Abstract
Rockburst (RB) is known as one of the deadliest and most destructive geotechnical events in deep underground spaces under high stresses. The complexity of the RB phenomenon and uncertainty arising from variability in geotechnical and geomechanical conditions makes its prediction very difficult. The current study is an attempt to address the suitability of the stochastic modeling approach for the evaluation of RB potential and to assess the effects of the contributing parameters on the phenomenon. To do this study, a database containing the major effective parameters on RB potential (i.e. stress concentration coefficient, brittleness coefficient, and elastic energy index) compiled from 335 case histories of RB in various underground projects worldwide was applied. Using this database, first, a new deterministic mathematical relation for predicting RB potential was developed using gene expression programming (GEP) method. Then, the RB phenomenon was simulated by the Monte Carlo (MC) method. The results reveal that stochastic modeling is a good means for modeling and evaluating the effects of the variability of contributing parameters on RB. Finally, sensitivity analysis was conducted to analyse the effects of the contributing parameters on RB potential. Sensitivity analysis showed that stress concentration coefficient, brittleness coefficient, and elastic energy index have a direct relationship with RB potential. Furthermore, the elastic energy index was found to be the most effective parameter on the RB potential with regression coefficient of + 0.50.
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References
Adoko AC, Gokceoglu C, Wu L, Zuo QJ (2013) Knowledge-based and data-driven fuzzy modeling for rockburst prediction. Int J Rock Mech Min Sci 61:86–95. https://doi.org/10.1016/j.ijrmms.2013.02.010
Adoko AC, Zvarivadza T (2018) A Bayesian Approach for Predicting Rockburst. 52nd US Rock Mech. Symp.
Afraei S, Shahriar K, Madani SH (2018) Statistical assessment of rock burst potential and contributions of considered predictor variables in the task. Tunn Undergr Sp Technol 72:250–271. https://doi.org/10.1016/j.tust.2017.10.009
Afraei S, Shahriar K, Madani SH (2019) Developing intelligent classification models for rock burst prediction after recognizing significant predictor variables, Section 2: Designing classifiers. Tunn Undergr Sp Technol 84:522–537. https://doi.org/10.1016/j.tust.2018.11.011
Bastami R, Aghajani Bazzazi A, Hamidian Shoormasti H, Ahangari K (2020) Prediction of blasting cost in limestone mines using gene expression programming model and artificial neural networks. J Min Environ 11:281–300
Bird GA (1981) Monte-Carlo simulation in an engineering context. Prog Astronaut Aeronaut 74:239–255
Cai M (2013) Principles of rock support in burst-prone ground. Tunn Undergr Sp Technol 36:46–56. https://doi.org/10.1016/J.TUST.2013.02.003
Copur H, Aydin H, Bilgin N et al (2014) Predicting performance of EPB TBMs by using a stochastic model implemented into a deterministic model. Tunn Undergr Sp Technol 42:1–14. https://doi.org/10.1016/J.TUST.2014.01.006
Dehghani H, Pourzafar M, Asadi zadeh M, (2021) Prediction and minimization of blast-induced flyrock using gene expression programming and cuckoo optimization algorithm. Environ Earth Sci 80:1–17. https://doi.org/10.1007/s12665-020-09300-z
Dong LJ, Li XB, Peng K (2013) Prediction of rockburst classification using random forest. Trans Nonferrous Met Soc China 23:472–477. https://doi.org/10.1016/S1003-6326(13)62487-5
Fawcett T (2006) An introduction to ROC analysis. Pattern Recognit Lett 27:861–874. https://doi.org/10.1016/j.patrec.2005.10.010
Feng X-T, Wang L (1994) Rockburst prediction based on neural networks. Trans Nonferrous Met Soc China 4:7–14
Ferreira C (2002) Gene Expression Programming in Problem Solving. Soft Computing and Industry. Springer, London, pp 635–653
Ferreira C (2006) Gene expression programming: mathematical modeling by an artificial intelligence. Springer-Verlag, Berlin
Ferreira C (2001) Gene expression programming: a new adaptive algorithm for solving problems. Complex Syst 13:87–129
