines in South Africa has unfortunately not received the same attention. The Hedley and Grant power-law strength formula, as given in Equation [1], was widely adopted as no suitable alternative was available. The K-value is typically modified to suit local geotechnical conditions. [1] where Ps = pillar strength K = in-situ strength of the rock mass in the pillar (typically assumed to be a downrated value of the UCS) w = pillar width h = pillar height α = 0.5 β = 0.75 Extensive work was done to determine the most appropriate value of K for different orebodies and commodities (e.g. see Malan and Napier, 2011). In contrast, almost no research has been done for areas where a geological alteration or other weak layers are present in the reef horizon or close to the reef (Couto, 2020). This has led to large mine-scale collapses of pillars. Hartzenberg, du Plessis, and Malan (2020) define the alteration layer as follows: ‘The hangingwall contact of the UG2 chromitite reef at these sites consists of pyroxenite. The pyroxenite layers have been exposed to hydrothermal fluid flow, serpentinization and layerparallel shearing. The resulting clay-like material (weak partings) is defined as the alteration zone.’ Alteration is a common term used in geology to describe the transformation of rocks and minerals due to various processes such as weathering, metamorphism, and hydrothermal activity. The Hartzenberg definition above is, however, adopted for this study as it refers to weak layers in the pillars which may affect the pillar

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Bord-and-pillar design for the UG2 Reef containing weak alteration layers strength. Some authors also simply refer to this alteration layer as a weak ‘clay layer‘ in the pillars. Spencer (1999) reported on the pillar failures at the Wonderkop chrome mine in the Bushveld Complex. The mine exploited the LG6/LG6a chromitite seams. Thick clay layers (up to 300 mm in some places) traversed the pillars in some areas. The original pillar design at the mine was done using the Hedley and Grant pillar strength formula. The pillar sizes were 12 m × 6 m and the mining height was 2 m. The K-value for the Hedley and Grant formula was assumed to be one-third of the third of the laboratory strength of the pillar material (27 MPa). The clay layers resulted in unexpected failure of the pillars and the mine was closed in May 1998, less than two years after stoping operations commenced. Another (unpublished) case study of a mine collapse in the Great Dyke in Zimbabwe, where a weak parting with infilling was also present in the pillars, is known to the authors. Malan and Napier (2011) indicated that geological alteration may be present in pillars in both the western and eastern Bushveld Complex. These have a detrimental effect on pillar strength and on overall mine stability. Any weak layers in the pillars need to be carefully taken into account during mine design. It is well known that the strength of rock samples tested in the laboratory is affected by the ‘boundary conditions’ imposed at the contact between the testing machine platens and the rock specimen. A low friction angle typically causes axial splitting of the specimens and a significant reduction in strength is noted compared to the typical shear failure at higher friction angles (see e.g. Peng, 1971; Jaeger and Cook, 1979; Wagner, 1980). Peng (1971) observed that significant tension can be induced if soft extruding contacts are used in compression testing. He also noted that the strength of granite samples tested in the laboratory can drop from as high as 207 MPa to 96 Mpa, depending on the types of inserts used between the specimens and the loading platens. For actual pillars where there is a low friction angle contact between the pillar and hangingwall, it seems that the strength behaviour may be analogous to that recorded in the laboratory. A significant decrease in pillar strength is therefore expected. It is, however, extremely difficult to determine the actual reduced pillar strength for practical design purposes. If the design is too conservative it affects the economic viability of the mine, whereas a less conservative design may lead to a mine-wide collapse. The collapse at the Everest platinum mine, where an alteration zone was present, was studied in detail by Couto and Malan (2023). The current paper extends this work to explore a possible practical

mine layout that may be used when these poor ground conditions are encountered.

Observations at Everest platinum mine The authors conducted two underground visits to Everest platinum mine to investigate the large-scale pillar collapse. The objective was to gain an improved understanding of the failure mechanism, obtain photographs of the failed pillars, and to identify areas suitable for calibration of the numerical models. Figure 1 illustrates a plan view of the mine and the different pillar failure zones. The initial pillar design, in the area where the collapse occurred, incorporated pillars with dimensions ranging from 5 m × 5 m to 6 m × 6 m depending on depth, with an average mining height of 2.1 m. Many of the pillars that could be measured during the underground visits where smaller than these sizes. The mine plan, based on survey offsets done prior to 2008, also indicated that the pillar cutting was done poorly. Many pillars were cut smaller than the design specifications. This is considered an important factor contributing to the failure of the pillars. The amount of pillar scaling could be estimated during the underground visits as the original boundaries of the pillars were still clearly visible on the hangingwall because of the shotcrete or whitewash colour imprints. The stoping width was measured at a number of points along both routes during the visits. Historical records indicate that the mining height varied between 2 m and 2.2 m. Measurements of the stoping height in the zone where no pillar failure occurred revealed an average value of 2.1 m. Closer to the declines, the stoping width gradually decreased, with a final stoping width of 1.3 m in the decline area. It therefore seems that a total amount of closure of at least 700 mm occurred in some areas. Tensile fracturing was observed in the hangingwall close to the declines. These discontinuities had a vertical displacement of approximately 2 cm and an opening displacement of 1 cm in some areas. The weathering of the alteration layer was evidenty because of exposure to atmospheric conditions. The presence of water and the high humidity had transformed the geological alteration layer into a weak ‘clay layer’ that seemed to have no cohesive properties and a very low friction angle. This needs to be tested in the laboratory in future to better quantify the properties. The alteration zone was squeezed out between the reef-hangingwall contact in many areas. Figures 2-9 illustrate photographs of the pillars taken during the underground visits. The presence of the alteration zone in the pillars is evident in some of these photographs and a close-up view is given in Figure 7.

Figure 1—Plan view of the extent of pillar failure indicating the estimated collapsed area (Lombard, 2008) 246

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Figure 2—A pillar in the level 2 failure zone with horizontal joints and vertical tensile cracks visible

Figure 6—Pillar condition in the level 4 failure zone. The pillars are crushed, but some contact with the hangingwall is still maintained. The large spans indicate that the pillars were not cut to the planned design

Figure 3—Failure of a pillar facilitated by the alteration zone and the presence of subhorizontal jointing in the level 2 failure zone

Figure 7—A close-up view of the alteration layer in the level 4 failure zone. The material is wet and it shows evidence of slickenside surfaces. There is a gap between the pillar material and the hangingwall in this area

Figure 4—A pillar in the level 3 failure zone illustrating extensive scaling and failure. The core of this pillar is deemed to be still intact Figure 8—Tensile cracks in the hangingwall of the level 5 failure zone

Figure 5—A pillar in the level 3 failure zone. The original size of the pillar is clearly indicated by the change in colour on the hangingwall The Journal of the Southern African Institute of Mining and Metallurgy

Figure 9—Completely crushed pillars adjacent to the decline VOLUME 123

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Bord-and-pillar design for the UG2 Reef containing weak alteration layers Numerical modelling calibration As described in Couto and Malan (2023), TEXAN modelling with the limit equilibrium model was used to simulate the pillar failure at Everest platinum mine. The model is described in detail in Napier and Malan (2007, 2021). The limit equilibrium model is an elegant model to use for pillars where there is a weak layer present at the hangingwall/pillar contact as the model contains a frictional interface at this position. The drawback of the model, however, is that it is symmetrical, with partings at both the hangingwall and footwall contacts, and the friction angle is similar for these partings. The limit equilibrium model contains a large number of parameters and various simulations were conducted to obtain a best calibration of the model. The details of these simulations are given in Couto and Malan (2023) and will not be repeated here. Table I illustrate the calibrated parameters. Two areas were simulated, referred to as the collapsed area and the intact area. The collapsed area was in the level 5 area in Figure 1 and the intact area was in level 1. As explained below, the only difference in calibrated values for the two areas was the interface friction angle. The reason for the difference

Table I

Calibrated model parameters (see Couto and Malan (2022) for a definition of the parameters) Parameter

Value

Intact strength intercept

30.0 MPa

Intact strength slope

4.6

Residual strength intercept

4.0 MPa

Residual strength slope

4.6

Effective seam height

2.0 m

Intact rock Young’s modulus

90 000.0 MPa

Intact rock Poisson’s ratio

0.2

Interface friction angle - Collapsed area

10°

Interface friction angle - Intact area Seam stiffness

25° 45 000 MPa/m

is described in Couto and Malan (2023). It was assumed that the presence of water was an important difference between the intact and the collapsed areas. The alteration layer was dry in the intact area and moist in the collapsed area. The friction angle of the pillar contact was, therefore, probably lower in the collapsed area than in the intact area. No laboratory test results of these friction angles are available and this material needs to be tested in future. It should be noted that the limit equilibrium model does not include a cohesion component. This implies a zero cohesion, which is considered to be a good approximation of the characteristics of the alteration layer. The parameters given in Table I (with the lower friction angle) were used as a first approximation of the pillar strength to design a pillar layout for areas with a geological alteration layer similar to the ground conditions at Everest platinum mine. As a cautionary note, this is only a preliminary model calibration and it needs to be refined in future. Calibration of the limit equilibrium model remains a challenge owing to the large number of parameters involved. The simulated conditions of the pillars for the two areas mentioned above using these parameters are shown in Figure 10. The simulation agrees with the underground observations for these two areas. The pillars on the edges of the collapsed area are still intact, but this is due to the fact that the modelled area is relatively small and these pillars are next to the artificial abutments in the model. It was encouraging that the same parameters, apart from the value of the friction angle of the interfaces, could be used to simulate the two areas. The geological alteration is clearly detrimental to the stability of UG2 pillars, especially when it is exposed to water or high humidity. Careful simulation of the two areas and the actual pillar shapes allowed for the back-calculation of the K-value for the Hedley and Grant pillar formula. For this back-calculation, the pillars were simulated as rigid pillars and the average pillar stress (APS) values were calculated for each pillar. For the collapsed area, the pillars failed at these APS values and this was therefore assumed to be the maximum strength of the pillars. The calculated average K-value for the collapsed area was 19 MPa. The value for some of these failed pillars was below 10 MPa and K = 10 MPa may therefore be a good approximation to use for the Hedley and Grant formula for these types of pillars. This will result in extremely conservative layouts and it illustrates the effect of these alteration layers on pillar strength.

Figure 10—Simulation of pillar failure for the two areas. The orange colour denotes failure and the yellow denotes intact pillars (after Couto and Malan, 2022) 248

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Bord-and-pillar design for the UG2 Reef containing weak alteration layers Mine design considerations Large-scale collapses and the traditional empirical pillar design methods indicate that alternative mine layouts are required where geological alteration layers are present. The mining layouts considered below are for a bord-and-pillar mining method in a tabular, shallow-dipping orebody, such as those typically encountered in the Bushveld Complex in South Africa. It is therefore an important problem to solve to ensure that mechanized mining can be implemented in the future, even for these orebodies that contain weak geological alteration layers. This study highlighted three critical factors that influenced the overall stability of the pillars when encountering geological alteration. These factors need to be considered during any design, regardless of the mining layout. ³ The ingress and management of groundwater. The presence of water should be limited as far as practically possible. ³ The ongoing monitoring of pillar sizes is critical to ensure that the pillars are cut as per the design specification. The monitoring should also be extended to existing pillars to record any early signs of pillar scaling. ³ The use of regional or barrier pillars is critical to compartmentalize the mine. This will prevent mine-wide collapses. To ensure economically viable mining operations, a minimum extraction ratio needs to be attained. This will require small in-panel pillar sizes, together with regional pillars to ensure regional stability.

Figure 11—Proposed mining layout

Layouts

A number of alternative mining layouts were considered. Owing to the requirement of a mechanized mining operation and the characteristics of the orebody (narrow seam, tabular, flat-dipping), the only practical option was a compartmentalized bord-and-pillar mining method. The mining layout considered is based on rock engineering and practical mining knowledge with the objective of achieving the highest possible extraction ratio. The proposed mining layout for these geotechnical conditions is shown in Figure 11. Note that the diagram shows only part of the layout to illustrate the inclusion of barrier pillars. Each ‘compartment’ will contain 144 pillars of size 7 m × 7 m and will be surrounded by large barrier pillars with holings at specified distances. The modelling was based on a depth of 200 m. The limit equilibrium model parameters obtained from the calibration exercise described above were used for the simulations. This is deemed a worst-case scenario in terms of pillar strength. The proposed mining layout allows maximum extraction with protection of infrastructure, entrances, and exits. This layout can be problematic with regard to the mining sequencing if not followed strictly as per the mine scheduling. Conventional mining methods require a specialized crew allocation based on the either development, ledging, or stoping. Bord-and-pillar mining does not require the specialized crew for on-reef development. The proposed mining layout will, however, require the allocation of specialized crews for both development and stoping to ensure the availability of mining blocks as scheduled by the mine planner. The large barrier pillars will require optimized ventilation layouts to ensure airflow and adequate cooling. A rock engineering benefit of a compartmentalized layout and the pre-development of mining blocks will be the early identification of a change in geological conditions. This will allow for better planning in terms of larger geological structures such as potholes and aspects such as optimum mining directions relative to joint orientations. This will allow for safer mining conditions and more mining flexibility. Compartmentalization will allow for each mining block to achieve an extraction ratio (which includes the barrier pillars) that typically varies from 69% to 74% while maintaining the overall stability of the mining operation. Table II shows the difference in extraction ratio for different size barrier pillars. Layout 1 is the traditional Everest platinum mine layout, which is used as a baseline with which to compare the proposed new extraction ratios. Layout 2 shows the decrease in extraction ratio if pillars are designed with more conservative parameters using a traditional bord-and-pillar layout. Layout 3 is the proposed new layout for different barrier pillar sizes.

Total area (m²)

Pillar area (m²)

Mined area (m²)

Extraction %

1 (7 m x 7 m pillars)

148 225

35 721

112 504

75.9

148 225

59 290

88 935

60.0

3 (15 m barrier)

133 225

35 589

97 636

73.3

3 (20 m barrier)

136 900

38 704

98 196

71.7

3 (25 m barrier)

140 625

42 149

98 476

70.0

3 (30 m barrier)

144 400

45 924

98 476

68.2

3 (35 m barrier)

148 225

49 049

99 176

66.9

3 (35 m split barrier)

148 225

46 074

102 151

68.9

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Bord-and-pillar design for the UG2 Reef containing weak alteration layers Figures 12 to 16 illustrate the simulated pillar failure for different barrier pillar widths. The objective of this modelling was to determine if the barrier pillars will survive the complete collapse of all the in-panel pillars on a scale similar to the Everest platinum mine collapse. Note the extensive failure of the in-panel pillars in all cases. Some spalling is noted on the 15 m and 20 m wide barrier pillars after the collapse of the in-panel pillars. For the current model calibration, it is therefore recommended to use at least 25 m wide pillars. To ensure safe travelling throughout the mine in case of large collapses, the split barrier option presented in Figure 17 may be a good solution. The simulated amount of scaling on the pillars is only minor and not more extensive than that experienced by the solid 35 m wide pillars. This option gives an extraction ratio of 69%. Although less than the typical 75%, it should be considered that it is very difficult to maintain excavation stability for these ground conditions and the slightly lower extraction ratio will make safe mining possible. Figure 14—Simulated pillar failure if the barrier pillars are of a size 25 m × 25 m. The orange colour denotes failure and the yellow denotes intact rock

Figure 12—Simulated pillar failure if the barrier pillars are of a size 15 m × 15 m. The orange colour denotes failure and the yellow denotes intact rock Figure 15—Simulated pillar failure if the barrier pillars are of a size 30 m × 30 m. The orange colour denotes failure and the yellow denotes intact rock

Figure 13—Simulated pillar failure if the barrier pillars are of a size 20 m × 20 m. The orange colour denotes failure and the yellow denotes intact rock 250

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Figure 16—Simulated pillar failure if the barrier pillars are of a size 35 m × 35 m. The orange colour denotes failure and the yellow denotes intact rock The Journal of the Southern African Institute of Mining and Metallurgy

Bord-and-pillar design for the UG2 Reef containing weak alteration layers on the preliminary model calibration and this needs to be refined in future. The limit equilibrium model needs to be calibrated for sitespecific conditions before stable pillar sizes can be determined. Although encouraging results were obtained, calibration of the limit equilibrium model, and any other alternative inelastic model and modelling approach that will be used remains a challenge. Laboratory testing is required to determine the rock strengths as well as the friction angles of the wet and dry alteration zone material.

Acknowledgements This work formed part of the MSc study of Paul Michael Couto at the University of Pretoria.

