Abstract
In rock mechanics, the study of shear strength on the structural surface is crucial to evaluating the stability of engineering rock mass. In order to determine the shear strength, a key parameter is the joint roughness coefficient (JRC). To express and analyze JRC values, Ye et al. have proposed JRC neutrosophic numbers (JRC-NNs) and fitting functions of JRC-NNs, which are obtained by the classical statistics and curve fitting in the current method. Although the JRC-NNs and JRC-NN functions contain much more information (partial determinate and partial indeterminate information) than the crisp JRC values and functions in classical methods, the JRC functions and the JRC-NN functions may also lose some useful information in the fitting process and result in the function distortion of JRC values. Sometimes, some complex fitting functions may also result in the difficulty of their expressions and analyses in actual applications. To solve these issues, we can combine the neutrosophic numbers with neutrosophic statistics to realize the neutrosophic statistical analysis of JRC-NNs for easily analyzing the characteristics (scale effect and anisotropy) of JRC values. In this study, by means of the neutrosophic average values and standard deviations of JRC-NNs, rather than fitting functions, we directly analyze the scale effect and anisotropy characteristics of JRC values based on an actual case. The analysis results of the case demonstrate the feasibility and effectiveness of the proposed neutrosophic statistical analysis of JRC-NNs and can overcome the insufficiencies of the classical statistics and fitting functions. The main advantages of this study are that the proposed neutrosophic statistical analysis method not only avoids information loss but also shows its simplicity and effectiveness in the characteristic analysis of JRC.
Highlights
The engineering experience shows that rock mass may deform and destroy along the weak structural surfaces
We originally propose a neutrosophic statistical method of joint roughness coefficient (JRC)-neutrosophic numbers (NNs) to indirectly analyze the scale effect and anisotropy of JRC values by means of the neutrosophic average values and standard deviations of JRC neutrosophic numbers (JRC-NNs) (JRC values), respectively, to overcome the insufficiencies of existing analysis methods
According to the JRC data obtained in an actual case and the expressions and operations of JRC-NNs, we provided a new neutrosophic statistical analysis method based on the neutrosophic statistical algorithm of the neutrosophic average values and the standard deviations of JRC-NNs in different columns and different rows
Summary
The engineering experience shows that rock mass may deform and destroy along the weak structural surfaces. To quantify the anisotropic roughness of joint surfaces effectively, a variogram function and a new index were proposed by Chen et al [4] based on the digital image processing technique, and they studied the scale effect by calculating the JRC values of different sample lengths [5] All of these traditional methods do not consider the uncertainties of JRC values in real rock engineering practice. In. Section 5, the neutrosophic average values and standard deviations of the 10 JRC-NNs of different sample lengths in each measurement orientations are given based on the proposed neutrosophic statistical algorithm and used for the anisotropic analysis of JRC values.
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