GEPSOFT (2014) GeneXproTools version 5.0. Available online: http://www.gepsoft.com
Ghasemi E, Gholizadeh H (2019) Development of two empirical correlations for tunnel squeezing prediction using binary logistic regression and linear discriminant analysis. Geotech Geol Eng 37:3435–3446. https://doi.org/10.1007/s10706-018-00758-0
Ghasemi E, Shahriar K, Sharifzadeh M, Hashemolhosseini H (2010) Quantifying the uncertainty of pillar safety factor by Monte Carlo simulation - a case study. Arch Min Sci 55:623–635
Ghasemi E, Sari M, Ataei M (2012) Development of an empirical model for predicting the effects of controllable blasting parameters on flyrock distance in surface mines. Int J Rock Mech Min Sci 52:163–170. https://doi.org/10.1016/j.ijrmms.2012.03.011
Ghasemi E, Gholizadeh H, Adoko AC (2020) Evaluation of rockburst occurrence and intensity in underground structures using decision tree approach. Eng Comput 36:213–225. https://doi.org/10.1007/s00366-018-00695-9
Gong FQ, Li XB (2007) A distance discriminant analysis method for prediction of possibility and classification of rockburst and its application. Chinese J Rock Mech Eng 26:1012–1018
Güllü H (2012) Prediction of peak ground acceleration by genetic expression programming and regression: A comparison using likelihood-based measure. Eng Geol 141–142:92–113. https://doi.org/10.1016/J.ENGGEO.2012.05.010
Hajihassani M, Abdullah SS, Asteris PG, Armaghani DJ (2019) A gene expression programming model for predicting tunnel convergence. Appl Sci 9:4650. https://doi.org/10.3390/app9214650
Han J, Pei J, Kamber M (2011) Data mining: concepts and techniques, 3rd edn. Morgon Kaufmann Publisher, Waltham
Hoang ND, Tien Bui D (2018) Spatial prediction of rainfall-induced shallow landslides using gene expression programming integrated with GIS: a case study in Vietnam. Nat Hazards 92:1871–1887. https://doi.org/10.1007/s11069-018-3286-z
Hosmer D, Lemeshow S (2000) Applied logistic models, 2nd edn. Wiley, New York
Husein Malkawi AI, Hassan WF, Abdulla FA (2000) Uncertainty and reliability analysis applied to slope stability. Struct Saf 22:161–187. https://doi.org/10.1016/S0167-4730(00)00006-0
İnce İ, Bozdağ A, Fener M, Kahraman S (2019) Estimation of uniaxial compressive strength of pyroclastic rocks (Cappadocia, Turkey) by gene expression programming. Arab J Geosci 12:1–13. https://doi.org/10.1007/s12517-019-4953-4
Jahed Armaghani D, Faradonbeh RS, Momeni E et al (2018a) Performance prediction of tunnel boring machine through developing a gene expression programming equation. Eng Comput 34:129–141. https://doi.org/10.1007/s00366-017-0526-x
Jahed Armaghani D, Safari V, Fahimifar A et al (2018b) Uniaxial compressive strength prediction through a new technique based on gene expression programming. Neural Comput Appl 30:3523–3532. https://doi.org/10.1007/s00521-017-2939-2
Kadkhodaei MH, Ghasemi E (2019) Development of a GEP model to assess CERCHAR abrasivity index of rocks based on geomechanical properties. J Min Environ 10:917–928
Kadkhodaei MH, Ghasemi E (2022) Development of a semi-quantitative framework to assess rockburst risk using risk matrix and logistic model tree. Geotech Geol Eng. https://doi.org/10.1007/S10706-022-02122-9
Ke B, Khandelwal M, Asteris PG et al (2021) Rock-burst occurrence prediction based on optimized naïve bayes models. IEEE Access 9:91347–91360. https://doi.org/10.1109/ACCESS.2021.3089205
Li N, Feng X, Jimenez R (2017) Predicting rock burst hazard with incomplete data using Bayesian networks. Tunn Undergr Sp Technol 61:61–70. https://doi.org/10.1016/j.tust.2016.09.010
Li C, Zhou J, Armaghani DJ, Li X (2021) Stability analysis of underground mine hard rock pillars via combination of finite difference methods, neural networks, and Monte Carlo simulation techniques. Undergr Sp 6:379–395. https://doi.org/10.1016/J.UNDSP.2020.05.005
Li D, Liu Z, Armaghani DJ et al (2022) Novel ensemble intelligence methodologies for rockburst assessment in complex and variable environments. Sci Rep 12:1–23. https://doi.org/10.1038/s41598-022-05594-0
