Abstract
Hard rock pillar is a crucial rock mass structure to maintain the stability of underground mine. It needs of special attention to analyze its stability from the point of rock mass quality. In this paper, the geological strength index (GSI) representing the rock mass quality of the hard rock pillar is examined as a new influence factor of stability, and combined with the conventional parameters (uniaxial compressive strength (UCS) of intact rock mass, width of pillar (w), height of pillar (h), the ratio of pillar width to its height (w/h)) to complete the stochastic assessment of the stability of hard rock pillar. The 47 actual cases of hard rock pillar improved by numerical simulation software Flac3D. An empirical formula fitted by the Least Square method and artificial intelligence prediction models are used to estimate the pillar strength combining with the pillar stress to conduct the probability and reliability analysis in the Monte Carlo simulation. The result of stochastic assessment showed that UCS and w still play a vital role in maintaining pillar stability, but the influence of GSI cannot be ignored. It found that the GSI has a greater influence on the sloughing pillars in comparison with stable and failed hard rock pillars. Concluding remarks is that GSI has crucial effects on the stability of hard rock pillars as well as UCS of the rock mass and shape of pillars (w and h). Thus, the GSI should be considered as one of input parameter for pillar design and stability assessment in underground mines.
Article highlights
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A new empirical formula and artificial intelligence models considering five parameters(GSI, UCS, w, h and H) are developed with the improved 47 actual cases of hard rock pillar to estimate the pillar strength.
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Two pillar performance functions are determined by the Monte Carlo Simulation technique to complete the stochastic assessment based on the probability and reliability analysis of stability conditions of hard rock pillars.
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The probability of different conditions of pillars can well indicate the relationship between the new (GSI) and traditional influencing factors (UCS, w, h and H) and the stability of pillars.
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The GSI index has a greater influence on the sloughing pillars in comparison with stable and failed hard rock pillars.
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References
Armaghani DJ, Mahdiyar A, Hasanipanah M, Faradonbeh RS, Khandelwal M, Amnieh HB (2016) Risk assessment and prediction of flyrock distance by combined multiple regression analysis and Monte Carlo simulation of quarry blasting. Rock Mech Rock Eng 49(9):3631–3641. https://doi.org/10.1007/s00603-016-1015-z
Arthur FA, Hyder R, Tiile RN, Ge MC (2016) Pillar stability analysis at Missouri S&T dolomitic limestone experimental mine. 50th US rock mechanics/geomechanics symposium. American Rock Mechanics Association. Houston, Texas, USA, pp 26–29
Bennett KP, Mangasarian OL (1992) Robust linear programming discrimination of two linearly inseparable sets. Optim Methods Softw 1(1):23–34. https://doi.org/10.1080/10556789208805504
Bieniawski ZT (1989) Engineering rock mass classifications. Wiley, New York, pp 1–272
Brady BHG, Brown ET (1985) Rock mechanics for underground mining. Allen and Unwin, London, pp 1–527
Cauvin M, Verdel T, Salmon R (2009) Modeling uncertainties in mining pillar stability analysis. Risk Anal 29(10):1371–1380. https://doi.org/10.1111/j.1539-6924.2009.01237.x
Chinyowa W C, Zvarivadza T (2015) A review of pillar design for platinum mining to enhance stability: a Zimbabwean case study. In 49th US Rock mechanics/geomechanics symposium. American Rock Mechanics Association
Dehghan S, Shahriar K, Maarefvand P, Goshtasbi K (2013) 3-D numerical modelling of Domino failure of hard rock pillars in Fetr6 Chromite Mine, Iran, and comparison with empirical methods. J Cent South Univ 20:541–549. https://doi.org/10.1007/s11771-013-1517-8
Deng J, Yue Z, Tham LG, Zhu H (2003) Pillar design by combining finite element methods, neural networks and reliability: a case study of the Feng Huangshan copper mine, China. Int J Rock Mech Min Sci 40(4):585–599. https://doi.org/10.1016/S1365-1609(03)00042-X