References Couto, P.M. 2022. The effect of geological alterations on pillar strength. MSc. (Applied Science: Mining) dissertation, University of Pretoria. Figure 17—Simulated pillar failure for ‘split’ barrier pillars of a size 35 m × 35 m (each portion 15 m × 35 m). The orange colour denotes failure and the yellow denotes intact rock

Couto, P.M. and Malan, D.F. 2023. A limit equilibrium model to simulate the large-scale pillar collapse at th Everest Platinum Mine. Rock Mechanics and Rock Engineering, vol. 56. pp. 183–197.

Conclusions

Hartzenburg, A.G, du Plessis, M, and Malan, D.F. 2020. The effect of alteration layers on UG2 pillar behaviour in the Bushveld Complex. Rock Mechanics for Natural Resources and Infrastructure Development. Fontoura, R. and Mendoza, P. (eds). International Society for Rock Mechanics and Rock Engineering, Lisbon. pp. 2309–2331

We investigated the effect of geological alteration layers on hard rock pillar strength. These alteration layers are found in the Bushveld Complex in South Africa where the pyroxenite has been exposed to hydrothermal fluid flow, serpentinization, and layer-parallel shearing. The resulting clay-like material and the weak partings substantially reduce pillar strength. Almost no information is currently available in the literature on appropriate design methodologies if weak layers are present in the pillars. The classical empirical pillar strength formulae are not applicable and their use for these pillars has already resulted in a number of minewide collapses. We propose an alternative numerical modelling approach to determine the stability of the bord-and-pillar layouts. The pillar shapes are mostly irregular in the hard rock mines and the displacement discontinuity boundary element method is the preferred analysis technique for mine-wide simulations. A limit equilibrium model is used to simulate the edge failure zone. A calibration of this model can then be used to design alternative layouts and appropriate barrier pillar sizes and spacings. The collapse of the Everest platinum mine is used as a case study to test the application of the proposed methodology. Two areas were simulated, namely part of the collapsed area and a second area with larger pillars that is still stable. This allowed for a first-order calibration of the limit equilibrium model. The effect of friction angle on the weak partings was illustrated by these models. The calibrated values for the two areas were identical, except for a 10° friction angle for the collapsed area and 25° friction angle for the stable area. This difference seemed reasonable owing to the presence of water in the collapsed area, which resulted in weathering of the alteration layer and a decrease in the friction angle. Barrier pillars will be necessary to compartmentalize the mine in areas where the alteration zones are present. The numerical modelling indicated that for the preliminary calibration of the model parameters, the barrier pillars will remain stable even in the case of large scale collapses, provided their width exceeds 25 m. Main access routes to the mining areas should ideally be protected by a double row of pillars at least 15 m wide, to provide for a safe travelling way. As a cautionary note, these pillar widths are based The Journal of the Southern African Institute of Mining and Metallurgy

Hedley, D.G.F. and Grant F. 1972. Stope pillar design for the Elliot Lake uranium mines. Journal of the Canadian Institute of Mining and Metallurgy, vol. 65. pp. 37–44. Jaeger J.C. and Cook, N.G.W. 1979. Fundamentals of Rock Mechanics, 3rd edn. Chapman and Hall, London. 576 pp. Lombard, J. 2008. Large collapse of hangingwall over the declines from Strike 0 to Strike 5 – Everest Platinum mine. Internal mine report RED 103/08, 12 December 2008. Malan, D.F. and Napier, J.A.L. 2011. The design of stable pillars in the Bushveld Complex mines: A problem solved? Journal of the Southern African Institute of Mining and Metallurgy, vol. 111. pp. 821–836. Martin, C.D. and Maybee, W.G. 2000. The strength of hard rock pillars. International Journal of Rock Mechanics and Mining Sciences, vol. 37. pp. 1239–1246. Napier, J.A.L and Malan, D.F. 2007. The computational analysis of shallow depth tabular mining problems. Journal of the Southern African Institute of Mining and Metallurgy, vol. 107. pp. 725–742. Napier, J.A.L. and Malan D.F. 2021. A limit equilibrium model of tabular mine pillar failure. Rock Mechanics and Rock Engineering, vol. 54. pp. 71–89. Peng, S.D. 1971. Stresses within elastic circular cylinders loaded uniaxially and triaxially. International Journal of Rock Mechanics and Mining Sciences, vol. 8. pp. 399–432. Spencer, D. 1999. A case study of a pillar system failure at shallow depth in a chrome mine. Proceedings of SARES99, 2nd Southern African Rock Engineering Symposium, Johannesburg, South Africa. Hagan, T.O. (ed.). South African National Institute of Rock Engineering. pp. 53–59. Van der Merwe, N. 2006. Beyond Coalbrook: What did we really learn? Journal of the Southern African Institute of Mining and Metallurgy, vol. 106. pp. 857–868. Wagner, H. 1980. Pillar design in coal mines. Journal of the South African Institute of Mining and Metallurgy, vol. 80. pp. 37–45 . VOLUME 123

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SAIMM HYBRID Bord-and-pillar design for the UG2 Reef containing weak alteration layers CONFERENCE

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The SAIMM is proud to announce its 3rd conference around the topic of Tailings. Since the inaugural conference, which raised ĴìÐ ĨīďťăÐ ďå ĴðăðĊæĮ ĊÌ ÐĊÆďķīæÐÌ ÆďăăÅďīĴðďĊ ÅÐĴœÐÐĊ the various role players in the tailings industry, and the 2nd ÆďĊåÐīÐĊÆÐș œìðÆì åďÆķĮÐÌ ďĊ ÐĉÅīÆðĊæ ĴìÐ :ăďÅă AĊÌķĮĴīř wĴĊÌīÌ ďĊ }ðăðĊæĮ TĊæÐĉÐĊĴ ȧ:Aw}TȨș ĴìÐīÐ ìĮ ÅÐÐĊ ĉķÆì ĨīďæīÐĮĮȘ qīďæīÐĮĮ ðĊ ĴÐīĉĮ ďå ÅÐĴĴÐī ķĊÌÐīĮĴĊÌðĊæ ďå ĴìÐ īÐĪķðīÐĉÐĊĴĮ ĊÌ ðĉĨăðÆĴðďĊĮ ďå ĴìÐ :Aw}Tș ĨīďæīÐĮĮ ðĊ ĴÐīĉĮ of improved geotechnical understanding of how tailings dams work, progress in terms of involving stakeholders and progress in terms of working towards improved safety performance Ĵìīďķæì ÆďĉĨăðĊÆÐ œðĴì ĴìÐ :Aw}TȘ }ìÐīÐ ìŒÐ ķĊåďīĴķĊĴÐăř ăĮď ÅÐÐĊ åķīĴìÐī ĴðăðĊæĮ Ìĉ åðăķīÐĮș œìðÆì ĮķææÐĮĴĮ ĴìĴ ĴìÐīÐ ðĮ ĮĴðăă œďīā Ĵď ÅÐ ÌďĊÐ ĊÌ ăÐĮĮďĊĮ Ĵď ÅÐ ăÐīĊĴȘ This conference focuses on the future of tailings for the next generation. In a future of new standards, expectations and ĨďĮĮðÅðăðĴðÐĮ ȭ œìĴ ďĨĨďīĴķĊðĴðÐĮ ÐŘðĮĴȟ ĊÌ ďĊ ĴìÐ ŦðĨ ĮðÌÐș œìĴ īÐ ĴìÐ īÐĮðÌķă īðĮāĮȟ >ďœ ÆĊ ĴðăðĊæĮ ÅÐ īÐÌķÆÐÌș īÐÆăðĉÐÌ ďī īÐķĮÐÌȟ >ďœ ÆĊ ÐŘðĮĴðĊæ ĴÐÆìĊďăďæðÐĮ ÅÐ ðĉĨīďŒÐÌș ĊÌ ĊÐœ ĴÐÆìĊďăďæðÐĮ ÅÐÆďĉÐ ĴìÐ ĊÐœ ĊďīĉăȘ ìĴ ðĉĨÆĴĮș ďĊÆÐ ÆďĊĮðÌÐīÐÌ ÆÆÐĨĴÅăÐș īÐ Ċď ăďĊæÐī ÆÆÐĨĴÐÌș ĊÌ ìďœ Ìď œÐ ÅÐĮĴ ÌÌīÐĮĮ ĴìÐĮÐȟ Join us in exploring these exciting topics in a forum with participation with all the key role players in the tailings industry.

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Calibration of the limit equilibrium pillar failure model using physical models R.P. Els1 and D.F. Malan1

Afﬁliation: 1Department of Mining Engineering,

University of Pretoria, South Africa.

Correspondence to: D.F. Malan

Email: francois.malan@up.ac.za

Dates: Received: 25 Feb. 2023 Revised: 31 May 2023 Accepted: 13 June 2023 Published: May 2023

Synopsis The limit equilibrium model, used in displacement discontinuity codes, is a popular method to simulate pillar failure. This paper investigates the use of physical modelling to calibrate this model. For the experiments, an artificial pillar material was prepared and cubes were poured using the standard 100 mm × 100 mm civil engineering concrete moulds. The friction angle between the cubes and the platens of the testing machine was varied by using soap and sandpaper. Different modes of failure were observed depending on the friction angle. Of interest is that significant loadshedding was recorded for some specimens which visually remained mostly intact. This highlights the difficulty of classifying pillars as failed or intact in underground stopes where spalling is observed. The laboratory models enabled a more precise calibration of the limit equilibrium model compared to previous attempts. Guidelines to assist with calibration of the model are given in the paper. The limit equilibrium model appears to be a useful approximation of the pillar failure as it could simulate the stress-strain behaviour of the laboratory models.

Keywords limit equilibrium model, calibration, physical modelling, pillar failure, friction angle.

How to cite: Els, R.P. and Malan, D.F. 2023 Calibration of the limit equilibrium pillar failure model using physical models. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 5. pp. 253–264 DOI ID: http://dx.doi.org/10.17159/24119717/2655/2023

Introduction Pillar design for bord-and-pillar layouts is typically done using empirical methods (see Martin and Maybee, 2000; van der Merwe and Madden, 2010). The empirical pillar strength equations are, however, not applicable to all geotechnical areas and there is a risk that the equations are used in mining areas where they are not a good approximation of pillar strength (Malan and Napier, 2011). For example, the weak alteration zones occasionally found in the pillars in the Bushveld Complex reduce the pillar strength and this may lead to mine-wide collapses (Couto and Malan, 2023). A popular alternative is to use numerical modelling, with an appropriate constitutive model, to simulate the rock failure and pillar strength (Sainoki and Mitri, 2017). The failure criteria are typically complex with a large number of parameters to calibrate. These models may therefore not always provide a good prediction of pillar strength and do not always replicate the correct failure mechanism (Malan and Napier, 2011). A popular approach to simulate pillar failure is to use a limit equilibrium model in a displacement discontinuity code (du Plessis, Malan, and Napier, 2011; Napier and Malan, 2021). This approach is useful as it combines the ability of the displacement discontinuity method to simulate tabular excavations on a

Table I

Example of the parameters used in the limit equilibrium model (after Napier and Malan, 2021) Parameter

Value

Intact strength intercept, σci

73.0 MPa 7.0

Intact strength slope, mi

46.0 MPa

Residual strength intercept, σc Residual strength slope, m

4.6

Effective seam height, H

3.0 m

Intact rock Young’s modulus, E

70 000.0 MPa

Intact rock Poisson’s ratio, ν

0.2

Fracture zone interface friction angle, φI

20°

Field stress normal to excavation plane

60.0 MPa

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Calibration of the limit equilibrium pillar failure model using physical models

Figure 1—The important components of the limit equilibrium model. The diagram at the top illustrates the forces acting on a thin slice of rock inside the pillar. The diagram at the bottom illustrates the strength failure envelopes and the associated parameters (after Wessels and Malan, 2023)

mine-wide scale with the limit equilibrium model to simulate onreef pillar failure. It can simulate the spalling of the pillars, complete pillar failure and the resulting stress transfer to adjacent pillars. This approach is particularly attractive for simulating large-scale bordand-pillar layouts with irregular pillars (Wessels and Malan, 2023) as well as conventional layouts in the Bushveld Complex with crush pillars (du Plessis, Malan, and Napier, 2011). A drawback of the limit equilibrium model is the large number of parameters to calibrate. Table I illustrates the parameters to be calibrated when using this model. Previous attempts to calibrate the model typically involved running simulations with a range of parameter values and comparing the results to underground observations (Napier and Malan, 2021). An improved understanding of the contribution of the various parameters and a calibration strategy is required. The limit equilibrium model is based on a force equilibrium analysis of a slice of rock in a pillar. The pillar material is bound by frictional parting planes at the hangingwall and footwall contacts (Figure 1). The physical models described in this paper were used to study the effect of this friction angle on pillar strength. In the numerical model, the pillar material can fail and the strength of this material is defined by two envelopes describing the intact strength and the residual strength (Figure 1). These are defined by strength intercept parameters and slope parameters. This basic model can be extended to simulate time-dependent pillar spalling (Wessels and Malan, 2023), but this is not considered in this paper. An unexplored method to calibrate the parameters shown in Table I is the use of physical models in the laboratory. The use of physical models in rock engineering is described in Napier and Ozbay (1994) and Ozbay, Dede, and Napier (1996). These laboratory models are now seldom used in South Africa, probably owing to the availability of complex numerical modelling codes and the high cost of conducting laboratory experiments. The limit equilibrium model is, however, an excellent example where physical models may 254

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be of benefit to better understand the applicability of the numerical model and to devise an improved calibration strategy. This paper describes the initial laboratory experiments that were conducted on model pillars made of an artificial material. One of the objectives of the study was to investigate the effect of friction angle on the hangingwall and footwall ‘partings’ which delineated the pillar. This was of interest owing to recent modelling that highlighted the detrimental effect of weak layers at these contact planes (Couto and Malan, 2023). The main aim of the experiments was, however, an attempt to validate and calibrate the limit equilibrium model.

Laboratory experiments on artificial pillars Sample preparation and test methodology The work was conducted using an artificial material that could be cast. The strength selected for the artificial material was low to ensure that the tests could be easily done in the presses available in the laboratory. The specimens were cast using the standard moulds used for preparing concrete cubes for civil engineering projects (Figure 2). This resulted in specimens with a side length of 100 mm. The casting of the artificial material had a benefit compared to using actual rock as a large number of samples could be cast and tested. The four sides of the cubes inside the moulds were also flat and parallel and two of these opposing sides were used as the contact surfaces with the testing machine. In contrast, achieving flat, parallel surfaces with actual rock material requires expensive and timeconsuming sample preparation. Rock samples also typically result in a large variability in strength when conducting laboratory testing. It was hoped that the artificial material would give more consistent results. The drawback of using the standard moulds was that all the ‘pillars’ tested were cubes with a width to height ratio of unity. The tests were conducted using the 50 kN testing machine in the concrete laboratory of the Engineering 4.0 facility at the University of Pretoria (Figure 3). The Journal of the Southern African Institute of Mining and Metallurgy

Calibration of the limit equilibrium pillar failure model using physical models

Figure 2—Casting of the cubes using the concrete test molds. The completed samples are shown on the right during the curing process

Figure 4—The tilt device built to measure the friction angle. The photograph on the left illustrates the cube sliding on the steel used for the platen. That was the base case and it gave a friction angle of 21°. The photograph on the right is for the sandpaper, giving a friction angle of 38° Figure 3—The Lloyd EZ50 testing machine used for the testing of the cubes

Table II

Composition of the artificial material used to cast the cubes Constituent

Relative density (RD)

Proportion (kg/m3)

Percentage mass (%)

Kaolin

2.70

269.62

16.40

Fly ash

2.22

787.54

43.24

Cement mixture

2.20

87.50

10.00

Water

1.00

499.04

30.36

Total

1643.7

100.00

The artificial material used by Jacobsz et al. (2018) and Schoeman (2020) for cave mine modelling in a centrifuge provided the basis for selecting the material for this project. Schoeman (2020) describes a material that was designed to replicate the brittle fracture behaviour of rock, but also to be weak enough to cave. The initial experiments with this material for the pillar project indicated that it was too weak and difficult to handle without breaking the samples. Cement was thus added to the mixture to improve its strength. No sand was added to the mixture. The final composition of the artificial material used by the authors is shown in Table II. Although the mixture contains materials typically associated with geopolymer cement and concrete, the material is not classified as a geopolymer as it contains the cement mixture. For the experiments, it was planned that all the specimens should have the same composition and dimensions. The only parameter varied was the boundary conditions at the platen contacts to study the effect of the contact friction angle. The ‘normal’ contact condition was with the steel platen directly applied to the cube. Two other frictional conditions were introduced by using a commercial soap material (to reduce the friction) and sandpaper The Journal of the Southern African Institute of Mining and Metallurgy

(to increase the friction) on the contacts between the steel and the cube. The same boundary condition was applied on the top and bottom contact of the cube to simulate the symmetrical attributes of the limit equilibrium model. The soap was grated material and it worked well, but several experiments had to be conducted to refine the sandpaper interface. One attempt was to fold the sandpaper in order to have a sandpaper contact against both the sample and the platen. After trial and error, it was found that glueing the two sides of the sandpaper together gave the most consistent results. For these samples, the contact condition was therefore the rough sandpaper against both the steel platen and the sample, which substantially increased the friction angle. It is known from the literature that the basic friction angles of planar rock surfaces can be determined by means of tilt tests (Alejano et al., 2018). To determine the friction angle of the three types of boundary conditions described above, a simple tilt device was constructed. This is illustrated in Figure 4. A screw mechanism was implemented to ensure that the angle can be gradually increased. The ISRM-suggested method for the tilt test (Alejano et al., 2018) requires that at least five repetitions be performed and the median of the result taken to give the basic friction angle ϕb = median βi=1,…,5. It was found that the artificial material cubes gave consistent friction angle values throughout and there was no need to determine the median of the five results. The samples against the steel platen gave a friction angle of 21°, the soap contact reduced it to 16°, and the sandpaper increased it to 38°. The set-up of the platen contact conditions in the testing press are depicted in Figure 5.

