Expression and Analysis of Scale Effect and Anisotropy of Joint Roughness Coefficient Values Using Confidence Neutrosophic Number Cubic Values

Abstract

The JRC data collected from a rock mass joint surface difficultly obtain enough large-scale
JRC sample data, but small-scale JRC sample data, which usually contain indeterminate and
incomplete information due to the limitation of the measurement environment, measurement
technology, and other factors. In this case, the existing representation and analysis methods of the
JRC sample data almost all lack the measures of confidence levels in the sample data analysis. In
this paper, we propose the concept and expression method of confidence neutrosophic number
cubic values (CNNCVs), and then establish CNNCVs of joint roughness coefficient (JRC) (JRCCNNCVs) from the limited/small-scale JRC sample data subject to the normal distribution and
confidence level of the JRC sample data to analyze the scale effect and anisotropy of JRC values. In
the analysis process, the JRC-CNNCVs are first conversed from the JRC sample data (multi-valued
sets) in view of their distribution characteristics and confidence level. Next, JRC-CNNCVs are
applied to analyze the scale effect and anisotropy of the JRC values by an actual case, and then the
effectiveness and rationality of the proposed expression and analysis method using JRC-CNNCVs
are proved by the actual case in a JRC multi-valued environment. From a perspective of probabilistic
estimation, the established expression and analysis method makes the JRC expression and analysis
more reasonable and reliable under the condition of small-scale sample data.