Ding H, Li G, Dong X, Lin Y (2018) Prediction of pillar stability for underground mines using the stochastic gradient boosting technique. IEEE Access 6:69253–69264. https://doi.org/10.1109/ACCESS.2018.2880466
Ding S, Su C, Yu J (2011) An optimizing BP neural network algorithm based on genetic algorithm. Artif Intell Rev 36(2):153–162. https://doi.org/10.1007/s10462-011-9208-z
Esterhuizen E, Mark C, Murphy MM (2010) Numerical model calibration for simulating coal pillars, gob and overburden response. In: Proceedings of the 29th international conference on ground control in mining, Morgantown, pp 46–57
Esterhuizen GS, Dolinar DR, Ellenberger JL (2008) Pillar strength and design methodology for stone mines. In: Proceedings of the 27th international conference on ground control in mining. West Virginia University, Morgantown WV, pp 241–253
Gaddy FL (1956) A study of the ultimate strength of coal as related to the absolute size of the cubical specimens tested. West Virginia Polytech Bull 112:1–27
Garza-Cruz TV, Pierce M, Board M (2018) Effect of shear stresses on pillar stability-a back-analysis of the troy mine experience to forward predict pillar performance at Montanore. In: 52nd US rock mechanics/geomechanics symposium. American Rock Mechanics Association. Seattle, Washington: 17–20 June, pp 1–13
Ghasemi E, Kalhori H, Bagherpour R (2017) Stability assessment of hard rock pillars using two intelligent classification techniques: a comparative study. Tunn Undergr Space Technol 68:32–37. https://doi.org/10.1016/j.tust.2017.05.012
Ghasemi E, Shahriar K, Sharifzadeh M (2010a) A new method for risk assessment of pillar recovery operation. Saf Sci 48:1304–1312. https://doi.org/10.1016/j.ssci.2010.04.008
Ghasemi E, Shahriar K, Sharifzadeh M, Hashemolhosseini H (2010b) Quantifying the uncertainty of pillar safety factor by Monte Carlo simulation—a case study. Arch Min Sci 55(3):623–635
Gong FQ, Yan JY, Li XB (2018) A new criterion of rock burst proneness based on the linear energy storage law and the residual elastic energy index. Chin J Rock Mech Eng 37(9):1993–2014
González-Nicieza C, Álvarez-Fernández MI, Menéndez-Díaz A, Álvarez-Vigil AE (2006) A comparative analysis of pillar design methods and its application to marble mines. Rock Mech Rock Eng 39(5):421–444. https://doi.org/10.1007/s00603-005-0078-z
Griffiths DV, Fenton GA, Lemons CB (2002) Probabilistic analysis of underground pillar stability. Int J Numer Anal Meth Geomech 26(8):775–791. https://doi.org/10.1002/nag.222
Hernandez H (2017) Multivariate probability theory: Determination of probability density functions. ForsChem Res Rep. https://doi.org/10.13140/RG.2.2.28214.60481
Hoek E (1994) Strength of rock and rock masses. News J Int Soc Rock Mech 2(2):4–16
Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci Geomech Abstr 34:1165–1186. https://doi.org/10.1016/S1365-1609(97)80069-X
Hoek E, Brown ET (2019) The Hoek-Brown failure criterion and GSI–2018 edition. J Rock Mech Geotech Eng 11(3):445–463. https://doi.org/10.1016/j.jrmge.2018.08.001
Hoek E, Diederichs MS (2006) Empirical estimation of rock mass modulus. Int J Rock Mech Min Sci 43(2):203–215. https://doi.org/10.1016/j.ijrmms.2005.06.005
Hoek E, Kaiser PK, Bawden WF (1995) Support of underground excavations in hard rock. A.A. Balkema, Rotterdam
Houari R, Bounceur A, Kechadi M, Tari A, Euler R (2016) Dimensionality reduction in data mining: a Copula approach. Expert Syst Appl 64:247–260. https://doi.org/10.1016/j.eswa.2016.07.041
Hudyma MR (1988) Rib pillar design in open stope mining. MASc. thesis, The University of British Columbia, Vancouver, Canada, pp 1–184
Idris MA, Saiang D, Nordlund E (2015) Stochastic assessment of pillar stability at Laisvall mine using Artificial Neural Network. Tunn Undergr Space Technol 49:307–319. https://doi.org/10.1016/j.tust.2015.05.003
Itasca (2012) FLAC3D–Fast Langrangian analysis of continua in three dimension, Version 5.0. www.itascacg.com
Kim JG, Abdellah WR, Yang HS (2019) Parametric stability analysis of pillar performance at Nohyun limestone mine, South Korea—a case study. Arab J Geosci 12(12):390. https://doi.org/10.1007/s12517-019-4550-6
