Evolution law and calculation model of shale permeability under true triaxial constant volumetric stress conditions

In the true stress environment of deep underground formations, rock masses are subjected to triaxial stresses, and the variations in principal stresses play a decisive role in their mechanical behavior. Therefore, we conducted experiments under true triaxial conditions with constant volumetric stress, altering the magnitudes of two principal stresses – the intermediate principal stress (σ2) and either the maximum or minimum principal stress (σ1 or σ3) – to investigate the evolution of shale permeability (k). The results demonstrate that: (1) When σ2 is perpendicular to bedding, k decreases with increasing σ2, indicating a dominant compaction effect. (2) When σ2 is parallel to bedding, k increases with increasing σ2, reflecting fracture propagation. (3) The range of permeability variation is greater under constant σ1 than under constant σ3 because elevated deviatoric stress intensifies deformation anisotropy. (4)A strain differentiation index (Cₛ) was introduced to quantify strain anisotropy, showing that higher Cs values correspond to greater permeability sensitivity. Based on these findings, a permeability model under true triaxial constant-volumetric stress was established, incorporating the effects of pore compaction, fracture propagation, and structural differentiation. The model exhibits excellent agreement with experimental data (R2 > 0.98). The conclusions of this study provide critical insights for shale gas extraction.