Test results Figure 6 illustrates the typical failure mode of the cubes. The observed mode of failure was consistent for each of the three types of platen boundary conditions and the photographs in the figure are representative of the failure mode for each type. Immediately evident is that the low friction angle specimens underwent axial splitting, while the normal platen conditions with a higher friction VOLUME 123

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a) Normal platen contacts

b) Grated soap contacts

c) Glued sandpaper contacts

b) Normal platen contacts (21o)

c) Sandpaper contacts (38o)

Figure 5—Different boundary conditions used in the laboratory tests

a) Grated soap contacts (16o)

Figure 6—Failure modes for the different boundary conditions. For the sandpaper contact, note the shear failure from the top left edge to the bottom right edge

angle led to an ‘hourglass’ failure pattern. These two failure patterns are reminiscent of actual pillar failures observed underground (Malan and Napier, 2011). Further examples of the different types of pillar failures and the effect of a weak layer on pillar strength are given in Wagner (1980) and Esterhuizen and Ellenberger (2007). The sandpaper boundary condition typically led to the formation of an inclined shear between two opposing sides from a top to a bottom corner. These laboratory tests are therefore useful to test the limit equilibrium model as three distinctly different modes of failure are observed. It was initially not clear if the limit equilibrium model is a good approximation for all three cases. Figures 7 to 9 illustrate the load deformation behaviour of the specimens. The material is weak (peak strength approx. 1 MPa for the cubes with the normal platen conditions) and the post-peak behaviour could be captured by the test equipment. Surprisingly, there is significant variability in the test results, although the specimens were from the same mix. As the tests could not be conducted on the same day, it is not clear if different curing times played a role and this needs to be investigated in future. For all the tests, some ‘settling’ of the platen on the cube occurred at the beginning of the tests, resulting in the initial flat portions of the curves. This was particularly prominent for the soap contact as the relatively thick layer of soap had to be compacted first. It should be noted that the test conditions may have affected these initial test results and this needs to be explored in future. A spherical seat was not used during the test set-up. The edges of samples in contact with the testing machine were nevertheless considered parallel as two opposing sides of the cubes from inside the moulds were used as the contact surfaces. However, no flatness or parallelism measurements were made. The thickness of the soap layer was controlled by using 256

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the same volume of grated soap for each test and efforts were made to spread this soap uniformly across the surface of the specimens to give a constant thickness. This was a crude method and the results should therefore be considered as showing trends rather than providing absolute values. Consideration should be given to how this can be better controlled and measured in future. The initial compaction phase was followed by elastic compression, peak stress, and the post-failure part of the curve. The peak stress for the samples with the soap boundary condition was substantially smaller than for the other two types of tests.

Figure 7—Stress-strain results for the cube tests with normal platen conditions (21° friction) The Journal of the Southern African Institute of Mining and Metallurgy

Calibration of the limit equilibrium pillar failure model using physical models

Figure 8—Stress-strain results for the cube tests with the soap boundary conditions (16° friction)

Figure 9—Stress-strain results for the cube tests with the sandpaper boundary conditions (38° friction)

Figure 10—Stress-strain curve and the associated stages of failure for a cube test with soap boundary conditions (16° friction angle). Enlarged photographs are given below the graph The Journal of the Southern African Institute of Mining and Metallurgy

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Figure 11— Stress-strain curve and the associated stages of failure for a cube test with normal boundary conditions (21° friction angle). Enlarged photographs are given below the graph

A particular test for each boundary condition was examined in detail and photographs of the state of failure of the ‘pillar’ were included on the graphs. Figure 10 illustrates a test result with a soap boundary condition. The soap layer needs to be compressed during the early part of the test and therefore significant strain occurs for some samples before the stress starts increasing. In contrast to the test with the other boundary conditions, fracturing is observed only at the peak stress. The strength is also significantly lower. Note that the fracturing recorded for these experiments is based on visual observations only. It is recommended that other techniques, such as acoustic emission monitoring, be used in future to detect the possible earlier onset of fracturing. For the normal boundary condition test shown in Figure 11, some fracturing is observed before the peak stress. Significant load-shedding occurs at 2% strain while the sample still appears to be mostly intact. At the end of the test, the core of the pillar still appears to be intact, but significant load-shedding has occurred. This is an important observation in terms of evaluating undergound pillars that are spalling and still appear to be intact. These pillars 258

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may in fact be already failed. Failure is evident at the end of the test in the form of an ‘hourglass’ shape. The test with the highest friction angle is shown in Figure 12. The fracturing again starts before the peak strength is achieved. At the end of the test, the inclined fracture running from the top left corner to the bottom right is again visible. Table III gives a summary of the results with the three friction angles as well as the average peak strengths calculated from the results. Although there is significant variability, there is a trend of increasing peak strength with an increase in friction angle. This is also predicted by the limit equilibrium model modelling and the laboratory testing confirms this attribute of the model. The 38° friction angle did not result in much stronger pillars than the 21° friction angle. This is attributed to the different mechanism of failure (the inclined shear failure). In the next section we investigate the ability of the limit equilibrium model to simulate these results by considering an analytical model of a square pillar. The Journal of the Southern African Institute of Mining and Metallurgy

Calibration of the limit equilibrium pillar failure model using physical models

Figure 12— Stress-strain curve and the associated stages of failure for a cube test with sandpaper boundary conditions (38° friction angle). Enlarged photographs are given below the graph

Table III

Summary of test results Boundary condition

Average friction angle (°)

Average peak strength (MPa)

Normal platen

0.91

Soap

0.43

Glued sandpaper

1.03

An analytical limit equilibrium model of a square pillar Napier and Malan (2021) derived an analytical solution for the failure of a square pillar, assuming a limit equilibrium model (Figure 13). The detailed derivation of the model will not be repeated here and only a few key equations and additional interpretations are given below. The reader should consult the reference for additional information. The Journal of the Southern African Institute of Mining and Metallurgy

Figure 13—Top view of a square pillar with the intact core shown (after Napier and Malan, 2021). The parameter α0 defines the width of the intact core. The pillar is completely fractured for α0 = 0 and it is intact for α0 = a VOLUME 123

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Calibration of the limit equilibrium pillar failure model using physical models From Figure 13, the width of the square pillar is w=2a. It is assumed that for a limit equilibrium model, the scaled average pillar stress (APS) is expressed by a weighted combination of the average of the stresses in the intact core region and in the surrounding fractured region. Napier and Malan (2021) showed that the scaled APS, A, as a function of the scaled pillar strain, X, can be given by [1] where the scaled fracture zone length parameter ϕ is given by [2] The parameter ϕ can be considered as a pillar damage variable that ranges from ϕ = 0 for an intact pillar to ϕ = 1 for a pillar that is completely fractured. Based on Figure 13, it follows that [3] In terms of the other scaled parameters, it follows that [4]

[10] The APS for a friction angle of φI = 0 for a pillar completely fractured will therefore be Q. To gain insight into the effect of the friction angle, Equation [9] was used to plot A* as a function of friction angle φI. This is illustrated in Figure 14. Note that the y-intercept is the Q value. The graph therefore correctly predicts that for the parameter values selected. Figure 14 provides a possible method to calibrate the residual strength in the model, σc, from laboratory testing. If ‘pillars’ can be tested at different interface friction angles, a function fitted to the data can be extrapolated to determine the y-intercept. From this value and the intact strength of the material, the residual strength value can be computed by using Equation [8]. This methodology is illustrated in Figure 15. The same parameter values as Figure 14 were used, but only seven data-points for different friction angles were plotted. The fitted exponential function predicted a y-intercept of 0.45. For the known parameter = 1 MPa, the residual strength can be calculated from Equation [8] as 0.45 MPa. This is a reasonable approximation of the correct value of 0.5 MPa.

where σ–n is the average stress across the pillar (the intact core as well as the fractured edge zone) and is the intact uniaxial strength. In terms of the scaled strain, [5] where ε0 is the average strain at the point where the pillar stress reaches the postulated intact uniaxial strength . The other parameters in Equations [1] and [2] are [6] [7] [8] where mi is the slope of the intact limit equilibrium strength envelope, m is the slope of the residual limit equilibrium strength envelope, is the intact rock uniaxial strength, and σc is the residual strength after failure (Figure 1 shows an example of these strength envelopes). The parameters w and h are the width and height of the pillar respectively. Furthermore, μI = tanφI is the coefficient of friction at the interfaces of the pillar with the hangingwall and footwall and φI is the interface friction angle. These parameters are also given in Table I. From Equation [1], the scaled APS, A*, for the pillar when the pillar is completely fractured, ϕ = 1, is given by the simplified equation (Napier and Malan, 2021):

Figure 14—Scaled APS as a function of friction angle. This is for a square pillar that is completely fractured through. Parameters = 1 MPa, σc = 0.5 MPa, m = 2, w = 0.1 m, and h = 0.1 m

[9] A number of properties of the model are evident from the solution given in Equation [9], and these may be useful when calibrating the model using the laboratory test results. If σc = 0 (or Q = 0), then the residual APS when the pillar is fractured through will be zero. Values of σc > 0 need to be selected. Furthermore, if the friction angle φI tends to zero, (or β → 0), the residual APS is given by the following solution: 260

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Figure 15—A few selected data-points of scaled APS as a function of friction angle. Parameters = 1 MPa, σc = 0.5 MPa, m=2, w=0.1 m, and h = 0.1 m The Journal of the Southern African Institute of Mining and Metallurgy

Calibration of the limit equilibrium pillar failure model using physical models

Figure 16—Laboratory data for the completely failed specimens with a fitted exponential function. This gives a value of Q = 0.067

analytical model (Equations [4] and [5]) to enable a comparison to be made. The origin of the laboratory data was also shifted to the left as the analytical model cannot consider the initial ‘compaction’ during the early stages of the test. This compaction was particularly prominent for the soap layer. The fitted data is shown in Figures 17, 18, and 19. This was done by trial and error by modifying mi and m to give the best fit. Reasonably good fits between the model and the laboratory data for all three types of test were obtained. The calibrated parameter values are shown in Table IV. It was very encouraging that the experimental curves could be replicated. The only difference between the tests was the friction angle and surprisingly, the curves could be replicated with similar values for the other parameters. The only exception was that a lower value for m was used for the specimen with the highest friction angle (38°). This is not unexpected considering that different failure mechanisms were observed for the three groups of laboratory specimens and the limit equilibrium model is only a simplified approximation.

Figure 16 illustrates the actual laboratory data at the different friction angles. The final residual stresses in Figures 10, 11, and 12 (normalized to the intact uniaxial strength, 0.91 MPa) were used for this plot and it is therefore assumed that the laboratory specimens are fractured throughout at these points on the graphs. The data in Figure 16 predicts a y-intercept of 0.067. For the known = 0.91 MPa (average of the specimens with a parameter normal platen contact), the residual strength can be calculated from Equation [8] as 0.06 MPa. This was rounded to a value of 0.1 MPa for the additional steps in the calibration process described below. This seems a useful method to calibrate the residual strength parameters, σc, but it is recommended that additional tests be done in future with a greater variety of friction angles to verify this approach. As a first attempt to calibrate the remaining parameters (mi and m), an attempt was made to fit Equation [1] to the stress-strain data presented in Figures 10, 11, and 12. The known and calculated parameter values were used and mi and m fitted. The data from the laboratory tests was scaled similar to the method used for the

Figure 18—A comparison between the laboratory data (also shown in Figure 10) and the analytical limit equilibrium model for a square pillar (blue curve). Soap boundary conditions (16° friction angle)

Figure 17—A comparison between the laboratory data (also shown in Figure 11) and the analytical limit equilibrium model for a square pillar (blue curve). Normal platen boundary conditions (21° friction angle)

Figure 19—A comparison between the laboratory data (also shown in Figure 12) and the analytical limit equilibrium model for a square pillar (blue curve). Sandpaper boundary conditions (38° friction angle)

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Calibration of the limit equilibrium pillar failure model using physical models Also, of value for the calibration process is that the limit equilibrium model can predict strain softening or hardening after the onset of failure. According to Napier and Malan (2021), the condition for immediate softening at the onset of failure for a square pillar is [11] where β, M, and Q are given in Equations [6] to [8]. Furthermore, the constraint that the final pillar stress (AFinal) is greater than the APS at the onset of failure (AInitial) is given by [12] Equations [11] and [12] define whether there is initial softening or hardening of the APS at the onset of failure and the residual hardenend or softened state when the pillar is completely fractured. These values were calculated for the calibrated parameters in Table IV and correctly predict that, for all three cases, there will be immediate softening after failure and the final APS will be less than the APS at which the initial failure occurred. The two conditions given in Equations [11] and [12] are valuable constraints that can assist during model calibration.

Guidelines to assist with calibration of the limit equilibrium model The steps followed to obtain an improved calibration of the limit equilibrium model can be summarized as follows.

³ Laboratory testing to determine the intact rock uniaxial strength. For the experiments in the paper, this was assumed to be the strength of cubes tested using normal conditions on the platens. It needs to be confirmed how well this agrees with the standard ISRM test methodology to determine the uniaxial compressive strength. The effect of other parameters such as humidity and temperature also need to be studied as these may affect the rock material strength in the underground excavations. ³ Laboratory testing to determine the shear strength of any weak interfaces present in the pillar. Weak alteration zones in the Bushveld Complex are typically thick clay layers and have a different friction angle in dry and wet conditions (Couto and Malan, 2023). These layers and the infilling need to be carefully tested using a shear box setup and appropriate test methodologies. ³ Cube testing of intact pillar material at different friction angles may assist to estimate the residual strength of material when using the limit equilibrium solution for a square pillar as described above. Sample preparation using actual rock will be arduous and varying the friction angle between the sample and the test platens is also a difficult practical problem. ³ The very weak material used for the experiments in this study made it easy to obtain the complete stress-strain curves. For actual rock specimens, a stiff testing machine with servo-control may be required.

Table IV

Calibration of limit equilibrium model for the laboratory specimens Parameter

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Soap contact

Normal contact

Sandpaper contact

Intact strength intercept,

0.9 MPa

Intact strength slope, mi

7.0

Residual strength intercept, σc

0.1 MPa

Residual strength slope, m

7.0

3.5

Pillar height, h

0.1 m

Pillar width, w

0.1 m

Interface friction angle, φI

16°

21°

38°

0.111

1.0

0.5

2.007

2.687

2.734

0.111 < 0.499 Immediate softening

0.111 < 0.427 Immediate softening

0.111 < 0.268 Immediate softening

0.111 0.454 AFinal < AInitial

0.111 0.328 AFinal < AInitial

0.111 0.320 AFinal < AInitial

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Calibration of the limit equilibrium pillar failure model using physical models ³ The analytical limit equilibrium model presented in Napier and Malan (2021) is a valuable tool for testing cubic samples, and this should be studied in detail to ensure its correct application. The limit equilibrium is an elegant and relatively simple model, to represent pillar failure in displacement discontinuity boundary element codes. This enables the study of mine-wide geometries where pillar failure is encountered on a large scale. If there are complex pillar failure mechanisms however, such as that caused by major inclined discontinuities traversing the pillars, the limit equilibrium may not be able to simulate the failure behaviour well. Care should also be exercised regarding the presence of weak layers. The limit equilibrium model is a symmetrical model, but pillars are frequently encountered where there is only one weak plane present, at for example the hangingwall contact. Further work is required to extend the model to cater for these asymmetrical pillar geometries. In summary, calibration remains a challenge and a larger number of back-analysis studies will have to be conducted before the model can be used with confidence to predict the pillar strength and layout stability for new mining projects.

