True Triaxial Strength and Failure Modes of Cubic Rock Specimens with Unloading the Minor Principal Stress

True triaxial tests have been carried out on granite, sandstone and cement mortar using cubic specimens with the process of unloading the minor principal stress. The strengths and failure modes of the three rock materials are studied in the processes of unloading σ ₃ and loading σ ₁ by the newly developed true triaxial test system under different σ ₂, aiming to study the mechanical responses of the rock in underground excavation at depth. It shows that the rock strength increases with the raising of the intermediate principal stress σ ₂ when σ ₃ is unloaded to zero. The true triaxial strength criterion by the power-law relationship can be used to fit the testing data. The “best-fitting” material parameters A and n (A > 1.4 and n < 1.0) are almost located in the same range as expected by Al-Ajmi and Zimmerman (Int J Rock Mech Min Sci 563 42(3):431–439, 2005). It indicates that the end effect caused by the height-to-width ratio of the cubic specimens will not significantly affect the testing results under true triaxial tests. Both the strength and failure modes of cubic rock specimens under true triaxial unloading condition are affected by the intermediate principal stress. When σ ₂ increases to a critical value for the strong and hard rocks (R4, R5 and R6), the rock failure mode may change from shear to slabbing. However, for medium strong and weak rocks (R3 and R2), even with a relatively high intermediate principal stress, they tend to fail in shear after a large amount of plastic deformation. The maximum extension strain criterion Stacey (Int J Rock Mech Min Sci Geomech Abstr 651 18(6):469–474, 1981) can be used to explain the change of failure mode from shear to slabbing for strong and hard rocks under true triaxial unloading test condition.