Risk assessment in a rock slope stability analysis using a Mamdani fuzzy controller

Matos, Yago Machado Pereira de; Dantas Neto, Silvrano Adonias; Barreto, Guilherme de Alencar

doi:10.1590/0370-44672022760061

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Civil Engineering • REM, Int. Eng. J. 76 (4) • Oct-Dec 2023 • https://doi.org/10.1590/0370-44672022760061 copy

Risk assessment in a rock slope stability analysis using a Mamdani fuzzy controller

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

The shearing behavior of discontinuities is one of the factors with major influence on rock slope stability analysis, which is predictable when adopting different analytical models. However, these methodologies, generally of a purely deterministic nature, do not allow an assessment of the influence of the variability of the input parameters of the models on the shear behavior of unfilled rock discontinuities and, consequently, on the risk involved in the rock slope stability analyses. The purpose of this article is to present a methodology for rock slope risk assessment based on the development of a model to predict the shear behavior of unfilled rock discontinuity considering the variability of its input parameters, using a Mamdani fuzzy controller. The input variables of the model are the boundary normal stiffness and initial normal stress acting on the discontinuity, its roughness, the uniaxial compressive strength, the basic angle of friction of the intact rock and the shear displacement imposed on the discontinuity. The model outputs are the membership functions for the shear strength and dilation of the unfilled rock discontinuity, and from which the membership function can be defined for the factor of safety of the rock slope considering the failure mechanism governed by discontinuity. The results reveal the use and importance of fuzzy logic and fuzzy number operations in assessing the risk in rock slopes and may be used even in situations where there are major uncertainties on the existing information of the characteristics of the unfilled discontinuities.

Keywords:
unfilled joints; rock slope stability analysis; risk assessment; Mamdani

Authors	Methodology	Main conclusions
*Dantas Neto et al.* (2017)**DANTAS NETO, S. A.; INDRARATNA, B.; OLIVEIRA, D. A. F.; ASSIS, A. P. Modelling the shear behaviour of clean rock discontinuities using artificial neural networks. Rock Mech Rock Eng, v. 50, p. 1817-1831, 2017.	Proposed a model to predict the shear behaviour of clean rock joints developed by using a multilayer perceptron. A rock slope stability problem was also used as an example for applying the model in practice.	The developed neural model was able to express the influence of the input variables in the shearing behavior of joints and may be an alternative to the existing analytical models which sometimes require certain parameters obtained from large-scale laboratory tests which are not always available.
*Matos et al.* (2019aMATOS, Y. M. P.; DANTAS NETO, S. A.; BARRETO, G. A. A Takagi-Sugeno fuzzy model for predicting the clean rock joints shear strength. REM: Int. Eng. J., v. 72, n. 2, p. 193-198, 2019a., 2019b**MATOS, Y. M. P.; DANTAS NETO, S. A.; BARRETO, G. A. Predicting the shear strength of unfilled rock joints with the first-order Takagi-Sugeno fuzzy approach. Soils and Rocks, v. 42, n. 1, p. 21-29, 2019b.)	Developed Takagi-Sugeno fuzzy systems for predicting shear strength of clean rock joints incorporating uncertainties in the variables that govern their shear behavior.	Despite the proposed models present the advantage of considering the uncertainties of their input variables, their responses are still deterministic.
*Azarafza et al.* (2020)**AZARAFZA, M.; AKGÜN, H.; FEIZI-DERAKHSHI, M. R.; AZARAFZA, M.; RAHNAMARAD, J.; DERAKHSHANI, R. Discontinuous rock slope stability analysis under blocky structural sliding by fuzzy key-block analysis method. Heliyon, v. 6, n. 5, e03907, 2020.	Presented a fuzzy logical decision-making algorithm based on block theory to determine discontinuous rock slope reliability by classifying the slope into expressive classes such as stable or unstable.	The proposed algorithm is relatively simple, requires low computational cost, has excellent compatibility, provides intuitive and experimental satisfaction and can be used by students and less experienced people.
*Ahangari Nanehkaran et al.* (2022)**AHANGARI NANEHKARAN, Y.; PUSATLI, T.; CHENGYONG, J.; CHEN, J.; CEMILOGLU, A.; AZARAFZA, M.; DERAKHSHANI, R. Application of machine learning techniques for the estimation of the safety factor in slope stability analysis. Water, v. 14, n. 22, 37-43, 2022.	Investigated the performance of multilayer perceptron, support vector machines, k-nearest neighbors, decision tree and random forest models to predict the soil slope safety factors (FS).	Slope height, total slope angle, dry density, cohesion and internal friction angle were considered to predict the FS for 70 slopes. Among the five machine learning models, the multilayer perceptron was found to be the most reliable for predicting FS.
*Nanehkaran et al.* (2023)**NANEHKARAN, Y. A.; LICAI, Z.; CHENGYONG, J.; CHEN, J.; ANWAR, S.; AZARAFZA, M.; DERAKHSHANI, R. Comparative analysis for slope stability by using machine learning methods. Applied Sciences, v. 13, n. 3, 1555, 2023.	Provided a comparative analysis between multilayer perceptron, decision tree, support vector machines and random forest learning algorithms to predict soil slope safety factors, using a dataset of 100 records of slopes.	The paper tried to fill the gap in traditional analysis procedures based on advanced methods in slope stability assessments. The multilayer perceptron achieved the highest accuracy and precision in predicting the FS.

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