Conclusions The work described in this paper illustrated that laboratory experiments, using an artificial rock material, is a valuable tool to assist with the calibration and validation of complex failure models, such as the limit equilibrium model. Physical experiments to assist with rock engineering studies has been neglected in South Africa in modern times and this capability needs to be rebuilt. The tests on the artificial pillars confirmed once again that the interfaces between the pillar and hangingwall, and the pillar and footwall, have a significant effect on the pillar strength. For these tests, there was approximately a 60% reduction in average pillar strength (Table II) when the friction angle on the interface decreases from 38° to 16°. The limit equilibrium model could simulate the reduction in pillar strength for a decrease in friction angle on the interfaces. It also successfully simulated the stress-strain behaviour of the pillars. This work therefore illustrates the value of the model, provided the parameters can be calibrated. A drawback of the current model is that it assumes a symmetrical geometry with weak partings at both the hangingwall and footwall. This could be easily replicated in the laboratory with the artificial pillars, but is rarely encountered in underground stopes where only one weak plane may be present. Further work therefore needs to be done to extend the model to account for asymmetric conditions. Additional laboratory work using a wider range of friction angles will also be useful to verify the calibration methodology proposed in the paper. It is not easy to find suitable materials to reduce or increase the friction angle on the interface in a stepwise fashion. It was also disappointing that the artificial pillar material still resulted in significant variability in strength for the various samples tested. The reasons for this need to be explored to reduce this variability in future experiments.

References Alejano, L.R., Muralha, J., Ulusay, R., Li, C. C., Pérez-Rey I., Karakul, H., Chryssanthakis, P., and Aydan, Ö. 2018. ISRM suggested method for determining the basic friction angle of planar rock surfaces by means of tilt tests. Rock Mechanics and Rock Engineering, vol. 51. pp. 3853–3859. Couto, P.M. and Malan, D.F. 2023. A limit equilibrium model to simulate the large-scale pillar collapse at the Everest Platinum Mine. Rock Mechanics and Rock Engineering, vol. 56. pp. 183–197. Du Plessis, M., Malan, D.F., and Napier, J.A.L. 2011. Evaluation of a limit equilibrium model to simulate crush pillar behaviour. Journal of the Southern African Institute of Mining and Metallurgy, vol. 111. pp. 875–885. Esterhuizen, G.S. and Ellenberger, J.L. 2007. Effects of weak bands on pillar stability in stone mines: Field observations and numerical model assessment. Proceedings of the 26th International Conference on Ground Control in Mining, Morgantown, W.V. Peng, S.S., Mark. C., and Finfinger, G. (eds). https://www. cdc.gov/niosh/mining/userfiles/works/pdfs/eowbo.pdf Jacobsz, S., Kearsley, E. P., Cumming-Potvin, D., and Wesseloo, J. 2018. Modelling cave mining in the geotechnical centrifuge. Physical Modelling in Geotechnics, vol. 2. CRC Press. Malan, D.F. and Napier, J.A.L. 2011. The design of stable pillars in the Bushveld mines: A problem solved? Journal of the Southern African Institute of Mining and Metallurgy, vol. 111. pp. 821–836. Martin, C.D. and Maybee, W.G. 2000. The strength of hard-rock pillars. International Journal of Rock Mechanics and Mining Sciences, vol. 37. pp. 1239–1246. Napier, J.A.L. and Malan, D.F. 2021. A limit equilibrium model of tabular mine pillar failure. Rock Mechanics and Rock Engineering, vol. 54. pp. 71–89. Napier, J.A.L. and Ozbay, M.U. 1994. The role of physical modelling in the calibration of numerical models. Application of Numerical Modelling in Geotechnical Engineering. Proceedings of the SANGORM Symposium, Pretoria. South African National Institute of Rock Engineering, Johannesburg. Ozbay, M.U., Dede, T., and Napier, J.A.L. 1996. Physical and numerical modelling of rock fracture. Journal of the South African Institute of Mining and Metallurgy, vol. 96, no. 7. pp. 317-327. Sainoki, A. and Mitri, H.S. 2017. Numerical investigation into pillar failure induced by time-dependent skin degradation. International Journal of Mining Science and Technology, vol. 27, no. 4. pp. 591–597. Schoeman, N. 2020. The effect of overburden and horizontal confining stress state on cave mining propagation. MEng dissertation, University of Pretoria. Van der Merwe, J.N. and Madden, B.J. 2010. Rock Engineering for Underground Coal Mining. 2nd edn. Special Publications Series 8, Southern African Institute of Mining and Metallurgy, Johannesburg.

Acknowledgements

Wagner, H. 1980. Pillar design in coal mines. Journal of the South African Institute of Mining and Metallurgy, vol. 80. pp. 37–45.

This work forms part of an MEng study by Ruan Els at the University of Pretoria. The authors would like to thank the Civil Engineering Department of the University of Pretoria for the use of their facility and equipment.

Wessels, D.G. and Malan, D.F. 2023. A limit equilibrium model to simulate timedependent pillar scaling. Rock Mechanics and Rock Engineering, vol. 56. pp. 3773–3786.

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BACKGROUND The theme of this second geometallurgy conference ‘Geomet meets Big Data’ is inspired by the growing interest and focus on big datasets, machine learning, novel sensors, digital twins and 4IR in the mining industry. The concept of Geometallurgy goes back to some of the earliest mining activities when mineral recognition, mining, separation, and concentration were undertaken simultaneously. Over time, changes in operational structures, product expansion and specialisation ultimately led to the diminishment and breakdown of this holistic approach. In the last two decades, Geometallurgy has become a sophisticated yet o entirely logical return to this integrated approach to g mine planning. In a world of exponentially increasing ore heterogeneity and metallurgical complexity coupled with a demand for improved sustainability, Geometallurgy is effectively a highly structured, integrated multi-disciplinary collaboration for optimizing the value of an ore deposit. This conference provides a platform for the discussion ďå ĮďĉÐ ďå ĴìÐ ĊÐœÐĮĴ ÌÐŒÐăďĨĉÐĊĴĮ ðĊ ĴìÐ ťÐăÌ ďå geometallurgy and a celebration of the success of Geometallurgy integration and value-add.

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FOR FURTHER INFORMATION CONTACT: VOLUME 123 The Journal of the Southern African Institute of Mining and Metallurgy E-mail: gugu@saimm.co.za Conference Co-ordinator Tel: +27 11 538-0237, Web: www.saimm.co.za

MAYGugu 2023 Charlie,

A study of UG2 pillar strength using a new pillar database T.E. Oates1 and D.F. Malan1

Afﬁliation: 1Department of Mining Engineering,

University of Pretoria, South Africa.

Correspondence to: D.F. Malan

Email: francois.malan@up.ac.za

Dates: Received: 3 Mar. 2023 Revised: 21 Apr. 2023 Accepted: 20 May 2023 Published: May 2023

How to cite: Oates, T.E. and Malan, D.F. 2023 A study of UG2 pillar strength using a new pillar database. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 5. pp. 265–274

Synopsis A recent experimental pillar extraction project at a UG2 bord-and-pillar mine presented a unique opportunity to compile a new pillar database. Currently, the South African hard rock bordand-pillar mines are designed using the Hedley and Grant formula with a modified K-value. This empirically derived formula was developed for uranium mines in the Elliot Lake district of Canada. The use of this formula for the design of pillars in South Africa is questionable. Very few pillar failures have nevertheless been observed and its current calibrations for the various reef types are possibly too conservative. A new UG2 pillar database of 66 pillars, of which seven are classified as failed, was compiled by the authors. This enabled a revised ‘first-order’ calibration of the K-value for the Hedley and Grant formula. The new estimated value for the UG2 is K = 75 MPa. This gives a pillar strength that is more conservative than the PlatMine formula. This work should nevertheless be considered as only a preliminary calibration as the database was small. Further work is also required to determine whether the exponents in the formula for the width and height parameters are appropriate for UG2 pillars.

Keywords pillar strength, UG2, K-value, Hedley and Grant formula.

Introduction DOI ID: http://dx.doi.org/10.17159/24119717/2656/2023

Empirically derived pillar strength formulae are commonly used in the global coal and hard rock mining industries. The hallmark coal pillar strength formula proposed by Salamon and Munro (1967) has been used in the design of many South African collieries. The success of this empirically derived formula can be attributed to the size of the original database used, and the fact that all the pillars included are from South African mines. The database included 125 pillar cases of which 27 were failed. The updated South African coal pillar database, used by van der Merwe and Mathey (2013) included 86 failed pillar cases and 337 intact pillar cases. As a more recent development, van der Merwe (2019) noted a major shortcoming of the statistical back-analysis of coal pillar strength as it relies on the ‘as-mined’ pillar dimensions and ignores time-related pillar scaling with subsequent reduction in pillar width. By considering this, an equation for pillar strength which predicts significantly greater pillar strength than the previous statistical analyses was derived. Van der Merwe‘s paper gives valuable databases of failed and intact cases. An important aspect related to coal is that the pillar shapes and layouts of the bord-and-pillar mines in South Africa do not differ greatly, and this facilitates the development of empirically-derived pillar strength formulae. In contrast, the Hedley and Grant (1972) pillar strength formula, which is still being used for the design of pillars in the hard rock mining industry of South Africa, was derived based on a data-set of only 28 pillars. This included only three crushed pillars and two partially crushed pillars. The source of this database was quartzite pillars in the Elliot Lake district of Canada and it did not include any South African pillars. The use of this formula in the South African mining industry is therefore questionable (Malan and Napier, 2011). It should be noted that both the Hedley and Grant and Salamon equations assume a power law strength formulation; the motivation for this is given below. Following the work by Hedley and Grant (1972), there have been several other attempts to develop hard rock pillar strength formulae. These are given by Martin and Maybee (2000) and are listed in Table I. These formulae were developed based on observed pillar failures. Note the small number of pillars in most of the databases used. It is clear that the formulae take the form of either a power- or linear-type equation. These equations have been used to predict the pillar strength for a wide range of pillar shapes and rock mass strengths.

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A study of UG2 pillar strength using a new pillar database Table I

Different empirical strength formulae for hard rock pillars (after Martin and Maybee, 2000) Vc (MPa)

Rock mass

No. of pillars

[3]

230

Quartzites

[4]

Metasediments

[5]

100

Limestone

[6]

Canadian Shield

[7]

240

Limestone/Skarn

[8]

Hard rocks

178a

Reference

Pillar strength formulas (MPa)

[3] Hedley and Grant (1972) [4] Von Kimmelmann (1984) [5] Krauland and Soder (1987) [6] Potvin, Hudyama, and Miller (1989) [7] Sjöberg (1992) [8] Lunder and Pakalnis (1997. Some discussion on the original adoption of the power-law formula for the coal mining industry is insightful. The general form of the equation is given as [1] where σp (MPa) is the pillar strength, K (MPa) is the strength of a unit volume of coal, w is the width of the pillar, h is the mining height, and α and β are exponents. The selection of a power-law equation was motivated by Salamon and Munro (1967) as follows: ‘The strength of a pillar depends on the strength of the material of which it is composed, its volume and its shape. Presumably, the effect of shape is due to the constraint imposed on the pillar by the roof and floor through friction or cohesion. The volume and shape of square pillars are completely defined by their width (w) and height (h). The most commonly-occurring pillar strength formula in the literature is a simple power function composed of these variables.’ The emphasis on square pillars in the quote above is evident and its application to irregular-shaped pillars is uncertain. Work was conducted in the PlatMine research programme to develop local pillar strength formulae for the platinum industry. Watson et al. (2008) compiled a database of 179 Merensky Reef pillars, of which 109 were stable. In 2020, Watson et al. (2021) developed a new UG2 pillar strength formula for the platinum industry based on a larger data-set of 167 UG2 pillars. The conventional crush pillar layouts of the mines (Figure 1), from which these data-sets were compiled, differ from the shallow bord-and-pillar mines in the Bushveld Complex. Most of the pillar width:height ratios in the PlatMine database ranged between 1.5 and 4, and the heights were in the limited range of 1.5 m to 2 m. It should also be noted that the crush pillars in the conventional layouts are typically irregular in size, and this may cause difficulties when calibrating a strength formula for an assumed square pillar. 266

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Figure 1—Example of a mine layout illustrating some of the pillars included in the PlatMine UG2 pillar database (Watson et al., 2021)

An experimental pillar extraction project at a mine in the eastern Bushveld Complex offered a unique opportunity to the authors to compile a new database of UG2 pillars in a mechanized bord-and-pillar mine. This database enabled an improved calibration of the Hedley and Grant formula. This can be used in areas of similar geotechnical conditions and layouts to optimize pillar design. As a cautionary note, however, this new calibration should be carefully tested in trial sections with suitable instrumentation and monitoring before it is adopted. The database is limited in size, and it should be expanded in future to verify its applicability.

Observations of pillar condition in an experimental pillar mining area The experimental pillar mining area is illustrated in Figure 2. The site is described in Watson et al. (2021). The mine established this experimental section in an attempt determine the strength of UG2 chromitite pillars. A central pillar (pillar A in Figure 2) was instrumented, and the surrounding pillars were progressively The Journal of the Southern African Institute of Mining and Metallurgy

A study of UG2 pillar strength using a new pillar database

Figure 2—Layout of the experimental pillar mining area. Pillars in blue were gradually reduced in size to increase the load on the central pillar. The final geometry of the area when the experiment was terminated is shown on the right. The instrumented pillar is indicated as pillar A (after Napier and Malan, 2021)

mined until failure of the central pillar occurred. The central pillar showed signs of limited scaling, while the small neighbouring pillars were severely fractured. A peak average pillar stress (APS) value of 160 MPa acting on the pillar was inferred (although it should be noted that the stress measurements were done in the hangingwall above the central pillar and not directly in the pillar). Further details on the measurements recorded are described in Watson et al. (2021). As can be seen in Figure 2, the experiment resulted in pillars of different sizes and the observations indicated these are at varying degrees of stability. This is particularly valuable to estimate pillar strength as it is in the same area and therefore in the same geotechnical area. Napier and Malan (2021) simulated this area using a displacement discontinuity code and a limit equilibrium failure model. They found it difficult to reconcile the simulated APS of the central pillar with the peak APS value presented in Watson et al. (2021). Napier and Malan (2021) simulated a peak APS in the order of 40-50 MPa for simulations where the central pillar failed, and 60-70 MPa for simulations where the pillar was still intact. The reason for the large discrepancy between the measured peak APS and the simulated APS is not known. An aspect that should be considered with these experiments is that strength variability will be encountered when conducting underground pillar strength experiments. As an example, Figure 3 illustrates the data collected by Cook, Hodgson, and Hojem (1971) in an attempt to verify the Salamon power-law strength formula. These were actual underground strength tests of large coal pillars loaded to failure. The

In June 2021 a number of underground visits were conducted to assess the pillar conditions at the mine. A total of 66 pillars in six different areas (Figure 4) were selected for detailed observations and for populating the database. The pillars selected for the database typically fell into the following categories: ³ Pillars with dimensions smaller than the design specifications ³ Pillars in the experimental project area ³ Pillars with ‘anomalous’ behaviour ³ ‘Normal’ pillars at different depths. Only limited observations were recorded in the old areas of the mine owing to the following reason. Pillars with ‘anomalous’ behaviour or with dimensions smaller than the design specifications are rehabilitated by the mine using shotcrete and a double row of resin bolts spaced 1 m × 1 m. Apart from examining the integrity of the shotcrete lining, visual observations of these pillars were not useful for making meaningful statements about pillar stability.

Figure 3—Experimental work to test the in-situ strength of coal pillars (after Cook, Hodgson, and Hojem, 1971). Note the large variability in the pillar strength data

Figure 4—Areas of the mine where the pillar data was collected

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significant scatter of the data is striking. It is reasonable to assume that a similar variability will be found for the in-situ testing of hard rock pillars. This is concerning, as a single underground hard rock pillar reduction test may therefore not be enough to verify the applicability of any formula. This emphasizes the need of building large site-specific pillar databases to obtain improved estimates of pillar strength.

