Laboratory experiments subjecting sandstone to true-triaxial cyclic loading have demonstrated that energy evolution and rock damage mechanisms depend fundamentally on the specific principal-stress path applied. Researchers observed that cyclic loading and unloading along an individual principal-stress direction consistently induced strain variations across all three spatial directions, establishing that three-dimensional deformation coupling governs the mechanical response. The investigation revealed that varying the cycling path among the maximum, intermediate, and minimum principal-stress directions produces pronounced differences in how energy is stored, dissipated, and transformed into physical damage within the rock matrix.

The investigation was designed to clarify the energy evolution and damage mechanisms occurring in the surrounding rock of deep roadways when subjected to complex excavation-induced disturbances. To replicate these multi-axial subsurface conditions, the research team conducted a comprehensive series of laboratory mechanical tests on sandstone specimens. The testing program integrated conventional true-triaxial compression tests, graded loading and unloading tests directed along different principal-stress axes, and single-cycle loading and unloading tests, allowing the authors to isolate the influence of directional stress changes on the material.

All experimental procedures were executed utilizing an in-house-developed TAWZ-5000/3000 computer-controlled true-triaxial rock testing system.

To quantitatively evaluate the internal mechanical processes, the researchers developed an energy-calculation framework that directly incorporates deformation and work contributions across all three principal-stress directions. This analytical framework was formulated specifically to account for the three-dimensional strain coupling observed during testing, ensuring that multi-axial deformation is accurately reflected in the calculated energy partitions. Alongside this framework, damage evolution under the contrasting principal-stress paths was systematically evaluated through a damage variable based on dissipated energy, accompanied by continuous acoustic emission monitoring during deformation.

The resulting stress-strain curves demonstrated the formation of distinct hysteresis loops during cyclic loading and unloading. The areas enclosed by these hysteresis loops expanded nonlinearly as the loading-unloading stress levels increased, reflecting a progressively larger amount of energy dissipated during each successive loading stage. Crucially, loading or unloading applied along a single principal-stress direction produced measurable strain responses not only along the active axis but simultaneously along the remaining two orthogonal directions, confirming the presence of strong three-dimensional deformation coupling throughout the test series.

Systematic comparisons between the stress paths revealed contrasting internal energy partitions depending on which principal-stress component underwent cycling. Under cyclic loading of the maximum principal stress, designated as sigma one, the dissipated-energy ratio rose progressively as stress levels increased. This persistent increase in the dissipated-energy ratio reflected a sustained accumulation of irreversible deformation and internal damage driven by higher maximum principal stresses. In sharp contrast, cycling the intermediate principal stress, designated as sigma two, led to a progressive increase in the elastic-energy ratio while the dissipated-energy ratio remained comparatively low, demonstrating that the sandstone retains a substantial capacity for elastic energy storage under intermediate-principal-stress cycling.

A markedly different failure pattern emerged during cyclic loading and unloading of the minimum principal stress, designated as sigma three. Under this stress path, dissipated energy increased at an accelerated rate rather than in a steady progression. Following the completion of testing, specimens subjected to minimum-principal-stress cycling exhibited the most pronounced macroscopic cracking observed across the entire experimental program.

These experimental observations provide direct empirical evidence regarding path-dependent energy evolution and structural damage mechanisms in deep rock subjected to excavation disturbances. By tracking the distinct behaviors of sandstone under individual principal-stress paths, the study provides technical insights into how directional stress changes and reduced confinement dictate rock degradation. The authors conclude that these findings contribute directly to improving stability assessment methodologies and designing effective surrounding rock control measures in deep underground roadways.

Subject of Research: True-triaxial energy evolution and damage mechanisms in sandstone

Article Title: Energy evolution and damage mechanisms of sandstone under true triaxial loading and unloading along different principal-stress paths

Article References: Zhang, Q., Zhao, G., Meng, X., Sun, J., Liu, C., Xu, W., Liu, Z., Gu, Q., & Wang, Y. (2026). Energy evolution and damage mechanisms of sandstone under true triaxial loading and unloading along different principal-stress paths. Geomechanics and Geophysics for Geo-Energy and Geo-Resources. https://doi.org/10.1007/s40948-026-01271-y

Image Credits: AI Generated

DOI: 10.1007/s40948-026-01271-y

Keywords: sandstone, true triaxial testing, energy evolution, rock damage mechanisms, principal stress paths, acoustic emission, three-dimensional strain coupling, deep roadway stability, Energy, evolution, damage, mechanisms