Košťák B (1971) Pillar strength prediction from representative sample of hard rock. Int J Rock Mech Min Sci Geomech Abstr 8(5):523–526. https://doi.org/10.1016/1365-1609(71)90016-5
Kostecki T, Spearing AJS (2015) Influence of backfill on coal pillar strength and floor bearing capacity in weak floor statuses in the Illinois basin. Int J Rock Mech Min Sci 76:55–67. https://doi.org/10.1016/j.ijrmms.2014.11.011
Kumar A, Waclawik P, Singh R, Ram S, Korbel J (2019) Performance of a coal pillar at deeper cover: field and simulation studies. Int J Rock Mech Min Sci 113:322–332. https://doi.org/10.1016/j.ijrmms.2018.10.006
Li J, Cheng J, Shi J, Huang F (2012) Brief introduction of back propagation (BP) neural network algorithm and its improvement. Adv Comput Sci Inf Eng 2:553–558. https://doi.org/10.1007/978-3-642-30223-7_87
Li X, Li D, Liu Z, Zhao G, Wang W (2013) Determination of the minimum thickness of crown pillar for safe exploitation of a subsea gold mine based on numerical modelling. Int J Rock Mech Min Sci 57:42–56. https://doi.org/10.1016/j.ijrmms.2012.08.005
Li XB, Zhou J, Wang SF, Liu B (2017) Review and practice of deep mining for solid mineral resources. Chin J Nonferrous Metals 27(7):1236–1262
Li F, Yang Y, Fan X, Xu B, Ju Y, Wang Y, Chen J (2018) Numerical analysis of the hydrofracturing behaviours and mechanisms of heterogeneous reservoir rock using the continuum-based discrete element method considering pre-existing fractures. Geomech Geophys Geo-Energy Geo-Resourc 4(4):383–401. https://doi.org/10.1007/s40948-018-0095-5
Li C, Zhou J, Armaghani DJ, Li X (2020a) Stability analysis of underground mine hard rock pillars via combination of finite difference methods, neural networks, and Monte Carlo simulation techniques. Undergr Space. https://doi.org/10.1016/j.undsp.2020.05.005
Li ZQ, Li XL, Yu JB, Cao WD, Liu ZF, Wang M, Wang XH (2020b) Influence of existing natural fractures and beddings on the formation of fracture network during hydraulic fracturing based on the extended finite element method. Geomech Geophys Geo-Energy Geo-Resourc 6(4):1–13. https://doi.org/10.1007/s40948-020-00180-y
Li E, Zhou J, Shi X, Armaghani DJ, Yu Z, Chen X, Huang P (2020c) Developing a hybrid model of salp swarm algorithm-based support vector machine to predict the strength of fiber-reinforced cemented paste backfill. Eng Comput 1–22. https://doi.org/10.1007/s00366-020-01014-x
Lunder PJ, Pakalnis R (1997) Determination of the strength of hard rock mine pillars. Can Inst Min Bull 90(1013):51–55
Machuca L, Sutton M, Grow R., Andrews P (2015) Geotechnical approach to stope and pillar optimisation at Granny Smith Mine. In Proceedings of the international seminar on design methods in underground mining. Australian Centre for Geomechanics, pp 215–232. https://doi.org/https://doi.org/10.36487/ACG_rep/1511_10_Machuca.
Ma T, Wang L, Suorineni FT, Tang C (2016) Numerical analysis on failure modes and mechanisms of mine pillars under shear loading. Shock Vib 1:1–14. https://doi.org/10.1155/2016/6195482
Maritz J, Malan D, Piper P (2012) Estimating pillar stresses in complex multi-reef layouts. Southern Hemisphere International Rock Engineering Symposium, Sun City, South Africa, 2012 14–17:125–143
Melchers RE, Beck AT (2018) Structural reliability analysis and prediction. Wiley, New York, p 514
Monjezi M, Hesami SM, Khandelwal M (2011) Superiority of neural networks for pillar stress prediction in bord and pillar method. Arab J Geosci 4(5–6):845–853. https://doi.org/10.1007/s12517-009-0101-x
Mortazavi A, Hassani FP, Shabani M (2009) A numerical investigation of rock pillar failure mechanism in underground openings. Comput Geotech 36(5):691–697. https://doi.org/10.1016/j.compgeo.2008.11.004
Najafi M, Jalali SE, Bafghi ARY, Sereshki F (2011) Prediction of the confidence interval for stability analysis of chain pillars in coal mines. Saf Sci 49(5):651–657. https://doi.org/10.1016/j.ssci.2010.11.005
Najafi M, Jalali SE, Sereshki F, Bafghi ARY (2016) Probabilistic analysis of stability of chain pillars in Tabas coal mine in Iran using Monte Carlo simulation. J Min Environ 7(1):25–35
Oke J, Esterhuizen GS (2017) Improving hard rock pillar design by including rock mass classification and failure mechanisms. In: 51st US rock mechanics/geomechanics symposium, San Francisco, California, 25–28 June.