Data collection Site observations

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A study of UG2 pillar strength using a new pillar database The following information was collected for each pillar: ³ Dimensions of the pillar ³ Photographs of each side of the pillar ³ Comments on geological structures in or nearby the pillar ³ The pillar classification based on Figure 5. The pillar classification proposed by Esterhuizen et al. (2006) was used to categorize the pillars (Figure 5). They based this classification on the systems developed by Lane, Yanske, and Roberts (1999), Siefert et al. (2003), Krauland and Soder (1987), Lunder (1994), and Pritchard and Hedley (1993). The similarity of the classification system, for the different databases in literature, enables their use in a larger, consolidated database. Esterhuizen et al. (2006) noted that pillars with a classification of 3 and below are typically made safe with regular scaling procedures and may require occasional rib bolting or screen. Pillars classified as 4 and above are generally barricaded off and require extensive support systems to preserve the integrity of the pillars. Regarding the current study, the classification was modified and pillars 1-2 were defined as stable, 3 as unstable, and 4-5 as failed. This slight modification was used as it was considered a more appropriate ranking of pillar behaviour at the UG2 mine. Pillars classified as failed were deemed to no longer function as stable pillars with an intact core which can carry the required tributary area load. Pillars in the unstable and stable categories used in this study were considered functional pillars that still carry their full load. It should be noted that this is a subjective measure based on the extent of fracturing and visual condition recorded for a pillar. This is a potential flaw in all studies, including the previous PlatMine study, that attempt to classify pillars based on visual observations alone. Measurement techniques to objectively determine if the core of the pillar is still intact, and the magnitude of the load carried, are unfortunately too expensive and time-consuming.

The experimental pillar project area was the only area in the mine where pillars in each of the categories could be found. It should be noted that all the failed and unstable pillars in the database are from the 25 pillars in the experimental pillar project area. A total of 7 of the 25 pillars in the area were classified as failed and are circled in red in Figure 6. An example of a Class 5 failed pillar is shown in Figure 7. A total of 5 of the 25 pillars were classified as unstable and are circled in yellow in Figure 6. Based on the classification system, the centre pillar (Figure 8) was classified as a Class 3 unstable pillar. The remaining pillars in the experimental project area were classified as Class 1-2 stable pillars and are circled in green in Figure 6. An example of a pillar in this class is shown in Figure 9. The other pillars in the database are classified as either stable or ‘geologically disturbed’ (Class G) pillars. Class G pillars were recorded as a separate class as the failure of these pillars is driven

Figure 6—Pillar stability classification in the experimental project area

Figure 5—A pillar classification system based on extent of damage (Esterhuizen, et al., 2006) 268

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Figure 7—A Class 5 failed pillar in the pillar project area The Journal of the Southern African Institute of Mining and Metallurgy

A study of UG2 pillar strength using a new pillar database the applicability of the rule (Maritz and Malan, 2023). The pillar database described in this paper should be re-examined in future if improved methods are developed to cater for pillars that are not square. The distribution of the effective width to height ratios of the pillars is shown in Figure 13. It is noteworthy that all pillars in the database with an effective width to height ratio smaller than approximately 1.5 were classified as either failed or unstable.

Figure 8—The central instrumented pillar in the pillar project area. This pillar was classified as a Class 3 unstable pillar Figure 10—(a) An example of closely spaced joints sets found for the geologically disturbed pillars. (b) Scaling along the multiple joint sets observed in the areas near potholes

Figure 9—A Class 2 stable pillar in the pillar project area

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Figure 11—Distribution of pillar stability in the database. The APS values on the y-axis are discussed in the following section. Note that the unstable pillars typically had a W/H < 1.5

120%

30 Frequency Cumulative %

Frequency

by multiple joint sets (Figure 10a) and proximity to reef rolls and potholes. Figure 10b shows the type of scaling observed for these pillars. Figure 11 summarizes the different pillar classifications in the database for various width to height ratios (W/H) and the simulated APS values (described in the following section). The surface topography around the mine is mountainous, making it difficult to determine the precise mining depth for the different areas. The overburden was nevertheless assumed to be flat above each of the modelled sections to simplify the modelling. The depths of the pillars in this database were calculated by determining the centre of mass of the overburden above the modelled areas. Deswick mine planning software was used to calculate the centre of mass using the surface contour mapping and excavation layers (Deswick, 2021). The depth distribution of the pillars in the database is shown in Figure 12. The effective widths for the pillars were calculated using the ‘perimeter rule’ method proposed by Wagner (1974). Malan and Napier (2011) highlight the problems associated with the use of this method. The perimeter rule is nevertheless widely adopted in the industry. Further work is currently under way to determine

100%

80%

60%

40%

20%

0% 230

250

270

290

310

330

350

370

Pillar Depths (m) Figure 12—The distribution of pillar depths in the pillar database VOLUME 123

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A study of UG2 pillar strength using a new pillar database 120%

25 Frequency Cumulative %

100%

Frequency

80% 15 60% 10 40% 5

20%

0.5

1.5

2.5

3.5

Effective Width to Height Ratios Figure 13—The distribution of effective pillar width to height ratios in the database

Numerical simulations to estimate pillar stress A database of pillar behaviour is of value only if the stress acting on each pillar can be estimated. For the earlier studies on pillar strength, such as Salamon and Munro (1967) and Hedley and Grant (1972), the pillar stress was estimated using tributary area theory (TAT). TAT is a conservative approach as it assumes a regular layout, with all pillars of equal size, with the layout continuing to infinity in all directions. The effect of large pillars and abutments are not considered (see Napier and Malan, 2011). A more accurate approach was used for this study by simulating the average pillar stress (APS) using numerical modelling techniques. The TEXAN code used in this study is a displacement discontinuity boundary element code that was specifically developed to simulate bord-and-pillar layouts. It incorporates the use of triangular boundary elements to enable an accurate representation of irregular-shaped pillars and layouts (Napier and Malan, 2007; Esterhuyse and Malan, 2018). The code can explicitly simulate small pillars and the crushing of the pillars using a limit equilibrium model. The use of TEXAN to simulate small crush pillars is described in du Plessis and Malan (2018). Owing the restrictions on the number of elements that can be practically solved in TEXAN (270 000 elements in the version used by the authors), smaller areas were simulated in detail for this study and not the entire mine. To simplify the digitizing of the outlines and the meshing procedure, the pillar outlines were approximated by using straight line segments. The mined areas were covered using a triangular mesh. In terms of element sizes, the centroids of adjacent triangular elements are spaced approximately 1 m apart, but this varied from area to area. Where necessary, elements were modelled with the centroids spaced approximately 0.5 m apart to accurately simulate the APS values of the smaller pillars. This spacing is referred to as the ‘element size’ in this paper, but this is not strictly correct as the meshes consisted of triangular elements. The pillars of interest also had to be meshed for the APS calculations. In displacement discontinuity codes, any area not covered by elements is considered as solid material and therefore not all the pillars had to be meshed to get an accurate solution. Also note that element size can affect the simulated pillar APS values –this is described in Napier and Malan (2011). The six areas of the mine visited (Figure 3) were simulated using TEXAN. The depths of the different areas are given in Table II. The overburden density was assumed to be 3100 kg/m3. This requires further verification. The other model parameters were 270

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Figure 14—The mesh used for the simulation of the pillar project area. The individual triangular elements are too small to be visible in the figure

Figure 15—The mesh used for one of the pillars simulated in the pillar project area

Young’s modulus = 70 000 GPa, Possion’s ratio = 0.2. The elastic parameters were only estimated values for the particular rock mass, but are nevertheless considered acceptable. Young’s modulus does not affect pillar APS values unless total closure occurs. The pillars were simulated as ‘rigid’ pillars that were not allowed to deform. Figure 14 illustrates the mesh used to simulate one of the areas, namely the experimental pillar project area. Approximately 230 000 elements were used to simulate the 500 m x 500 m layout. The APS values for all the pillars in the database were calculated using these simulations. Figure 15 illustrates the mesh used for one particular pillar within this model to illustrate the element size.

Rock strength A geotechnical testing programme on the rock types in the stratigraphy of the UG2 reef was conducted by the mine. The The Journal of the Southern African Institute of Mining and Metallurgy

A study of UG2 pillar strength using a new pillar database Table II

Depths of the areas used for the modelling Area of the mine

Number of pillars in database

Simulated depth (m)

Section 5 South

330

Section 6 South

347

Section 7 South

339

Section 8 South

335

Section 6 North

353

Section 9 North

245 Figure 16—Distribution of pillar classifications in the database

Table III

UCS values for the UG2 rock types as supplied by the mine UG2 Rock Types (UCS) Hangingwall

UG2 Reef

Footwall

Minimum (MPa)

136.1

61.5

136.8

Maximum (MPa)

158.2

141.5

152.6

Average (MPa)

147.1

116.5

144.7

information presented to the authors by the mine was the uniaxial compressive strength (UCS) of the pillar material given in Table III. Note that this is limited data and no additional information, such as number of tests, was available. The UCS of the chromitite reef varies significantly from 61.2 MPa to 141.5 MPa. The average UCS value for the reef was used when estimating the K-values for the older formulae in Table IV. Owing to the composite nature of the pillar material, this UCS gives only a crude estimation of the strength of the ‘bulk’ pillar material. Without large-scale in-situ tests similar to the experiments conducted by Bieniawski and van Heerden (1975), it is difficult to determine the actual strength of the rock mass material in the pillars. The seemingly large variation in UCS values may make it difficult to calibrate pillar strength formulae. The possible variation in pillar strength in different areas of a mine has been largely ignored to date. This needs to be studied in future, and it is also recommended that additional laboratory testing be done on the UG2 material.

Pillar strength estimation The Class G pillars were not included in the studies to estimate the pillar strength. The pillar data-set was also simplified by adopting the three categories shown in Figure 16. An analysis of the data using statistical methods was attempted, but this was not successful. The maximum likelihood estimation (MLE) used by Salamon and Munro (1967) and the overlap reduction technique used by van The Journal of the Southern African Institute of Mining and Metallurgy

der Merwe (2003) were not suitable for this study owing to the limited size of the database. Pillar failure also occurred in one area only where the mining height was constant. Furthermore, without variability in the height for the failed pillars, there is no accurate statistical method to determine the appropriate exponent for the height parameter. The pillar data-set was initially evaluated using the common hard-rock pillar strength formulae (Table IV). Figure 17 illustrates the formulae with adjusted K-values by using the new pillar database. Ideally, pillars in an unstable condition should be close to the failure envelopes with the red (failed) pillars above the line and green (stable) pillars below it. It is clear from the figure that the original Hedley and Grant calibration with K = 35 MPa is too conservative for this particular mine. Notably the Hedley and Grant (1972), Bieniawski and van Heerden (1975), and Obert and Duval (1967) formulae with an adjusted K = 65 MPa provide a good approximation of the pillar strength. This K-value was an arbitrary value of approximately two-thirds of the UCS of the pillar material. A preliminary calibration of the Hedley and Grant (1972) formula was done by the authors by adjusting the K-value to obtain a reasonable fit to the data. The Hedley and Grant (1972) formula is well established in the design of hard rock pillars in South Africa and, as no suitable alternative was available to the authors, this formula was recalibrated using this new data-set. Future work will need to be conducted to verify the applicability of the exponents for the width and height parameters in this formula. The estimated value of K was 75 MPa. The fitted curve is illustrated in Figure 18. This calibration seems to give a reasonable failure envelope to separate the failed and stable pillars with all the intact pillars below the envelope. Note that this line is only a first trial-and-error estimate done by hand. Additional data will be required to verify the most appropriate failure envelope as there is one failed pillar data-point far below the line. This may be an outlier, but further work needs to be done to refine this calibration with a larger database. Of particular significance, however, is that this calibration is substantially more conservative than the PlatMine formula and all the failed pillars are below the PlatMine strength envelope. This is one of the important findings of this study. VOLUME 123

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A study of UG2 pillar strength using a new pillar database Table IV

Relevant pillar strength formulae Authors

Formula

Hedley and Grant, 1972

α = 0.5 and β = 0.75

Watson, et al., 2021

α = 0.67 and β = 0.32

Bieniawski and van Heerden, 1975

A = 0.64 and B = 0.36

Obert and Duvall, 1967

A = 0.778 and B = 0.222

Figure 17—Various pillar strength formulae and the new pillar database. The failure envelopes were plotted using a mining height of 2.5 m

Conclusions The compilation of a new UG2 pillar database for a bord-andpillar mine in the eastern Bushveld Complex will assist with the development of locally derived and calibrated pillar strength formulae. This study illustrated that care should be exercised when using the traditional statistical methods employed to evaluate pillar databases. Owing to the limited variability in mining height in the database, it is difficult to determine the effect of pillar height on the strength of the pillar and to calibrate the exponent of the height parameter in a power-law strength equation. Analysis of the database indicates that the Hedley and Grant formula with a K-value of 35 MPa is too conservative for this particular mine. The ‘first-order’ calibration indicates that a value of K = 75 MPa may be more appropriate. Additional data will nevertheless be required to verify this value. Further work is also required to determine if the Hedley and Grant formula provides an accurate reflection of the changes in pillar strength for pillars at different widths and heights. Of interest is that this calibration is substantially more conservative than the PlatMine formula, and all the failed pillars in the new database are below the PlatMine 272

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Figure 18—A preliminary calibration of the Hedley and Grant formula for the new UG2 pillar data collected

strength envelope. As further cautionary note, this new calibration should be tested in trial sections with suitable instrumentation and monitoring before it is adopted at any mine.

Acknowledgements This work forms part of the MEng study of Thomas Oates at the University of Pretoria. The authors would like to thank Northam Platinum for permission to publish this data.

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Malan, D. and Napier, J. 2021. A review of the role of underground measurements in the historic development of rock engineering in South Africa. Journal of the Southern African Institute of Mining and Metallurgy, vol. 121. pp. 201–216.

Von Kimmelmann, M.R., Hyde, B., and Madgwick, R.J. 1984. The use of computer applications at BCL Limited in planning pillar extraction and design of mining layouts. Proceedings of the ISRM Symposium: Design and Performance of Underground Excavations. Brown, E.T. and Hudson J,A, (eds). British Geotechnical Society, London. pp. 53–63.

Maritz, J. and Malan, D.F. 2023. A review of the effect of pillar shape on pillar strength. Journal of the Southern African Institute of Mining and Metallurgy [in press]. Martin, C.D. and Maybee, W.G. 2000. The strength of hard rock pillars. International Journal of Rock Mechanics and Mining Sciences, vol. 37. pp. 1239–1246.

Wagner, H. 1974. Determination of the complete load-deformation characteristics of coal pillars. Advances in Rock Mechanics. Proceedings of the Third Congress of the International Society for Rock Mechanics, Denver, CO. Vol, II, part B.National Academy of Science, Washington. pp. 1076–1081.

Napier, J.A.L. and Malan, D.F. 2007. The computational analysis of shallow depth tabular mining problems. Journal of the Southern African Institute of Mining and Metallurgy, vol. 107. pp. 725–742.

Watson, B., Ryder, J.A., Kataka, M.O., Kuijpers, J.S., and Leteane, F.P. 2008. Merensky pillar strength formulae based on back-analysis of pillar failures at Impala Platinum. Journal of the Southern African Institute of Mining and Metallurgy, vol. 108. pp. 449–456.

Napier, J.A.L. and Malan, D.F. 2011. Numerical computation of average pillar stress and implications for pillar design. Journal of the Southern African Institute of Mining and Metallurgy, vol. 111. pp. 837–846.

Watson, B., Lamos, R., and Roberts, D. 2021. PlatMine pillar strength formula for UG2 Reef. Journal of the Southern African Institute of Mining and Metallurgy, vol. 121. pp. 437–448.

Napier, J.A.L. and Malan, D.F. 2021. A limit equilibrium model of tabular mine pillar failure. Rock Mechanics and Rock Engineering, vol. 54. pp. 71–89.

Watson, B.P., Theron, W., Fernandes, N., Kekana, W.O., Mahlangu, M.P., Betz, G., and Carpede, A. 2021. UG2 pillar strength: Verification of the PlatMine formula. Journal of the Southern African Institute of Mining and Metallurgy, vol. 121. pp. 449–456.

