Abstract: The incompetent structural plane was actually a combination of two mediums: medium 1 is elasto-brittle or strain-hardening material and medium 2 was strain-softening material,because it has different attribute in different environment or different parts.A cusp catastrophe model is presented to describe the behavior of sliding along one deep incompetent structural plane of a gravity dam foundation,and the sufficient conditions leading to instability are discussed.It is found that the instability of sliding relies mainly on the stiffness ratio k,the homogeneity index of the medium m and the geometry-mechanic parameter and that the reliability of the traditional limit analysis method is deficient.The influence of water fluctuation and prevention project is discussed too.It is indicated that the rising of water of the reservoir enlarges the material homogeneity and hence reduces the stiffness ratio k and that the instability of the dam may be posterior to the time when water comes to its peak.The prevention project enhances the potential of anti-sliding,and also has a new effect on enlarging the stiffness ratio k,which makes the instability of sliding occur more difficultly.