In nature, the mechanical properties of geological bodies are very complex, and their various mechanical parameters are vague, incomplete, imprecise, and indeterminate. However, we cannot express them by the crisp values in classical probability and statistics. In geotechnical engineering, we need to try our best to approximate exact values in indeterminate environments because determining the joint roughness coefficient (JRC) effectively is a key parameter in the shear strength between rock joint surfaces. In this original study, we first propose neutrosophic interval probability (NIP) and define the confidence degree based on the cosine measure between NIP and the ideal NIP. Then, we propose a new neutrosophic interval statistical number (NISN) by combining the neutrosophic number with the confidence degree to express indeterminate statistical information. Finally, we apply NISNs to express JRC under indeterminate (imprecise, incomplete, and uncertain, etc.) environments. By an actual case, the results demonstrate that NISNs are suitable and effective for JRC expressions and have the objective advantage.