Incorporation of uncertainty in estimating the rock mass uniaxial strength using a fuzzy inference system

Abstract

Due to its complex nature and inherent uncertainty, it is very hard to directly measure the uniaxial strength of jointed rock masses. In rock mechanics, it is a necessity to employ empirical equations and numerical methods for the estimation of rock mass uniaxial strength. In addition to the existing empirical equations and numerical methods, it is essential to pursuit approaches to incorporate uncertainty in estimating rock mass uniaxial strength. One of the promising techniques pertinent to such situations is the fuzzy inference system (FIS). In the application of FIS, it is expected that the problem or system under investigation should be uncertain and fuzzy, and calculations are drawn mostly from judgment and experience, rather than mathematical expressions. This study proposes a new method of estimating the rock mass uniaxial strength using fuzzy sets theory. For this purpose, three dominant elements essential for the determination of rock mass uniaxial strength; i.e., intact rock uniaxial strength, block size, and joint surface condition, were evaluated as fuzzy variables in the analysis involving the assignment of proper membership functions. A logical and systematic combination of three input variables was employed under a Mamdani rule-based FIS environment, which explicitly takes into account the expert knowledge using built lookup charts. To check the accuracy of the FIS model estimates, an extensive data set was compiled from the published sources. This data set used in the analysis covered a wide range of rock mass types in typical rock engineering projects. It was seen that the uniaxial strength values estimated by the proposed FIS model were mostly in fair agreement (R2 = 0.77) with those estimated by well-known empirical equations.