Strain Energy Density Evolution in Sandstone Under True Triaxial Compression at Different Loading Rates

To investigate the energy evolution laws of sandstone under true triaxial compression at various loading rates, a self-developed true triaxial disturbance unloading rock testing system was employed to conduct true triaxial compression tests. A true triaxial stress-balanced unloading test was designed based on the characteristics of the true triaxial stress–strain curve. The strain energy density evolution laws under true triaxial compression and their linear relationships were analyzed. Additionally, the influence of loading rates on energy evolution during true triaxial compression was further investigated. Our experiments reveal that as the σ₁ increases, elastic strain in the σ₂ and σ₃ directions decreases, while residual strain progressively increases, with the reduction in elastic strain surpassing the increase in residual strain. Moreover, during σ₁ loading, the elastic strain energy density (u^e) in the σ₂ and σ₃ directions decreases while the dissipated strain energy density (u^d) increases, with the u^e reduction exceeding the u^d increase. The evolution of u^d and u^e in the three principal stress directions and the overall strain energy density of sandstone followed a linear energy storage law. On the basis of this law and the true triaxial stress-balanced unloading test, a new method for calculating the true triaxial energy was proposed. We also found that the σ₁ loading rate significantly affects both the ratio of u^e and u^d to input strain energy density (u) and the energy storage limit of sandstone, the energy storage limit increases with higher loading rates. Based on the above research results, the elastic energy index of rockburst prediction index is discussed.