Abstract: In order to avoid the subjective factitiousness of instability criterions, the nonlinear catastrophe theory is applied to evaluate the stability of inhomogeneous slope. A numerical mechanical model in association with strength reduction FEM was adopted to analyze soil slope stability. Through establishing the cusp catastrophic model of the maximum horizontal displacement and strength reduction coefficient, the instability criterion was quantified as a determined catastrophe eigenvalue. Furthermore, safety factor was obtained according to the relationship between catastrophe eigenvalue of maximum horizontal displacement and zero in the presence of different strength reduction coefficients. The obtained safety factor was compared with that from other two criteria (plastic zone penetration and misconvergence) and Spencer’s procedure of limit equilibrium. Results indicate that the relation between slope stability and strength reduction coefficient can be quantified by this cusp catastrophic model and the catastrophe of slope instability process can be reflected. This instability criterion has high calculation precision and definite physical meaning.

Key words: inhomogeneous soil slope, cusp catastrophe theory, stability analysis, instability criterion, Drucker-Prager yield criteria, strength reduction method