<p>Unlike metals or synthetic materials, most rocks exhibit inherent discontinuities, such as fractures, joints, and crystalline structures. At specific scales, these features manifest as fluctuations in physical quantities and mechanical responses. Most classical rock mechanics models are derived from a continuum framework, which assumes that the material remains free of cracking or overlapping during deformation. Mathematically, this ensures the uniqueness of displacement solutions, representing compatible deformation that adheres to the laws of motion in Euclidean space. While theoretical research has addressed incompatible deformation in rock—providing partial differential equations and corresponding analytical solutions—these theories are primarily used to explain discontinuous phenomena (e.g., zonal failure) in underground engineering. However, such explanations remain largely speculative due to a lack of direct observation regarding microscopic fluctuations. In this study, a Digital Image Correlation (DIC) method was employed to perform visualized meso-scale creep tests on composite rock salt using a self-developed true triaxial visible creep apparatus. An incompatible deformation—characterized by one-dimensional strain fluctuations rather than a monotonic pattern—was directly observed. The analysis is then confined to Riemannian Space, which differs from Euclidean Space only by a non-zero curvature tensor. A new set of partial differential equations is developed, providing an analytical solution for a simplified one-dimensional rock mechanics problem that describes the intermediate state between a continuum and a discrete system. This study theoretically demonstrates that strain fluctuations originate from trigonometric terms within the solution. Through fitting analysis, it was found that the theoretical solution exhibits a high degree of agreement with the experimental data, thereby validating the reliability of the proposed framework.</p>