Obert, L. and Duvall, W. 1967. Rock Mechanics and the Design of Structures in Rock. Wiley. Potvin, Y., Hudyma, M.R., and Miller, H.D.S. 1989. Design guidelines for open stope support. CIM Bulletin, vol. 82. pp. 53–62. The Journal of the Southern African Institute of Mining and Metallurgy

York, G. and Canbulat, I. 1998. The scale effect, critical rock mass strength and pillar system design. Journal of the South African Institute of Mining and Metallurgy, vol. 98. pp. 23–37. VOLUME 123

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ABOUT THE EVENT The SAIMM through its committee for Diversity and Inclusion in the Minerals Industry (DIMI) and in collaboration with Women in Mining South Africa (WiMSA) is excited to announce its DIMI Dialogue 2023 focusing on the issues of diversity and inclusion in the mining and minerals industry. The Southern African minerals industry, just like the global minerals industry, still faces challenges when it comes to diversity and inclusivity in the workplace. While landscape might be changing due to various of companies embracing the need for a more representative and diverse workforce, there is still a lot to be done. Beside issues of gender disparity in the industry, safe spaces in the workplace, protective equipment, sanitation facilities,

pregnancy and childcare facilities are some of the challenges that continue to plague the sector. The industry also needs to go beyond workforce diversity to inclusion, by identifying %* %2% 1 (/ ".+) %û!.!*0 #!+#. ,$% Č #!* !.Č economic and cultural groups, creating safe spaces for them, providing support for them to grow into their roles. Creating conditions that promote inclusion on a daily basis can go a long way in retaining and advancing the careers of workforce and hence contribute to the long term growth of the minerals industry. DIMI provides a platform for discussion that can lead to the development of strategies for advancing and encouraging decisions that are in the best interest of a diverse workforce.

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A proposed method for optimizing coal pillar design using coalﬁeld-speciﬁc uniaxial compressive strength F.J.N. Bruwer1,2 and T.R. Stacey2

Afﬁliation: 1 Anglo American Platinum, South Africa. 2University of the Witwatersrand,

South Africa.

Correspondence to: F.J.N. Bruwer

Email: franz.bruwer@angloamerican.com

Dates: Received: 24 Mar. 2022 Revised: 16 May 2023 Accepted: 29 May 2023 Published: May 2023

How to cite: Bruwer, F.J.N. and Stacey, T.R. 2023 A proposed method for optimizing coal pillar design using coalﬁeld-speciﬁc uniaxial compressive strength. Journal of the Southern African Institute of Mining and Metallurgy, vol. 123, no. 5. pp. 275–286

Synopsis The research described considers whether the variability in coal material strength, as derived through a series of uniaxial compressive strength (UCS) tests, could be used to indicate the variability in coal pillar strength. The aim is to be able to use a distribution of UCS tests as input into the coal pillar strength calculation. This will allow the pillar design to be expressed in terms of a probability of failure rather than as the commonly used safety factor. To achieve this, the bulk strength factor associated with commonly used pillar strength formulae was replaced with a distribution of UCS results divided by an adjustment factor. The factor was determined so as to ensure that the resulting bulk strength does not deviate from the statistically determined bulk strength published in the original formulae. This approach enabled pillar strength distributions to be obtained using industry-accepted strength formulae, subsequently allowing for a probability of failure to be calculated for a specific pillar design. Using a regional coal material strength curve as a baseline, coalfields in which the coal is stronger than the regional mean can be identified and the pillar designs optimized. This is based on the stronger coals achieving lower probabilities of failure at similar safety factors. The research has considered actual UCS data from multiple mines in the Mpumalanga coalfields of South Africa, and has proved that the variability in material strength between coalfields could allow for some optimization using the proposed approach. Based on the data used in the study, a 2.78% increase in extraction could be achieved. However, further research will be required to validate the results of the study in an underground environment.

Keywords coal, pillar design, probability of failure, uniaxial compressive strength.

Introduction DOI ID: http://dx.doi.org/10.17159/24119717/2063/2023

Very few methods exist that allow for a pillar design to be based on the material strength in a specific coalfield. One example is the work by Salamon and Canbulat (2006). The advantage of such methods is that they allow for pillars in stronger coal strata to be optimized relative to weaker coals. There have been multiple attempts to extrapolate coal pillar strength from UCS test results; however, none of these studies was able to accurately correlate pillar strength with the strength of the intact rock mass. Unlike these studies, the research discussed in this report did not attempt to extrapolate pillar strength from UCS results, but rather investigated whether the variability in coal material strength, as observed in UCS data, could be used to estimate the variability in the strength of pillars. In so doing, the strength of a coal pillar can be expressed as a probability density function rather than a single strength value. This allows for the design to be expressed in terms of probability of failure rather than the more commonly used safety factor. As a result, the pillar size required to ensure stability could be optimized for coals with notably stronger material strengths.

Principles behind the research A probability of failure can be determined by expressing multiple safety factors in the form of a probability density function (Hoek, 2007). The safety factor constitutes the ratio between the capacity of a design and the demand or load induced on that design. A safety factor above unity would therefore indicate that the capacity is greater than the demand and the design will be stable. A safety factor below unity would indicate instability. The concept is mathematically expressed in Equation [1]. [1] By introducing a data distribution into either the capacity or the demand (or both), the resulting safety factor can be expressed as a probability density function. Empirical pillar strength equations make

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A proposed method for optimizing coal pillar design using coalﬁeld-speciﬁc uniaxial compressive strength use of a statistically determined bulk strength value, k, to express the strength of a unit cube of coal. In the current pillar strength formulae. This bulk strength is multiplied with an adjusted width to height ratio to estimate the strength of a pillar. The common powerlaw formula on which many of these pillar strength equations are based, is given in Equation [2]. [2] where S is the pillar strength, k is a statistically derived number related to the strength of the coal, h is the pillar height, w is the pillar width, and α and β are dimensionless constants.

original Salamon and Munro (1967) formula. The failure database was again updated by van der Merwe (2003) with an additional 28 failures, while the ‘unfailed’ data-set consisted of the same 98 cases described in Salamon and Munro’s (1967) study. Van der Merwe (2003) approached the data analysis with what has become known as the overlap reduction method. This method presented both the failed and unfailed data-sets as probability distributions, arguing that the ideal formula would result in a complete separation between the two curves. The concept is illustrated in Figure 1. The analysis resulted in the pillar strength formula in Equation [4]. [4]

Assumptions applied to the analysis The study made use of the following assumptions: ³ Pillar loading is accurately expressed by the application of the Tributary Area Theory (TAT), where every similar sized pillar carries an equal overburden load ³ The set of UCS results used in the study, obtained from various South African collieries in Mpumalanga Province, provides a realistic indication of the strength of, and variability in, the coal in Mpumalanga coalfields.

where h is the pillar height and w is the pillar width. In 2013 another update was made to the pillar failure database, this time by van der Merwe and Mathey (2013a). The updated database consisted of a total of 86 failed cases and 337 unfailed cases, and the analysis made use of both the overlap reduction and maximum likelihood methods. As a result, two formulae were produced. The maximum likelihood method provided Equation [5] while the overlap reduction approach resulted in Equation [6].

History of coal pillar strength estimation

[5]

Several authors (Bieniawski, 1968; Wagner, 1974; van Heerden, 1975) have attempted to extrapolate coal pillar strength by studying the strength of small coal samples. None of the tests, however, provided definitive results in estimating coal pillar strength. Salamon and Munro (1967) opted for an empirical solution, compiling a database consisting of 125 pillar ‘cases’. From the 125 data entries, 98 represented stable cases (unfailed) with the remaining 27 representing pillars that failed. Using the two data-sets, Salamon and Munro (1967) considered a probabilistic approach to describe the data, known as the maximum likelihood approach. The final pillar strength formula proposed by Salamon and Munro (1967) is shown in Equation [3]. [3] Madden et al., (1995) conducted a re-analysis of an updated pillar failure database which contained 17 additional failures compared with the Salamon and Munro (1967) database. The results correlated well with those obtained by Salamon and Munro (1967), and although a different strength formula was obtained, the difference was not sufficient to warrant the replacement of the

[6] With specific focus on the variability in the strength of coal between various seams, Madden and Hardman (1992) conducted a comparison between their pillar strength formula and that of Salamon and Munro (1967) using data from different seams. Interestingly, they found that the differences between individual seams were statistically very minor, and they concluded that an average strength value could be used to effectively represent the different seams. Bertuzzi (2016) found, in a comparison of coal strengths between Australia, South Africa, the USA, India, and the UK, that the coal strengths between the different reserves, although not exactly equal, were very similar. Contrary to this, van der Merwe (2016) stated that there is sufficient evidence indicating that the strength of coal is highly variable. A study by Salamon, Canbulat, and Ryder (2006), aimed at determining seam-specific strengths by means of back-analysis, also concluded that significant variations exist between coalfields. Van der Merwe and Mathey (2013a, 2013b) also highlighted the fact that the strength of coal varies between different coalfields and coal seams.

The use of uniaxial compressive strength in defining pillar strength

Figure 1—Illustration of the overlap between the stable and failed distributions as derived by the overlap reduction method (van der Merwe, 2003) 276

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There have been many attempts to use the UCS of coal to estimate pillar strength, none of which returned usable results. York and Canbulat (1998) provide a detailed summary of these attempts, all of which led to the conclusion that the extrapolation of pillar strength from a laboratory sample is significantly affected by the ‘scaling’ effect. The scaling effect refers to the estimated reduction in sample strength obtained with increasing size of the sample. A study of particular relevance to this report is that of Mark and Barton (1996), who investigated whether a stronger seam makes for a stronger pillar when extrapolating strength according to volume from laboratory coal samples. This was achieved by The Journal of the Southern African Institute of Mining and Metallurgy

A proposed method for optimizing coal pillar design using coalﬁeld-speciﬁc uniaxial compressive strength using UCS results from various seams to estimate the specific pillar strength associated with each seam. The pillar strengths were extrapolated using Gaddy’s (1956) relationship and factors of safety were calculated using the Analysis of Retreat Mining Pillar Stability (ARMPS) formula of Mark, Chase, and Campoli (1995). Safety factors were calculated for the approximately 100 case histories used in the development of the ARMPS formula, with the case histories providing an almost even split between failed and unfailed pillars. The assumption in the study was that the weaker coal material would make for weaker pillars that would therefore show failure at a higher safety factor. The study, however, showed that the use of a uniform bulk pillar strength provides a significantly better fit to the back-analysis of case histories compared to the results based on the individual coal seam strengths. From this, Mark and Barton (1996) concluded that the use of seam-specific strength becomes meaningless when designing coal pillars, and that the use of a uniform bulk strength value of 6.2 MPa is preferred (specific to the US coalfields). Mark and Barton (1996) argued that one of the key reasons that laboratory results are not suited to the estimation of pillar strength is because a pillar is significantly influenced by geological features not represented in the sample. As a result, the laboratory sample will not only be significantly stronger, but the failure mechanisms for sample and pillar will differ. This being the case, full-scale pillar testing is currently not feasible, and even if it were, multiple pillar tests would be required to provide sufficient understanding of the variability in pillar strength within a specific coalfield. Additionally, to conduct a fair comparison between the strengths in various coalfields, a common testing approach is required. Currently one of the most common and relatively inexpensive indications of rock strength remains the UCS test. Despite all its shortfalls in describing pillar strength, it still provides an indication of the strength of the material. The use of a single bulk strength value in the design of pillars also limits the ability to conduct any optimization between reserves.

Research methodology From a literature study it is clear that historical attempts to extrapolate pillar strength from UCS results by means of scaling did not provide reliable results unless cubic samples larger than 1.5 m were used (Bieniawski, 1968). For the interested reader, van Heerden (1975) provides a summary of large-scale testing programmes conducted on coal samples. The approach adopted for this study was therefore to keep to the bulk strength values determined for each of the formulae by the original authors, introducing UCS results only as a means of expressing variability.

operations. To preserve confidentiality, the mining operations are not identified in the study. Most operations had limited UCS data available. However, three mines, referred to as A, B, and C, provided sufficient data to allow the variability in coal strength at each operation to be defined to a satisfactory confidence level. The data used in the study was compiled from various sources, collected over a number of years. As such, not all laboratory reports were available to confirm that the tests adhered to ISRM standard. In the absence of this information, the test results were accepted as representative and accurate. Table I provides a summary of the UCS data used in the study. In order to calculate a probability of failure from the UCS data, the data was expressed as probability density functions. To assist with analysis, the function curves were produced using the software program @Risk. The program allows the user to select the statistical function which best fits the distribution of data in a specific data-set by indicating a ‘fit ranking’ of the available functions. The function selected for the study was Lognormal as this function provided the best representation of the actual distribution of data in each of the data-sets. A comparison between the original data and the lognormal functions is shown in Table II. The resulting distributions are illustrated in Figure 2 to Figure 5.

Pillar database The South African pillar failure database was ideally suited to the study as it would allow for a direct comparison between the calculation method proposed in the study and the design methods currently used in industry. The latest iteration of the database contains a total of 424 pillar cases and covers a range of pillars at multiple depths (van der Merwe, 2021).

Adjustments to pillar strength formulae The current pillar strength formulae make use of a statistically determined bulk strength factor (k) to describe pillar strength. This factor, however, is constant regardless of the coalfield being

Table I

Summary of the UCS data-set used in the study Source

Number of data-points

Mean (Mpa)

Min. (Mpa)

Max. (Mpa)

Std. dev.

Mine A

22.4

12.3

40.5

8.9

Mine B

21.9

9.3

40.5

7.9

Mine C

29.4

22.0

38.5

5.3

Coal strength data

Multiple sources

24.1

7.6

48.8

9.7

Coal, being naturally inhomogeneous and anisotropic, differs in strength from one position in a coalfield to the next. It is this variability which requires design engineers to make use of a safety factor when defining a pillar design. To effectively understand the variability in a coal seam, sufficient data-points (UCS test results) are therefore required. Van der Merwe (2003) and van der Merwe and Mathey (2013) opted to exclude the Kliprivier and Vaal basin pillar data during the development of the linear, maximum likelihood, and overlap reduction strength formulae. Taking this into account, applying these formulae to data sourced from the Vaal Basin is outside of the intended scope of the exercise and could provide unrealistic results. The data used in the current study was therefore sourced only from mines located in the Mpumalanga coalfields. The total data-set consisted of 83 coal UCS results and covered multiple mining

Total data-set

24.6

7.6

48.8

8.7

The Journal of the Southern African Institute of Mining and Metallurgy

Table II

Comparison of original and best-fit data-sets Mean

Standard deviation

Data-set

Original

Lognormal curve

Original

Lognormal curve

Mine A

22.4

22.8

8.9

12.3

Mine B

21.9

7.9

8.0

Mine C

29.4

29.5

5.3

5.8

Total data-set

24.6

24.7

8.7

8.8

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Figure 2—UCS distribution for data obtained from mine A

Figure 3—UCS distribution for data obtained from mine B

Figure 4—UCS distribution for data obtained from mine C 278

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Figure 5—UCS distribution of the total data set

designed for. In order to introduce the variability of the UCS data into the calculation, adjustments were required to the existing pillar strength equations. It should be reiterated that the study is not aimed at extrapolating pillar strength from UCS results, but rather at describing the variability in pillar strength using the variability in UCS results. The intent was therefore to develop an approach that introduced the variability but returns a similar pillar strength to that obtained using the original formulae. This meant that the UCS had to be divided by a factor to ensure that the resulting bulk strength (k) used in the calculation is unchanged from the original formulae. The resulting strength parameter (k) used in the study was therefore calculated using Equation [7]. [7] An appropriate adjustment factor for each formula was calculated using the entire data-set of UCS results. This was to ensure that the final strength factor would be appropriate for any of the Mpumalanga coalfields without being biased to any specific mine or seam. This was achieved by using the mean strength from the total Mpumalanga data-set (24.66 MPa). The final adjustment factor calculated for each of the formulae, was therefore based on the most likely UCS from the Mpumalanga data-set which when divided by the factor, matches the original bulk strength value (k) from the unadjusted equations. The adjusted formulae are listed in Equations [8] to [11]. Adjusted Salamon and Munro (1967) formula: [8] Adjusted van der Merwe (2003) formula: [9] Adjusted maximum likelihood formula: [10] The Journal of the Southern African Institute of Mining and Metallurgy

Adjusted overlap reduction formula: [11] It should be noted that the adjusted formulae are a result of the distribution of UCS values used in this study and are not intended as universal formulae to be used for any operation within the Mpumalanga coalfields. Should a different UCS data-set be used, a different set of equations will be obtained. The aim of the formulae is merely to show the application of the proposed approach . Using the adjusted formulae, it is possible to calculate pillar strength using the strength of the coal material associated with a specific coalfield. Additionally, by expressing the material strength as a distribution of UCS values, the adjusted pillar strength formulae allowed the probability of failure to be calculated for different pillar scenarios.

