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The focus of the present study is to explain the stair-step brittle deformation evolutionary pattern of the landslide and reveal the corresponding internal physical mechanism. Based on the concept of high strength geological body (HSGB), similar to rock bridges in the intermittence jointed rock masses, a conceptual geological model and the corresponding mechanical model are successively outlined. Through reanalysing typical stair-step displacement records of a wedge rockslide, it was found that the HSGB model can reasonably explain the stair-step deformation feature and reveal its internal essence. Finally, a displacement criterion is derived through combining the two-dimensional renormalization group model with the shear creep constitutive model. By means of this displacement criterion, one can quantitatively describe the displacement ratio between the onset of the accelerating creep and brittle rupture of HSGB. In order to make the reader understand this displacement criterion better, a detailed application process is demonstrated through a case study. To some extent, the present study has shed light on the failure prediction of the HSGB-type landslide, whose stability is mainly controlled by HSGB.