Document Type: Original Research Paper

Author

Department of Earth Sciences Engineering, Arak University of Technology, Arak, Iran

Abstract

The uniaxial compressive strength of weak rocks (UCSWR) is among the essential parameters involved for the design of underground excavations, surface and underground mines, foundations in/on rock masses, and oil wells as an input factor of some analytical and empirical methods such as RMR and RMI. The direct standard approaches are difficult, expensive, and time-consuming, especially with highly fractured, highly porous, weak, and homogeneous rocks. Numerous endeavors have been made to develop indirect approaches of predicting UCSWR. In this research work, a new intelligence method, namely relevance vector regression (RVR), improved by the cuckoo search (CS) and harmony search (HS) algorithms is introduced to forecast UCSWR. The HS and CS algorithms are combined with RVR to determine the optimal values for the RVR controlling factors. The optimized models (RVR-HS and RVR-CS) are employed to the available data given in the open-source literature. In these models, the bulk density, Brazilian tensile strength test, point load index test, and ultrasonic test are used as the inputs, while UCSWR is the output parameter. The performances of the suggested predictive models are tested according to two performance indices, i.e. mean square error and determination coefficient. The results obtained show that RVR optimized by the HS model can be successfully utilized for estimation of UCSWR with R2 = 0.9903 and MSE = 0.0031203.

Keywords

[1]. Singh, R., Kainthola, A. and Singh, T. (2012). Estimation of elastic constant of rocks using an ANFIS approach. Appl Soft Comput. 12 (1): 40-45.

[2]. Armaghani, D.J., Mohamad, E.T., Momeni, E. and Narayanasamy, M.S. (2015). An adaptive neuro-fuzzy inference system for predicting unconfined compressive strength and Young’s modulus: a study on Main Range granite. Bull Eng Geology Envir. 74 (4): 1301-1319.

[3]. Kahraman, S., Fener, M. and Kozman, E. (2012). Predicting the compressive and tensile strength of rocks from indentation hardness index. J South Afr Inst Min Metall. 112 (5): 331-339.

[4]. Ghose A Empirical strength indices of Indian coals-an investigation. In: The 27th US Symposium on Rock Mechanics (USRMS), 1986. American Rock Mechanics Association.

[5]. Meulenkamp, F. and Grima, M.A. (1999). Application of neural networks for the prediction of the unconfined compressive strength (UCS) from Equotip hardness. Int J Rock Mech Min Sci. 36 (1): 29-39.

[6]. Singh, V., Singh, D. and Singh, T. (2001). Prediction of strength properties of some schistose rocks from petrographic properties using artificial neural networks. Int J Rock Mech Min Sci. 38 (2): 269-284.

[7]. Gokceoglu, C. and Zorlu, K. (2004). A fuzzy model to predict the uniaxial compressive strength and the modulus of elasticity of a problematic rock. Eng Appl Artif Intel. 17 (1): 61-72. doi:https://doi.org/10.1016/j. engappai.2003.11.006.

[8]. Sonmez, H., Tuncay, E. and Gokceoglu, C. (2004). Models to predict the uniaxial compressive strength and the modulus of elasticity for Ankara Agglomerate. Int J Rock Mech Min Sci. 41 (5): 717-729.

[9]. Fener, M., Kahraman, S., Bilgil, A. and Gunaydin, O. (2005). A comparative evaluation of indirect methods to estimate the compressive strength of rocks. Rock Mech Rock Eng. 38 (4): 329-343.

[10]. Kılıç, A. and Teymen, A. (2008). Determination of mechanical properties of rocks using simple methods. Bull Eng Geology Envir. 67 (2): 237-244.

[11]. Dehghan, S., Sattari, G., Chelgani, S.C. and Aliabadi, M. (2010). Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using regression and artificial neural networks. Min Sci Tech. 20 (1): 41-46.

[12]. Cevik, A., Sezer, E.A., Cabalar, A.F. and Gokceoglu, C. (2011). Modeling of the uniaxial compressive strength of some clay-bearing rocks using neural network. Appl Soft Comput. 11 (2): 2587-2594.

[13]. Yagiz, S., Sezer, E. and Gokceoglu, C. (2012). Artificial neural networks and nonlinear regression techniques to assess the influence of slake durability cycles on the prediction of uniaxial compressive strength and modulus of elasticity for carbonate rocks. In J Numer Anal Met Geomech. 36 (14): 1636-1650.

[14]. Minaeian, B. and Ahangari, K. (2013). Estimation of uniaxial compressive strength based on P-wave and Schmidt hammer rebound using statistical method. Arab J Geosci. 6 (6): 1925-1931.

[15]. Mishra, D. and Basu, A. (2013). Estimation of uniaxial compressive strength of rock materials by index tests using regression analysis and fuzzy inference system. Eng Geol. 160: 54-68.

