Regarding the normal component force acting on the side slope with bedding rock mass as initial defect of structure

buckling behavior of imperfect system in a critical state by using initial post-buckling theory and cusp cata strope model is studied

the mode amplitude equation of equilibrium stability for the side slope with bedding rock mass is established

and a bifurcation neighborhood and the criterion of stability for rock mass slope are derived. The results indicate that the initial defect correction term has determined relation with the ripping factor in cusp catastrophe model; compared with the ideal structure

the critical value for the side slope with bedding rock mass is much larger than its load value at bifurcation point

and is determined by its bifurcation set; the critical value in the real critical sense can be obtained only if the actual defect for side slope with bedding rock mass is considered.