Lin Y, Zhou K, Li J (2018) Application of cloud model in rock burst prediction and performance comparison with three machine learning algorithms. IEEE Access 6:30958–30968. https://doi.org/10.1109/ACCESS.2018.2839754
Liu Z, Shao J, Xu W, Meng Y (2013) Prediction of rock burst classification using the technique of cloud models with attribution weight. Nat Hazards 68:549–568. https://doi.org/10.1007/s11069-013-0635-9
Mollahasani A, Alavi AH, Gandomi AH (2011) Empirical modeling of plate load test moduli of soil via gene expression programming. Comput Geotech 38:281–286. https://doi.org/10.1016/J.COMPGEO.2010.11.008
Monjezi M, Baghestani M, Faradonbeh RS et al (2016) Modification and prediction of blast-induced ground vibrations based on both empirical and computational techniques. Eng Comput 32:717–728
Morin MA, Ficarazzo F (2006) Monte Carlo simulation as a tool to predict blasting fragmentation based on the Kuz-Ram model. Comput Geosci 32:352–359. https://doi.org/10.1016/J.CAGEO.2005.06.022
Palei SK, Das SK (2008) Sensitivity analysis of support safety factor for predicting the effects of contributing parameters on roof falls in underground coal mines. Int J Coal Geol 75:241–247. https://doi.org/10.1016/J.COAL.2008.05.004
Palisade Corporation (2021) Guide to using @RISK version 8.0. Risk analysis and simulation add-in for microsoft® excel. New York, Available online: https://www.palisade.com
Pu Y, Apel DB, Lingga B (2018a) Rockburst prediction in kimberlite using decision tree with incomplete data. J Sustain Min 17:158–165. https://doi.org/10.1016/j.jsm.2018.07.004
Pu Y, Apel DB, Wang C, Wilson B (2018b) Evaluation of burst liability in kimberlite using support vector machine. Acta Geophys 66:973–982. https://doi.org/10.1007/s11600-018-0178-2
Pu Y, Apel DB, Xu H (2019) Rockburst prediction in kimberlite with unsupervised learning method and support vector classifier. Tunn Undergr Sp Technol 90:12–18. https://doi.org/10.1016/j.tust.2019.04.019
Saltelli A (2002) Sensitivity analysis for importance assessment. Risk Anal 22:579–590. https://doi.org/10.1111/0272-4332.00040
Sari M (2009) The stochastic assessment of strength and deformability characteristics for a pyroclastic rock mass. Int J Rock Mech Min Sci 46:613–626. https://doi.org/10.1016/j.ijrmms.2008.07.007
Sari M, Selcuk AS, Karpuz C, Duzgun HSB (2009) Stochastic modeling of accident risks associated with an underground coal mine in Turkey. Saf Sci 47:78–87. https://doi.org/10.1016/J.SSCI.2007.12.004
Sari M, Karpuz C, Ayday C (2010) Estimating rock mass properties using Monte Carlo simulation: Ankara andesites. Comput Geosci 36:959–969. https://doi.org/10.1016/j.cageo.2010.02.001
Sari M, Ghasemi E, Ataei M (2014) Stochastic modeling approach for the evaluation of backbreak due to blasting operations in open pit mines. Rock Mech Rock Eng 47:771–783. https://doi.org/10.1007/s00603-013-0438-z
Shi X, Zhou J, Dong L et al (2010) Application of unascertained measurement model to prediction of classification of rockburst intensity. Chinese J Rock Eng 29:2720–2726
Shirani Faradonbeh R, Taheri A (2019) Long-term prediction of rockburst hazard in deep underground openings using three robust data mining techniques. Eng Comput 35:659–675. https://doi.org/10.1007/s00366-018-0624-4
Shirani Faradonbeh R, Jahed Armaghani D, Abd Majid MZ et al (2016) Prediction of ground vibration due to quarry blasting based on gene expression programming: a new model for peak particle velocity prediction. Int J Environ Sci Technol 13:1453–1464. https://doi.org/10.1007/s13762-016-0979-2
Shukla R, Khandelwal M, Kankar PK (2021) Prediction and assessment of rock burst using various meta-heuristic approaches. Mining, Metall Explor 38:1375–1381. https://doi.org/10.1007/s42461-021-00415-w
Song G, Yang S (2018) Probability and reliability analysis of pillar stability in South Africa. Int J Min Sci Technol 28:715–719. https://doi.org/10.1016/J.IJMST.2018.02.004
Ullah B, Kamran M, Rui Y (2022) Predictive modeling of short-term rockburst for the stability of subsurface structures using machine learning approaches: t-SNE, K-Means Clustering and XGBoost. Mathematics 10:449. https://doi.org/10.3390/MATH10030449