Calculation of pillar failure probabilities and validation of adjusted pillar strength formulae The four pillar strength formulae discussed in the previous section are all acceptable methods of calculating pillar strength and have been implemented by various mining houses in South Africa. In order to determine whether the adjustments to the formulae would alter the outcome, a comparison was conducted between the result from the adjusted formulae and those from the original formulae. To enable a direct comparison to be made, the results were stated in terms of safety factor, as probability of failure is beyond the application of the original formulae. Keeping in mind that the adjusted formulae will produce a distribution of safety factors in order to determine a probability of failure, expressing the results from the adjusted formulae in terms of a single safety factor would require the distribution of safety factors to be reduced to a single representative value. This can easily be achieved by using the mean of the distribution as it represents the safety factor that most frequently occurs in the resulting data distribution (the peak of the distribution curve). Figure 6 illustrates a distribution of safety factors, graphically indicating the difference between the probability of failure obtained from a distribution and VOLUME 123

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A proposed method for optimizing coal pillar design using coalﬁeld-speciﬁc uniaxial compressive strength then simulates results for a pre-set number of iterations. The UCS distributions discussed earlier were used as the input to the UCS parameters of the adjusted formulae. All calculations made use of 1000 iterations to produce a probability density function for each pillar scenario. The resulting distributions indicate the range of pillar strengths expected for each scenario. Using the distribution of pillar strengths as the input into the ‘capacity’ parameter in Equation [13], a distribution of safety factors is subsequently obtained in @Risk. [13] Figure 6—Illustration of a distribution of safety factors, indicating the probability of failure and the mean safety factor for the distribution

the mean of the distribution. In Figure 6, the probability of failure is indicated as the area below the curve for a safety factor less than unity, and is expressed as a percentage of the total area below the curve as shown in Equation [12]. [12] In calculating the distribution of safety factors using the adjusted formulae, the total data-set of 83 UCS values was used. With the adjustments based on the total data-set, the resulting distribution of safety factors should return similar results to the unadjusted formulae. In order to conduct the comparison, a set of baseline pillar scenarios was selected from the South African pillar failure database. The pillar parameters obtained from the database included the pillar width, height, bord width, and depth below surface. In keeping with the industry norm, an overburden density of 2500 kg/m3 was used in all calculations. Subsequently, the only parameter that changed in the comparison was the bulk strength factor (k). The calculations of pillar safety factor using the original formulae are discussed at length in the earlier sections of the report and will not be repeated here. The safety factors using the adjusted formulae were calculated as follows. The software program @Risk, allows the user to calculate a probability density function using a distribution of values as an input to an equation. The program

These distributions of safety factors are finally used to determine the mean safety factor for each scenario as well as the probability of failure. Probability density functions were calculated for all pillars in the South African pillar failure database (both failed and unfailed data-sets). An example of one of the 424 safety factor distributions (one distribution for each scenario in the database) obtained from @Risk is seen in Figure 7. The probability of failure is automatically calculated in @Risk as the area below the curve. In the example, this is 0.7% of the total area below the curve (based on a dividing line equal to a safety factor of unity). Table III summarizes the results for five randomly selected pillars from the failed data-set and five from the unfailed data-set. From these results, it can be seen that although isolated scenarios did not provide the exact same safety factor, the difference is never more than 0.01. These results validate the adjusted pillar strength formulae for use in the study. With the adjusted formulae validated for use, the calculated probabilities of failure were considered. Figure 8 and Figure 9 provide a graphical illustration of the calculated probabilities relative to the safety factors for both the failed and unfailed pillar data-sets. The graphs include the results of all four formulae, and interestingly, the relationship between safety factor and probability of failure remains constant regardless which formula is used. This could, however, be expected as the same distributions of variables were applied to all formulae. From Figure 8 and Figure 9, a probability of failure of 50% equates to a safety factor of 1.04. This aligns well with the assumption that a safety factor of unity, taken as the divide between stable and unstable pillars, should equate to a probability of failure

Figure 7—Example of a distribution of safety factors calculated using @Risk. The probability of failure for the distribution is 0.7%, with a mean safety factor of 3.39 280

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A proposed method for optimizing coal pillar design using coalﬁeld-speciﬁc uniaxial compressive strength Table III

Pillar case number

Unfailed

Failed

Database

Comparison of the safety factors obtained from the adjusted and original pillar strength formulae as calculated using the total UCS data-set

Original formula

Adjusted formula

Original formula

Adjusted formula

Original formula

Adjusted formula

Original formula

Adjusted formula

4.85

4.84

4.45

4.58

4.59

4.75

1.26

1.25

0.95

0.94

1.16

1.03

0.92

0.63

0.85

0.76

1.01

0.71

0.94

0.88

0.77

0.63

0.72

0.67

2.48

2.47

3.82

2.47

3.85

3.84

140

2.29

3.21

2.25

3.05

228

2.35

3.82

2.34

3.50

284

4.02

6.69

6.68

3.98

5.77

328

4.01

5.18

5.17

3.92

5.10

SF - Salamon

SF - van der Merwe

SF - maximum likelihood

SF - overlap reduction

Figure 8—Probability of failure plotted against safety factor for the failed pillar data-set

of 50%. For both graphs, a safety factor of 1.6 is obtained at a probability of failure of 13.8%. Finding a probability of failure that aligns to a safety factor of 1.6 was necessary as a safety factor of 1.6 is commonly accepted as a design threshold for a stable pillar. This same design threshold was required for the probability of failure obtained using the approach proposed in this study. A value of 13.8% was therefore selected as the probability threshold for the interpretation of the results discussed in the following section.

Results obtained from the proposed method In the previous section, we proposed a method with which pillar probability of failure can be calculated based on the laboratory The Journal of the Southern African Institute of Mining and Metallurgy

strength of samples from a specific coal seam or mine. The calculation of the probability of failure is key to the study as this forms the basis with which pillar optimization can be justified. This is done by designing a pillar to the same probability of failure as the baseline pillar obtained using the total UCS data-set (therefore the same pillar strength that would be obtained from the original unadjusted formulae). As a result, the final pillar would have a similar probability of failure as the baseline, but be designed to a lower safety factor provided the coal material is of a higher strength. To determine whether the variability in coal strength would allow for sufficient optimization in pillar size, the proposed method was applied to the data from mines A, B, and C outlined in Table I. VOLUME 123

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Figure 9—Probability of failure plotted against safety factor for the unfailed pillar data-set

Earlier in the report it was confirmed that the ‘failed’ and ‘nfailed’ data-sets from the pillar failure database yield similar probabilities of failure across a range of safety factors. The decision was therefore made to use only the ‘failed’ data-set for this part of the study, thus reducing the number of calculations required while still having sufficient data from which to draw conclusions. The ‘failed’ data-set consists of 87 pillar scenarios and would therefore produce 87 datapoints from which distributions could be plotted. In calculating the safety factors and probabilities of failure for each of the mines, the UCS distributions discussed earlier were applied to the adjusted pillar strength formulae. Figure 10 provides a graphical comparison of the safety factor distributions obtained from each of the four data-sets, being the total Mpumalanga data-set as well as the data from the three individual mines A, B, and C. The distributions in Figure 10 were not graphed using @Risk, as the distributions would not be used as input into further calculations. The distributions were

Figure 10—Comparison of safety factors and probabilities of failure obtained from the different data-sets 282

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therefore compiled by dividing the results into bins of safety factors and plotting the number of data-points per bin across the range of safety factors applicable. To determine whether the different distributions would allow for any pillar optimization, the distributions for each mine were compared to the original distribution from the total data-set (referred to as the baseline distribution). Should the distribution move towards a higher range of safety factors compared to the baseline distribution, the adjusted formula predicted higher pillar strengths, and pillar optimization would be possible. This would occur when the average UCS from the mine database is higher than the Mpumalanga mean, therefore inferring a stronger pillar material. Should the distribution move towards a lower range of safety factors, the adjusted pillar formula predicted lower pillar strengths and a larger pillar would be required to maintain the probability of failure indicated by the baseline distribution. Figures 11 to 13 provide graphical comparisons of the individual distributions to the baseline. Due to the distributions returning a bimodal curve, the harmonic mean from each distribution was used to provide a quantifiable measure for optimization. From Figures 11 to 13, it can be seen that the data-sets from mines A and B return lower safety factors compared to the baseline. Mine C, on the other hand, returns higher safety factors. This is in line with expectation when considering the mean UCS from the various data-sets (Table II). Mines A and B have mean UCS values of 22.4 MPa and 21.9 MPa respectively, compared to the total data-set mean of 24.6 MPa. Mine C, however, has a mean UCS of 29.4 MPa, indicating a stronger coal material compared to the Mpumalanga average. Based on these results, the pillars at mine C, could potentially be optimized in size without increasing the probability of failure. Figures 14 to Figure 16 graphically illustrate this effect. In these graphs, the adjusted formulae are compared with the results from the original formulae relative to the probabilities of failure obtained for each data-set. To determine the actual The Journal of the Southern African Institute of Mining and Metallurgy

A proposed method for optimizing coal pillar design using coalﬁeld-speciﬁc uniaxial compressive strength

Figure 11—Comparison of the mine A distribution to the baseline obtained from the total UCS data-set

Figure 15—Comparison of safety factors from the original and adjusted formulae using the mine B data-set

Figure 12—Comparison of the mine B distribution to the baseline obtained from the total UCS data-set

Figure 16—Comparison of safety factors from the original and adjusted formulae using the mine C data-set Figure 13—Comparison of the mine C distribution to the baseline obtained from the total UCS data-set

Figure 14—Comparison of safety factors from the original and adjusted formulae using the mine A data-set

shift in safety factor, a probability of failure of 13.8% was used, as determined from the baseline distribution, to represent a safety factor of 1.6 prior to any adjustment of the formulae. It should be noted that the graphs in Figure 14 to Figure 16 are only used to determine the difference in safety factor at the threshold probability of 13.8 %. The intent is therefore not to match the curve to a safety factor threshold of 1.6. The adjustment to the final pillar dimensions is conducted using the unadjusted formulae and is discussed later. To quantify the potential for optimization using the data from the various mines, a single mining scenario was required. This would allow for the actual changes in pillar dimensions to be The Journal of the Southern African Institute of Mining and Metallurgy

calculated and compared. This comparison was conducted using the parameters from Table IV. From the parameters in Table IV, the pillar load as calculated based on TAT is 6.33 MPa. The safety factors obtained from the original pillar strength formulae for this scenario are summarized in Table V. Using the difference in harmonic mean between the data-sets as illustrated in Figures 14 to 16, the allowable difference in safety factor was determined. Table VI summarizes the differences in harmonic means between the total and individual mine data-sets. The ‘optimized’ pillar would therefore be designed to the original pillar safety factor, plus or minus the difference, depending on whether the safety factor should increase or decrease. Table VII provides a summary of the updated pillar widths determined from the analysis. The calculations were based on perfectly square pillars. Parameters such as depth below surface, mining height, and bord width were unchanged. Based on the results from Table VII, the potential gain involves a reduction in pillar width of tbetween 0.8 m and 1.3 m. Due to practical mining considerations, a pillar width will not be adjusted by a value of 0.8 m or 1.3 m. The change would rather be made in increments of 0.5 m. This would mean that the pillar design values using the Salamon and Munro and maximum likelihood formulae would reduce by 1 m, and the van der Merwe and overlap reduction formulae by 0.5 m. To link this to the expected change in production profile, Table VIII provides a summary of the additional tons that could be mined per pillar based on these adjustments. VOLUME 123

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A proposed method for optimizing coal pillar design using coalﬁeld-speciﬁc uniaxial compressive strength Table IV

Table VIII

Mining scenario used for comparison

Gain in production tons per pillar based on the optimized pillar sizes

Depth (m)

100

Pillar width (m)

Bord width (m)

Mining height (m)

6.5

Load (MPa)

Formula

6.33

Table V

Safety factors obtained for the mining scenario using the original pillar strength formulae Formula

Salamon

Van der Merwe

Maximum likelihood

Overlap reduction

Safety factor

1.65

2.03

1.61

1.96

Salamon

VdM

Pillar width original (m)

11.0

Pillar width new (m)

10.0

10.5

10.0

10.5

Difference in width (m)

- 1.0

- 0.5

- 1.0

- 0.5

Gain in tons per pillar

157.50

80.63

157.50

80.63

Table IX

Increase in extraction percentage for each of the strength formulae compared to the base case used in the study Formula

Salamon

VdM

Original extraction (%)

60.49

Table VI

Updated extraction (%)

63.27

61.85

63.27

61.85

Difference in safety factors determined from the harmonic means of the distributions

Gain in extraction (%)

+ 2.78

+ 1.36

+ 2.78

+ 1.36

Data-set

Harmonic mean

Difference in SF

Mine A

1.10

0.09

Discussion

Mine B

1.06

0.13

Mine C

1.43

-0.24

From the results, it seems plausible that the method proposed in this study would allow for optimization of pillar design in situations where the coal material is stronger than the regional average. Multiple studies have concluded that pillar strength cannot be extrapolated from UCS results, the most notable being the study by Mark and Barton (1996). This being the case, the method proposed here does not attempt to extrapolate pillar strength from smaller samples by means of scaling, but rather matches the bulk pillar strength of the original formulae using the regional average UCS. The strength of a pillar is subsequently adjusted based on the UCS of the coal material specific to a seam or mine. A similar approach has been adopted in the hard-rock pillar design fraternity, with both Potvin, Hudyma, and Miller (1989) and Lunder and Pakalnis (1997) defining the pillar bulk strength by means of the UCS divided

Harmonic mean of total data-set – 1.19

The reduction in pillar sizes stipulated in Table VIII increases the extraction percentage as indicated in Table IX, providing an additional 2.78% for the Salamon and maximum likelihood formulae, and 1.36% for the van der Merwe and overlap reduction formulae. Although the increase appears marginal, it would allow for better resource utilization and could aid in extending the life of a mining operation.

Table VII

Updated pillar widths obtained from the analysis Data-set

Mine A

Mine B

Mine C

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Formula

Original width (m)

Updated width (m)

Difference (m)

Salamon

11.5

+ 0.5

VdM

11.3

+ 0.3

11.5

+ 0.5

11.3

+ 0.3

Salamon

11.7

+ 0.7

VdM

11.4

+ 0.4

11.8

+ 0.8

11.5

+ 0.5

Salamon

9.7

- 1.3

VdM

10.2

- 0.8

9.7

- 1.3

10.1

- 0.9

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A proposed method for optimizing coal pillar design using coalﬁeld-speciﬁc uniaxial compressive strength by an adjustment factor. Another approach commonly used in South African hard-rock mines, which supports the link between UCS and pillar strength, is to estimate the pillar bulk strength as one-third of the UCS (Ozbay,Ryder, and Jager, 1995). It is therefore not uncommon to use the UCS of a rock type to describe the expected pillar strength. Van der Merwe (2003) was also able to differentiate and rank the strength of various coals from weakest to strongest using a range of ‘small sample’ tests. What is different in our approach is the introduction of a distribution of UCS values for describing not only pillar strength, but also variability in pillar strength. This allows a pillar design to be expressed in terms of a probability of failure, which forms the basis on which optimization can be conducted. It should be noted that the use of probability of failure rather than safety factor as a basis for design is not a first in this field. Van der Merwe and Matthey (2013) and van der Merwe (2016) previously adopted a probability approach, which is currently in use on some mines. A question that remains unanswered, however, is whether the behaviour of a pillar can effectively be estimated using only the UCS of a material without considering the effect that jointing has on the stability of the pillar. The study by Mark and Barton (1996) indicates this as unlikely, based on the inability of a laboratory UCS test to account for natural discontinuities and imperfections in the larger mass. Esterhuizen (2000) studied the effect of jointing on pillar stability using field data from South African coal mines. He concluded that the weakening effect of jointing in a pillar reduces with increasing width to height and is largely dependent on the joint orientation. This presents a challenge as the orientation of jointing in a seam is generally not well defined prior to start of mining and, based on the abovementioned studies, should be accounted for in the pillar design before mining begins. Another consideration that should be taken into account is that the pillar strength formulae discussed in this report have been implemented in industry for many years without pillars failing abnormally as a result of jointing. This could be attributed to the fact that the pillars recorded in the South African pillar failure database provide an indication of actual pillar behaviour, including the effects of material imperfections, cleating, and discontinuities. This poses the question whether further adjustments to the pillar strength formulae to include the effect of discontinuities are in fact required, Regardless of whether the effect of discontinuities is sufficiently accounted for in the current pillar strength formulae, the use of UCS test data in expressing pillar strength seems prudent. Additionally, it provides a logical and viable means with which to express probability of failure, based not on the statistical back-analysis of pillar failure data, but on the variability of the coal material as determined by existing laboratory testing methods. These failure probabilities subsequently provide a means with which to potentially optimize pillar design on a mine. The method proposed in this paper does, however, require further validation, ideally by means of underground trials in a controlled environment, to ensure that pillar stability is maintained for as long as underground stability and surface protection are required.