[16]. Yesiloglu-Gultekin, N., Gokceoglu, C. and Sezer, E.A. (2013). Prediction of uniaxial compressive strength of granitic rocks by various nonlinear tools and comparison of their performances. Int J Rock Mech Min Sci. 62: 113-122.

[17]. Aboutaleb, S., Behnia, M., Bagherpour, R. and Bluekian, B. (2018). Using non-destructive tests for estimating uniaxial compressive strength and static Young’s modulus of carbonate rocks via some modeling techniques. Bull Eng Geology Envir. 77 (4): 1717-1728. doi:10.1007/s10064-017-1043-2.

[18]. Tipping, M.E. (2001). Sparse Bayesian learning and the relevance vector machine. J machine learn research. 1 (Jun): 211-244.

[19]. Nisha, M.G., Pillai, G. (2013). Nonlinear model predictive control with relevance vector regression and particle swarm optimization. J Control Theory App. 11 (4): 563-569.

[20]. Qin, Y. and Wang, F. (2011). Tunneling-induced ground surface settlement prediction based on relevance vector machine. In: 2011 International Conference on Electric Technology and Civil Engineering (ICETCE). IEEE, pp. 925-927.

[21]. Gholami, R., Moradzadeh, A., Maleki, S., Amiri, S. and Hanachi, J. (2014). Applications of artificial intelligence methods in prediction of permeability in hydrocarbon reservoirs. J Pet Sci Eng. 122: 643-656.

[22]. Lou, J., Jiang, Y., Shen, Q. and Wang, R. (2018). Failure prediction by relevance vector regression with improved quantum-inspired gravitational search. Journal of Network and Computer Applications. 103: 171-177.

[23]. Tipping ME The relevance vector machine. In: Advances in neural information processing systems. 2000. pp 652-658.

[24]. Geem, Z.W. (2009). Music-inspired harmony search algorithm: theory and applications, vol 191. Springer Verlag,

[25]. Geem, Z.W., Kim, J.H. and Loganathan, G. (2001). A new heuristic optimization algorithm: harmony search. Simulation. 76 (2): 60-68.

[26]. Moh’d Alia, O. and Mandava, R. (2011). The variants of the harmony search algorithm: an overview. Artificial Intelligence Review. 36 (1): 49-68.

[27]. Yuan, X., Zhao, J., Yang, Y. and Wang, Y. (2014). Hybrid parallel chaos optimization algorithm with harmony search algorithm. Appl Soft Comput. 17: 12-22.

[28]. Jaberipour, M. and Khorram, E. (2010). Two improved harmony search algorithms for solving engineering optimization problems. Communications in Nonlinear Science and Numerical Simulation 15 (11): 3316-3331

[29]. Rajabioun, R. (2011). Cuckoo optimization algorithm. Appl Soft Comput. 11 (8): 5508-5518.

[30]. Yang, X.S. and Deb, S. (2010). Engineering optimisation by cuckoo search. Int J Math Model Num Optim. 1 (4): 330-343.

[31]. Valian, E., Mohanna, S. and Tavakoli, S. (2011). Improved cuckoo search algorithm for feedforward neural network training. International Journal of Artificial Intelligence & Applications. 2 (3): 36-43.

[32]. Yildiz, A.R. (2013). Cuckoo search algorithm for the selection of optimal machining parameters in milling operations. Int J Adv Manuf Tech. 64 (1-4): 55-61.

[33]. Mohamad, E.T., Armaghani, D.J., Momeni, E. and Abad, S.V.A.N.K. (2015). Prediction of the unconfined compressive strength of soft rocks: a PSO-based ANN approach. Bull Eng Geology Envir. 74 (3): 745-757.

[34]. Fattahi, H. (2016). Application of improved support vector regression model for prediction of deformation modulus of a rock mass. Eng Comput. 32 (4): 567-580.

[35]. Fattahi H. and Moradi, A. (2017). Risk Assessment and Estimation of TBM Penetration Rate Using RES-Based Model. Geotech Geol Eng. 35 (1): 365-376.

[36]. Fattahi, H. (2016). Adaptive neuro fuzzy inference system based on fuzzy c–means clustering algorithm, a technique for estimation of TBM penetration rate. Int J Optim Civil Eng. 6 (2): 159-171.

[37]. Fattahi, H. (2017). Risk assessment and prediction of safety factor for circular failure slope using rock engineering systems. Environ Earth Sci. 76 (5): 224.

[38]. Fattahi, H. (2017). Applying soft computing methods to predict the uniaxial compressive strength of rocks from schmidt hammer rebound values. Computat Geosci. 21 (4): 665-681.

[39]. Fattahi, H. and Moradi, A. (2018). A new approach for estimation of the rock mass deformation modulus: a rock engineering systems-based model. Bull Eng Geology Envir. 77 (1): 363-374.

[40]. Babanouri, N. and Fattahi, H. (2018). Constitutive modeling of rock fractures by improved support vector regression. Environ Earth Sci. 77 (6): 243.