Wang S, ming, Zhou J, Li C qi, et al (2021) Rockburst prediction in hard rock mines developing bagging and boosting tree-based ensemble techniques. J Cent South Univ 28:527–542. https://doi.org/10.1007/S11771-021-4619-8
Wu S, Wu Z, Zhang C (2019) Rock burst prediction probability model based on case analysis. Tunn Undergr Sp Technol 93:103069. https://doi.org/10.1016/j.tust.2019.103069
Wu M, Ye Y, Wang Q, Hu N (2022) Development of rockburst research: a comprehensive review. Appl Sci 12:974. https://doi.org/10.3390/APP12030974
Xu C, Liu X, Wang E et al (2018) Rockburst prediction and classification based on the ideal-point method of information theory. Tunn Undergr Sp Technol 81:382–390. https://doi.org/10.1016/j.tust.2018.07.014
Xue Y, Bai C, Qiu D et al (2020) Predicting rockburst with database using particle swarm optimization and extreme learning machine. Tunn Undergr Sp Technol 98:103287. https://doi.org/10.1016/j.tust.2020.103287
Xue Y, Li G, Li Z, Wang P, Gong H, Kong F (2022) Intelligent prediction of rockburst based on Copula-MC oversampling architecture. Bull Eng Geol Environ 81:209. https://doi.org/10.1007/s10064-022-02659-2
Yang Y, Li X, Gao L, Shao X (2013) A new approach for predicting and collaborative evaluating the cutting force in face milling based on gene expression programming. J Netw Comput Appl 36:1540–1550. https://doi.org/10.1016/J.JNCA.2013.02.004
Ye J, Koopialipoor M, Zhou J et al (2021) A novel combination of tree-based modeling and Monte Carlo simulation for assessing risk levels of flyrock induced by mine blasting. Nat Resour Res 30:225–243. https://doi.org/10.1007/s11053-020-09730-3
Yin X, Liu Q, Pan Y et al (2021) Strength of stacking technique of ensemble learning in rockburst prediction with imbalanced data: comparison of eight single and ensemble models. Nat Resour Res 30:1795–1815. https://doi.org/10.1007/s11053-020-09787-0
You K, Park Y, Lee JS (2005) Risk analysis for determination of a tunnel support pattern. Tunn Undergr Sp Technol 20:479–486. https://doi.org/10.1016/J.TUST.2005.03.002
Zhang C, Feng XT, Zhou H et al (2012) Case histories of four extremely intense rockbursts in deep tunnels. Rock Mech Rock Eng 45:275–288. https://doi.org/10.1007/s00603-011-0218-6
Zhao H (2005) Classification of rockburst using support vector machine. Rock Soil Mech 26:642–644
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 50:629–644. https://doi.org/10.1016/j.ssci.2011.08.065
Zhou J, Li X, Mitri HS (2016a) Classification of rockburst in underground projects: comparison of ten supervised learning methods. J Comput Civ Eng 30:04016003. https://doi.org/10.1061/(asce)cp.1943-5487.0000553
Zhou K, Lin Y, Deng H et al (2016b) Prediction of rock burst classification using cloud model with entropy weight. Trans Nonferrous Met Soc China 26:1995–2002. https://doi.org/10.1016/S1003-6326(16)64313-3
Zhou J, Li X, Mitri HS (2018) Evaluation method of rockburst: State-of-the-art literature review. Tunn Undergr Sp Technol 81:632–659. https://doi.org/10.1016/j.tust.2018.08.029
Zhou J, Guo H, Koopialipoor M et al (2020a) Investigating the effective parameters on the risk levels of rockburst phenomena by developing a hybrid heuristic algorithm. Eng Comput 1:3. https://doi.org/10.1007/s00366-019-00908-9
Zhou J, Koopialipoor M, Li E, Armaghani DJ (2020b) Prediction of rockburst risk in underground projects developing a neuro-bee intelligent system. Bull Eng Geol Environ 79:4265–4279. https://doi.org/10.1007/s10064-020-01788-w
Zhu Y, Liu X, Zhou J (2008) Rockburst prediction analysis based on v-SVR algorithm. J China Coal Soc 33:277–281
Zweig MH, Campbell G (1993) Receiver-operating characteristic (ROC) plots: A fundamental evaluation tool in clinical medicine. Clin Chem 39:561–577. https://doi.org/10.1093/clinchem/39.4.561
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Kadkhodaei, M.H., Ghasemi, E. & Sari, M. Stochastic assessment of rockburst potential in underground spaces using Monte Carlo simulation. Environ Earth Sci 81, 447 (2022). https://doi.org/10.1007/s12665-022-10561-z
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DOI: https://doi.org/10.1007/s12665-022-10561-z