Abstract: The global rotation angle of a homogeneous soil slope induced by seism is well harmonize with the arc-sliding behavior of slope failure and so is a more superior parameter of deformation and stability than the permanent sliding displacement. And the strain energy because of transient seismic deformations is reversible and equivalent to the random fluctuation to a slope system, and critical rotation angle is an inherent property of slopes and independent of the seismic oscillation. Substantially, the critical rotation angle is in essence corresponds to the catastrophe point of the system potential energy. A cusp catastrophe model is set up based on the characters of seismic instability of homogeneous soil slope; and a method for determining the critical rotation angle of arc-sliding is proposed; and it is found that the critical rotation angle is only related to the constitutive model parameter m and of the constitutive model of soil in slide belt and the radius R of the arc slide belt and in essence represents the effect of many factors and deserving wide application.

Key words: slope engineering, seism, homogeneous soil slope, critical rotation angle, catastrophe