Mechanical characteristics of single cracked limestone in compression-shear fracture under hydro-mechanical coupling

•An unique double-stress peak-type nature of the deviatoric stress–strain curve of the single-cracked limestone was found.•The effect of crack inclination angle β on the equivalent crack stress intensity factor Ke and mixing factor Me was obtained.•A single-cracked limestone initiation model for hydro-mechanical coupling is proposed to predict the relationship between the initiation stress σci and the crack inclination angle β and water pressure P.