Investigation on the Indeterminate Information of Rock Joint Roughness through a Neutrosophic Number Approach

To better estimate the rock joint shear strength, accurately determining the rock joint roughness coefficient (JRC) is the first step faced by researchers and engineers. However, there are incomplete, imprecise, and indeterminate problems during the process of calculating the JRC. This paper proposed to investigate the indeterminate information of rock joint roughness through a neutrosophic number approach and, based on this information, reported a method to capture the incomplete, uncertain, and imprecise information of the JRC in uncertain environments. The uncertainties in the JRC determination were investigated by the regression correlations based on commonly used statistical parameters, which demonstrated the drawbacks of traditional JRC regression correlations in handling the indeterminate information of the JRC. Moreover, the commonly used statistical parameters cannot reflect the roughness contribution differences of the asperities with various scales, which induces additional indeterminate information. A method based on the neutrosophic number (NN) and spectral analysis was proposed to capture the indeterminate information of the JRC. The proposed method was then applied to determine the JRC values for sandstone joint samples collected from a rock landslide. The comparison between the JRC results obtained by the proposed method and experimental results validated the effectiveness of the NN. Additionally, comparisons made between the spectral analysis and common statistical parameters based on the NN also demonstrated the advantage of spectral analysis. Thus, the NN and spectral analysis combined can effectively handle the indeterminate information in the rock joint roughness.