Poulsen BA (2010) Coal pillar load calculation by pressure arch theory and near field extraction ratio. Int J Rock Mech Min Sci 47(7):1158–1165. https://doi.org/10.1016/j.ijrmms.2010.06.011
Python. https://www.python.org/
Qiu Y, Zhou J, Khandelwal M, Yang H, Yang P, Li C (2021) Performance evaluation of hybrid WOA-XGBoost, GWO-XGBoost and BO-XGBoost models to predict blast-induced ground vibration. Eng Comput. https://doi.org/10.1007/s00366-021-01393-9
Reed G, Mctyer K, Frith R (2017) An assessment of coal pillar system stability criteria based on a mechanistic evaluation of the interaction between coal pillars and the overburden. Int J Min Sci Technol 27(1):9–15. https://doi.org/10.1016/j.ijmst.2016.09.031
Renani HR, Martin CD (2018) Modeling the progressive failure of hard rock pillars. Tunn Undergr Space Technol 74:71–81. https://doi.org/10.1016/j.tust.2018.01.006
Rodriguez-Galiano V, Sanchez-Castillo M, Chica-Olmo M, Chica-Rivas M (2015) Machine learning predictive models for mineral prospectivity: an evaluation of neural networks, random forest, regression trees and support vector machines. Ore Geol Rev 71:804–818. https://doi.org/10.1016/j.oregeorev.2015.01.001
Sainoki A, Mitri HS (2017) Numerical investigation into pillar failure induced by time-dependent skin degradation. Int J Min Sci Technol 27(4):591–597. https://doi.org/10.1016/j.ijmst.2017.05.002
Salamon MDG (1970) Stability, instability and design of coal pillar workings. Int J Rock Mech Mining Sci Geomech Abstr 7(6):613–631. https://doi.org/10.1016/0148-9062(70)90022-7
Salamon MDG (1967) A method of designing bord and pillar workings. J South Afr Inst Min Metall 68(2):68–78
Salamon MDG, Munro AH (1967) A study of the strength of coal pillars. J South Afr Inst Min Metall 68(2):55–67
Shi G (2014) Data mining and knowledge discovery for geoscientists, 1st edn. Elsevier, Amsterdam
Siahmansouri A, Gholamnejad J, Marji MF (2012) A new method to predict ratio of width to height rock pillar in twin circular tunnels. J Geol Geosci 1:103. https://doi.org/10.4172/2329-6755.1000103
Sjöberg J (1992) Failure modes and pillar behaviour in the Zinkgruvan mine. In: Proceedings of 33rd U.S. rock mechanics symposium. A.A. Balkema, Rotterdam, Santa Fe, 8–10, June, pp 491–500
Song G, Yang S (2018) Probability and reliability analysis of pillar stability in South Africa. Int J Min Sci Technol 28(4):715–719. https://doi.org/10.1016/j.ijmst.2018.02.004
Tawadrous AS, Katsabanis PD (2007) Prediction of surface crown pillar stability using artificial neural networks. Int J Numer Anal Meth Geomech 31(7):917–931. https://doi.org/10.1002/nag.566
Van der Merwe JN (1993) Revised strength factor for coal in the Vaal Basin. J Southern Afr Inst Min Metall 93(3):71–77. https://hdl.handle.net/10520/AJA0038223X_2220
Vapnik VN (1995) The nature of statistical learning theory. Springer, New York
Wagner H (1980) Pillar design in coal mines. J Southern Afr Inst Min Metall 80(1):37–45. https://hdl.handle.net/10520/AJA0038223X_1290
Wang SM, Liu YS, Du K, Zhou J, Khandelwal M (2020a) Waveform features and failure patterns of hollow cylindrical sandstone specimens under repetitive impact and triaxial confinements. Geomech Geophys Geo-Energy Geo-resour 6(4):57. https://doi.org/10.1007/s40948-020-00183-9
Wang P, Wang S, Zhu C, Zhang Z (2020b) Classification and extent determination of rock slope using deep learning. Geomech Geophys Geo-Energy Geo-Resourc 6(1):1–12. https://doi.org/10.1007/s40948-020-00154-0
Wang SM, Zhou J, Li CQ, Armaghani DJ, Li XB, Mitri HS (2021) Rockburst prediction in hard rock mines developing bagging and boosting tree-based ensemble techniques. J Central South Univ 28(2):527–542
Wattimena RK (2014) Predicting the stability of hard rock pillars using multinomial logistic regression. Int J Rock Mech Min Sci 100(71):33–40. https://doi.org/10.1016/j.ijrmms.2014.03.015
Wattimena RK, Kramadibrata S, Sidi ID, Azizi MA (2013) Developing coal pillar stability chart using logistic regression. Int J Rock Mech Min Sci 58:55–60. https://doi.org/10.1016/j.ijrmms.2012.09.004
