Rheology has extremely significant influence on the long-term deformation and stability of engineering rock mass. Current experimental research on unloading rheology only considers the stress path under unloading confining pressure with the constant axial stress

however it is different from the process of stress adjustment in surrounding rock during tunnel excavating. Stepwise unloading rheological tests are conducted on sandy mudstone samples which are under unloading confining pressure with the axial compression or with the constant axial stress. The results show that the rheological deformation trends of rock samples under both unloading confining pressure are generally consistent. At the same initial confining pressure

the failure confining pressure under axial compression and the deviatoric stress are relatively higher than that under constant axial stress

but the ratio of long-term strength to failure stress is opposite. When the confining pressure unloads reach up to the point where the rock sample approaches failure

the growth rate of rheological strain under axial compression obviously becomes faster than that under constant axial stress

and the failure occurs more suddenly. The failure modes of rock samples under constant axial stress usually appear as one complete shear failure plane. By contrast

the failure modes of rock samples under axial compression are more complicated with a certain amount of secondary shear cracks and tension cracks

in addition to the controlled shear failure plane. Moreover

the secondary cracks increase with the increase of initial confining pressure. Therefore

the unloading confining pressure with the constant axial stress seems difficultly satisfy the requirement of engineering projects undergone a long-term deformation and stability of surrounding rock. The stress paths of tests should be conducted in more detail to simulate the actual stress change process of engineering rock mass. The results provide insights into the research on long-term deformation and stability of underground surrounding rock.