Elasticity and Characteristic Stress Thresholds of Shale under Deep In Situ Geological Conditions

The mechanical properties of shale are generally influenced by in situ geological conditions. However, the understanding of the effects of in situ geological conditions on the mechanical properties of shale is still immature. To address this problem, this paper provides insight into the elasticity and characteristic stress thresholds (i.e., the crack closure stress σ_cc, crack initiation stress σ_ci, and crack damage stress σ_cd) of shales with differently oriented bedding planes under deep in situ geological conditions. To accurately determine the elastic parameters and crack closure and initiation thresholds, a new method-i.e., the bidirectional iterative approximation (BIA) method-which iteratively approaches the upper and lower limit stresses of the linear elastic stress-strain regime, was proposed. Several triaxial compression experiments were performed on Longmaxi shale samples under coupled in situ stress and temperature conditions reflecting depths of 2000 and 4000 m in the study area. The results showed that the peak deviatoric stress (σ_p) of shale samples with the same bedding plane orientation increases as depth increases from 2000 m to 4000 m. In addition, the elastic modulus of the shale studied is more influenced by bedding plane orientation than by burial depth. However, the Poisson's ratios of the studied shale samples are very similar, indicating that for the studied depth conditions, the Poisson's ratio is not influenced by the geological conditions and bedding plane orientation. For the shale samples with the two typical bedding plane orientations tested (i.e., perpendicular and parallel to the axial loading direction) under 2000 and 4000 m geological conditions, the ratio of crack closure stress to peak deviatoric stress (σ_cc/σ_p) ranges from 24.83% to 25.16%, and the ratio of crack initiation stress to peak deviatoric stress (σ_ci/σ_p) ranges from 34.78% to 38.23%, indicating that the σ_cc/σ_p and σ_ci/σ_p ratios do not change much, and are less affected by the bedding plane orientation and depth conditions studied. Furthermore, as the in situ depth increases from 2000 m to 4000 m, the increase in σ_cd is significantly greater than that of σ_cc and σ_ci, indicating that σ_cd is more sensitive to changes in depth, and that the increase in depth has an obvious inhibitory effect on crack extension. The expected experimental results will provide the background for further constitutive modeling and numerical analysis of the shale gas reservoirs.