Xiong LX, Chen HJ, Li TB, Zhang Y (2018) Experimental study on the uniaxial compressive strength of artificial jointed rock mass specimen after high temperatures. Geomech Geophys Geo-Energy Geo-Resourc 4(3):201–213. https://doi.org/10.1007/s40948-018-0085-7
Yang WM, Geng Y, Zhou ZQ, Li LP, Gao CL, Wang MX, Zhang DS (2020) DEM numerical simulation study on fracture propagation of synchronous fracturing in a double fracture rock mass. Geomech Geophys Geo-Energy Geo-Resourc 6:1–19. https://doi.org/10.1007/s40948-020-00162-0
Yu Y, Deng KZ, Chen SE (2018) Mine size effects on coal pillar stress and their application for partial extraction. Sustainability 10(3):792. https://doi.org/10.3390/su10030792
Zhang Q, Huang X, Zhu H, Li J (2019) Quantitative assessments of the correlations between rock mass rating (RMR) and geological strength index (GSI). Tunn Undergr Space Technol 83:73–81. https://doi.org/10.1016/j.tust.2018.09.015
Zhou J, Li X, Shi X, Wei W, Wu B (2011) Predicting pillar stability for underground mine using Fisher discriminant analysis and SVM methods. Trans Nonferr Met Soc China 21(12):2734–2743. https://doi.org/10.1016/S1003-6326(11)61117-5
Zhou J, Li X, Shi X (2012) Long-term prediction model of rockburst in underground openings using heuristic algorithms and support vector machines. Saf Sci 50(4):629–644. https://doi.org/10.1016/j.ssci.2011.08.065
Zhou J, Li X, Mitri HS, Wang SM, Wei W (2013) Identification of large-scale goaf instability in underground mine using particle swarm optimization and support vector machine. Int J Min Sci Technol 23(5):701–707. https://doi.org/10.1016/j.ijmst.2013.08.014
Zhou J, Li X, Mitri HS (2015) Comparative performance of six supervised learning methods for the development of models of hard rock pillar stability prediction. Nat Hazards 79(1):291–316. https://doi.org/10.1007/s11069-015-1842-3
Zhou J, Aghili N, Ghaleini EN, Bui DT, Tahir MM, Koopialipoor M (2019a) A Monte Carlo simulation approach for effective assessment of flyrock based on intelligent system of neural network. Eng Comput 36:1–11. https://doi.org/10.1007/s00366-019-00726-z
Zhou J, Koopialipoor M, Murlidhar BR, Fatemi SA, Tahir MM, Armaghani DJ, Li C (2019b) Use of intelligent methods to design effective pattern parameters of mine blasting to minimize flyrock distance. Nat Resourc Res 29:625–639. https://doi.org/10.1007/s11053-019-09519-z
Zhou J, Li C, Koopialipoor M, Jahed Armaghani D, Thai Pham B (2021a) Development of a new methodology for estimating the amount of PPV in surface mines based on prediction and probabilistic models (GEP-MC). Int J Min Reclam Environ 35(1):48–68. https://doi.org/10.1080/17480930.2020.1734151
Zhou J, Qiu Y, Armaghani DJ, Zhang W, Li C, Zhu S, Tarinejad R (2021b) Predicting TBM penetration rate in hard rock condition: a comparative study among six XGB-based metaheuristic techniques. Geosci Front 12(3):101091. https://doi.org/10.1016/j.gsf.2020.09.020
Zhou J, Qiu Y, Zhu S, Armaghani DJ, Li C, Nguyen H, Yagiz S (2021c) Optimization of support vector machine through the use of metaheuristic algorithms in forecasting TBM advance rate. Eng Appl Artif Intel 97:104015
Zvarivadza T, Van der Merwe JN (2017) Reflections on narrow-reef platinum mining pillar design systems as applied to a large platinum exploration feasibility project. J Southern Afr Inst Min Metall 117(2):169–178. https://doi.org/10.17159/2411-9717/2017/v117n2a8
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This research is partially supported by the National Natural Science Foundation Project of China (Grant No. 41807259) and the Innovation-Driven Project of Central South University (2020CX040).
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Li, C., Zhou, J., Armaghani, D.J. et al. Stochastic assessment of hard rock pillar stability based on the geological strength index system. Geomech. Geophys. Geo-energ. Geo-resour. 7, 47 (2021). https://doi.org/10.1007/s40948-021-00243-8
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DOI: https://doi.org/10.1007/s40948-021-00243-8