A new method for classifying rock mass quality based on MCS and TOPSIS

  • L. Z. Wu
  • S. H. Li
  • M. ZhangEmail author
  • L. M. Zhang
Original Article


Rock mass quality classification is essential in rock engineering. In practical engineering the parameters of rock mass vary with sampling disturbance and testing instruments, however obey a certain distribution. In other words, the classification of rock mass quality includes an uncertainty caused by the randomness of the parameters of the rock mass in geological formations. Traditional rock mass classification methods ignore the effect of this parameter uncertainty. In this paper, we propose a new method for evaluating rock mass quality considering the effect of parameter uncertainty through a rigorous reliability analysis. The weights of the classification system indexes are obtained using the game theory, combined with the technique for order preference by similarity to ideal solution (TOPSIS) in determining the limit-state function for reliability analysis. Stochastic uncertainty analysis is performed based on Monte Carlo simulation (MCS) and the limit-state function established by TOPSIS. The rock mass quality classification grade is obtained based on the probability calculation. The TOPSIS model with accurate game theory weighting is evaluated using 25 sets of samples. The results confirmed the reliability of the model. In a case study of rock mass surrounding a cavern, we verified the proposed rock quality classification method using certainty and uncertainty methods in MATLAB. The results demonstrate that the MCS–TOPSIS coupled model is efficient and accurate for classifying rock mass quality, and this approach is easy to implement.


Monte Carlo simulation Technique for order preference by similarity to ideal solution Uncertainty Rock mass quality classification 



The research reported in this paper was supported by the National Key Research and Development Program of China (no. 2018YFC1504702), the National Natural Science Foundation of China (no. 41672282, 41772334), State Key Laboratory of Geohazard Prevention and Geoenvironment Prevention Independent Research Project (no. SKLGP2017Z003), the Youth Science and Technology Innovation Team in Sichuan Province (no. 2015TD0030), and the first author thanks the Innovative Team of Chengdu University of Technology.

Compliance with ethical standards

Conflict of interest

The authors of this manuscript declare that there is no conflict of interest regarding the publication of this manuscript.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Geohazard Prevention and Geoenvironment ProtectionChengdu University of TechnologyChengduPeople’s Republic of China
  2. 2.Faculty of EngineeringChina University of GeosciencesWuhanPeople’s Republic of China
  3. 3.Department of Civil and Environmental EngineeringThe Hong Kong University of Science and TechnologyKowloonHong Kong

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