Conclusion The research described in this paper was conducted on UCS data from actual mines, and proved the potential for pillar optimization by considering the difference in material strength obtained from UCS tests. Based on the data-sets considered, a potential increase The Journal of the Southern African Institute of Mining and Metallurgy

in extraction of up to 2.78% could be obtained without any change to the calculated probability of failure. The results assume, however, that the variability in pillar strength can be effectively described by the variability in UCS of a specific seam. The probability of failure is determined from a distribution of safety factors, which in turn is calculated from a distribution of UCS results used in pillar strength formulae adopted from existing methods. The results of the research confirm on a theoretical basis the applicability of the proposed optimization method. The additional extraction resulting from the optimization would aid in resource utilization as well as extending the life of mine. The results, however, do not imply that the proposed method can be implemented without due consideration. The assumption that the variability in small-scale test samples is representative of the variability in coal pillars remains to be confirmed. To ensure this approach does not compromise long-term pillar stability, further research is required. It is recommended that the optimized pillar sizes obtained from this approach be trialled in a controlled environment where abnormal pillar behaviour will not affect the rest of the mine. Once trial mining confirms that stable behaviour is maintained, the optimized design can be systematically introduced across the remainder of the mine.

References Bertuzzi, R., Douglas, K., and Mostyn G. 2016. An approach to model the strength of coal pillars. International Journal of Rock Mechanics and Mining Sciences, vol. 89. pp. 165–175. Bieniawski, Z.T. 1968. The effect of specimen size on compressive strength of coal. International Journal of Rock Mechanics and Mining Sciences, vol. 5. pp. 325–335. Esterhuizen, G. 2000. Jointing effects on pillar strength. Proceedings of the 19th Conference on Ground Control in Mining, Morgantown, WV. Peng, S.S. and Mark, C. (eds). West Virginia University. Gaddy, F.L. 1956. A study of the ultimate strength of coal as related to the absolute size of the cubical specimens tested. Bulletin 112, Engineering Experiment Station, Virginia Polytechnic Institute.` Hoek, E. 2007. Practical Rock Engineering. https://www.rocscience.com/assets/ resources/learning/hoek/Practical-Rock-Engineering-Full-Text.pdf [accessed 12 May 2020]. Lunder, P.J. and Pakalnis, R. 1997. Determination of the strength of hard-rock mine pillars. CIM Bulletin, vol, 90, no. 1013. pp. 51–55. Madden, B.J., Canbulat, I., Jack, B.W., and I'Rohaska, G.D. 1995. A reassessment of coal pillar design procedures. SlMRAC Final Project Report - COL021. CSIR Division of Mining Technology, Pretoria. Madden, B.J. and Hardman, D.R. 1992. Long-term stability of bord-and-pillar workings. Proceedings of the Symposium on Construction Over Mined Areas, May 1992., South African Institution of Civil Engineers. Mark, C. and Barton, T.M. 1996. The uniaxial compressive strength of coal: Should it be used to Design Pillars? Proceedings of the 15th International Conference on Ground Control in Mining, Golden, CO. Mark, C., Chase, F.E., and Campoli, A.A. 1995. Analysis of retreat mining pillar stability. Proceedings of the 14th International Conference on Ground Control in Mining, Morgantown, WV. West Virginia University. Ozbay, M.U., Ryder, J.A., and Jager, A.J. 1995. The design of pillar systems as practiced in shallow hard-rock tabular mines in South Africa. Journal of the South African Institute of Mining and Metallurgy, vol 95, Jan/Feb 1995: pp. 7–18.

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A proposed method for optimizing coal pillar design using coalﬁeld-speciﬁc uniaxial compressive strength Potvin, Y., Hudyma, M.R., and Miller H.D.S. 1989. Design guidelines for open stope support. Bulletin of the Canadian Institute of Mining and Metallurgy; vol. 82. 53262-.

Van der Merwe, J.N. and Mathey, M. 2013a. Update of coal pillar strength formulae for South African coal using two methods of analysis. Journal of the Southern African Institute of Mining and Metallurgy, vol. 113. pp. 841–847.

Salamon, M.D.G. and Munro, A.H. 1967. A study of the strength of coal pillars. Journal of the South African Institute of Mining and Metallurgy, vol 67, September 1967. pp. 55–67.

Van der Merwe, J.N. and Mathey, M. 2013b. Probability of failure of South African coal pillars. Journal of the Southern African Institute of Mining and Metallurgy, vol. 113. pp. 849–857.

Salamon, M.D.G., Canbulat, I., and Ryder, J.A. 2006. Development of seamspecific strength formulae for South African collieries. Final Report: Task 2.16. Coaltech, Johannesburg.

Van Heerden, W.L. 1975. In situ complete stress-strain characteristics of large coal specimens. Journal of the South African Institute of Mining and Metallurgy, vol 75, March 1975. pp. 207–217.

Van der Merwe, J.N. 2003. New pillar strength formula for South African coal. Journal of the South African Institute of Mining and Metallurgy, vol. 103. pp. 281–292.

Wagner, H. 1974. The determination of the complete load deformation characteristics of coal pillars. Proceedings of the 3rd International Congress of the International Society for Rock Mechanics, Denver, CO, December 1974. pp. 1076–1081.

Van der Merwe, J.N. 2016. A three-tier method of stability evaluation for coal mines in the Witbank and Highveld coalfields. Journal of the Southern African Institute of Mining and Metallurgy, vol. 116. pp. 1189–1194. Van der Merwe, J.N., 2021. Coal pillar database. [e-mail].

York, G. and Canbulat, I. 1998. The scale effect, critical rock mass strength and pillar system design. Journal of the South African Institute of Mining and Metallurgy, vol 98, January/February 1998. pp. 23–37.

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Company aﬃliates The following organizations have been admitted to the Institute as Company Aﬃliates 3M South Africa (Pty) Limited acQuire Technology Solutions AECOM SA (Pty) Ltd AEL Mining Services Limited African Pegmatite (Pty) Ltd Air Liquide (Pty) Ltd Alexander Proudfoot Africa (Pty) Ltd Allied Furnace Consultants AMEC Foster Wheeler AMIRA International Africa (Pty) Ltd ANDRITZ Delkowr(Pty) Ltd ANGLO Operations Proprietary Limited Anglogold Ashanti Ltd Arcus Gibb (Pty) Ltd ASPASA Aurecon South Africa (Pty) Ltd Aveng Engineering Aveng Mining Shafts and Underground Axiom Chemlab Supplies (Pty) Ltd Axis House Pty Ltd Bafokeng Rasimone Platinum Mine Barloworld Equipment -Mining BASF Holdings SA (Pty) Ltd BCL Limited Becker Mining (Pty) Ltd BedRock Mining Support Pty Ltd BHP Billiton Energy Coal SA Ltd Blue Cube Systems (Pty) Ltd Bluhm Burton Engineering Pty Ltd Bond Equipment (Pty) Ltd Bouygues Travaux Publics Caledonia Mining South Africa Plc Castle Lead Works CDM Group CGG Services SA Coalmin Process Technologies CC Concor Opencast Mining Concor Technicrete Council for Geoscience Library CRONIMET Mining Processing SA Pty Ltd CSIR Natural Resources and the Environment (NRE) Data Mine SA DDP Specialty Products South Africa (Pty) Ltd Digby Wells and Associates DRA Mineral Projects (Pty) Ltd DTP Mining - Bouygues Construction Duraset EHL Consulting Engineers (Pty) Ltd Elbroc Mining Products (Pty) Ltd ▶ x

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eThekwini Municipality Ex Mente Technologies (Pty) Ltd Expectra 2004 (Pty) Ltd Exxaro Coal (Pty) Ltd Exxaro Resources Limited Filtaquip (Pty) Ltd FLSmidth Minerals (Pty) Ltd Fluor Daniel SA ( Pty) Ltd Franki Africa (Pty) Ltd-JHB Fraser Alexander (Pty) Ltd G H H Mining Machines (Pty) Ltd Geobrugg Southern Africa (Pty) Ltd Glencore Gravitas Minerals (Pty) Ltd Hall Core Drilling (Pty) Ltd Hatch (Pty) Ltd Herrenknecht AG HPE Hydro Power Equipment (Pty) Ltd Huawei Technologies Africa (Pty) Ltd Immersive Technologies IMS Engineering (Pty) Ltd Ingwenya Mineral Processing (Pty) Ltd Ivanhoe Mines SA Kudumane Manganese Resources Leica Geosystems (Pty) Ltd Loesche South Africa (Pty) Ltd Longyear South Africa (Pty) Ltd Lull Storm Trading (Pty) Ltd Maccaferri SA (Pty) Ltd Magnetech (Pty) Ltd Magotteaux (Pty) Ltd Malvern Panalytical (Pty) Ltd Maptek (Pty) Ltd Maxam Dantex (Pty) Ltd MBE Minerals SA Pty Ltd MCC Contracts (Pty) Ltd MD Mineral Technologies SA (Pty) Ltd MDM Technical Africa (Pty) Ltd Metalock Engineering RSA (Pty)Ltd Metorex Limited Metso Minerals (South Africa) Pty Ltd Micromine Africa (Pty) Ltd MineARC South Africa (Pty) Ltd Minerals Council of South Africa Minerals Operations Executive (Pty) Ltd MineRP Holding (Pty) Ltd Mining Projections Concepts Mintek MIP Process Technologies (Pty) Limited MLB Investment CC Modular Mining Systems Africa (Pty) Ltd

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CARBON TAX ZOOZs A T ǡǟǡǢ

wZ }> 9tA U# }>' ZU}' } } Z9 }>' :OZ O TAUAU: AU# w}t t 15 NOVEMBER 2023 Ǥǣ ZU }>ș tZw' UNș LZ> UU'w t: t:

We acknowledge that the intent of carbon tax is to change user behaviour and reduce climate impact. SAIMM wants to evaluate ways to reduce its impact and ensure business viability.

his Colloquium, on the South African Carbon Tax, will provide an understanding of our own unique situation, in South Africa, compared to in the context of the global mining industry. This SA Carbon Tax policy was introduced by the SA government in June 2019, aimed at reducing the country’s greenhouse gas emissions. The aim of the tax is to create a ťĊĊÆðă ðĊÆÐĊĴðŒÐ åďī ÆďĉĨĊðÐĮ Ĵď īÐÌķÆÐ ĴìÐðī emissions by switching to cleaner technologies and adopting sustainable practices. Revenue generated from the tax should be used to fund initiatives aimed Ĵ ĨīďĉďĴðĊæ ÐĊÐīæř ÐŨÆðÐĊÆř ĊÌ īÐĊÐœÅăÐ ÐĊÐīæřȘ In short: it should be a policy instrument that supports international commitments, a source of revenue that can be used to support initiatives that promote renewable energy, which will in turn create new opportunities for businesses and promote job creation. AĊ ĮĨÐÆðťÆ ĮĴķÌðÐĮ ĨķÅăðĮìÐÌ ÅÐĴœÐÐĊ ǡǟǠǥ ĊÌ ǡǟǡǡș it show the negative impact of the carbon tax on economic growth is minimized when the revenue is fed back into the economy. The way carbon tax revenue is recycled back into the economy is important in terms of the extent of emissions reductions achieved. Is the South African carbon tax revenue being recycled ÐŨÆðÐĊĴăřȟ Zī ÐŒÐĊ ÆďīīÐÆĴăřȟ TďīÐďŒÐīș w īÅďĊ Tax and its implications for industry, necessitates an evaluation of alternatives to fossil fuel use.

This Colloquium will host presentations from universities, research institutes, development banks and renewable energy supply companies. This colloquium will will endeavour to create a platform for discussion around the following questions: x Are we, in the minerals and metals industry, adequately informed to answer questions about any īÅďĊ }Ř ĨďăðÆř ȧUĴðďĊă ďī :ăďÅăȨȟ x Are we projecting negativity due to the general discontent with the current state of affairs – ÐÆďĊďĉðÆș ĮďÆðă ĊÌ ĨďăðĴðÆăȟ x ìĴ ðĮ ďķī ÌÐťĊðĴðďĊ ďå īÐÆřÆăðĊæ ĴŘ īÐŒÐĊķÐ ȷÐŨÆðÐĊĴăřȸȟ #ďÐĮ ĴìðĮ ÌÐĨÐĊÌ ďĊ ĨÐīĮĨÐÆĴðŒÐȟ x AĮ ĴìÐ TðĊÐīăĮ ĊÌ TÐĴăĮ AĊÌķĮĴīř ÆăÐī ďĊ ĴìÐðī expectations of and from the South African Carbon }Ř ĨďăðÆřȟ x What exactly do we want as professionals and as an AĊÌķĮĴīřȟ x ìĴ ďĨĴðďĊĮ Ìď œÐ Į Ċ AĊÌķĮĴīř ìŒÐȟ #ď œÐ ìŒÐ Ċ ďĨĴðďĊ Ĵď ðĊŦķÐĊÆÐ ĴìÐ ĨďăðÆř ĊÌ ĴìÐ ĴŘ īÐŒÐĊķÐ īÐÆřÆăðĊæ Ĵ ăăȟ x Can we ask assistance to analyze the positive and negative aspects of our current strategy and its ÐŘÐÆķĴðďĊȟ

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MISTY HILLS CONFERENCE CENTRE MULDERSDRIFT, JOHANNESBURG

SOUTH AFRICA ONLINE VIA ZOOM

The World Conference on Sampling and Blending (WCSB), to be held in South Africa, 21-23 May 2024, is the eleventh such conference to promote the Theory of Sampling (TOS). The WCSB conference provide a meeting place for professionals interested in sampling theory, practice, experience, applications, and standards. The Conference will provide understanding and insights IRU DFDGHPLFV PDQXIDFWXUHUV HQJLQHHULQJ ²UPV DQG practitioners aiming to achieve representative sampling. 726 HIIHFWLYHO\ LGHQWL²HV WKH VRXUFH RI VDPSOLQJ variability and provides valuable solutions for minimising each source of sampling uncertainty. The aim of WCSB11 is to invite and encourage the diverse international sampling community to adopt and disseminate the concepts and ideas for a standardized approach to sampling embodied in the TOS. The Conference will also offer a forum for fruitful discussions between statisticians committed to ‘Measurement of Uncertainty’ (MU) and proponents of the TOS by offering a unifying foundation for development of better and more general standards. While the Theory of Sampling had its historical origins in the mining industry, today it also applies to sampling of a broad range of bulk materials, minerals, agricultural raw materials and products, the food, feed, and pharmaceutical industries, as well as sampling for environmental applications. WCSB11 is an HYHQW RI JOREDO VLJQL²FDQFH WKDW DLPV WR LPSURYH VDPSOLQJ practices in all sectors of science, technology, and industry, for consultants, managers, sampling and quality control staff, researchers, engineers, and manufacturers operating in many industries, The opportunity to meet,

exchange ideas, and share practical experiences will be a VLJQL²FDQW EHQH²W IRU DWWHQGHHV The proceedings of the Conference will be published in electronic format with a strict adherence to an editorial and peer review policy that will allow academics to attract the publication subsidy for published academic research. Adherence to these standards will enable the wider dissemination of the TOS in international VFLHQWL²F WHFKQRORJLFDO DQG LQGXVWULDO VHFWRUV :&6%V have helped to promote the teaching of TOS at universities, with postgraduate courses in TOS being taught in some countries. The Pierre Gy Gold Medal is awarded at each WCSB conference to individuals who have been most effective and successful around the world in disseminating and promoting TOS. This achievement will again be celebrated at WCSB11. The PHGDOOLVWV DUH D XQL²HG ERG\ RI FKDPSLRQV FDSDEOH RI teaching, promoting, and researching aspects of sampling theory and practice, supporting the efforts of original equipment manufacturers to uphold TOS rules of sample representativeness. WCSB conferences aim to develop D XQL²HG YLVLRQ IRU VSHFL²F TXDOLW\ FRQWURO SURWRFROV IRU sampling and blending activities, with participation and collaboration of industry professionals. The theme of sustainable science, technology, and industry introduced at WCSB10 is upheld, with emphasis on the UN World Development Goals number 9 and 12, addressing sustainable industry, innovation, and infrastructure, and responsible production and consumption. Topics around societal, industrial, and environmental aspects of particulate sampling in mining,

FOR FURTHER INFORMATION, CONTACT: Camielah Jardine, Head of Conferencing

E-mail: camielah@saimm.co.za Tel: +27 11 538-0237, Web: www.saimm.co.za