Fractional Catastrophe Model considering the Rheological Properties of Slope Faults

Abstract

Abstract Fault properties have an important influence on the sliding mode and long-term stability of slopes. In this paper, a cusp catastrophe theoretical model of an open-pit slope is established based on the mechanical model of plane sliding slope instability. The model considers time effects, the rheological properties of fault locking sections, and the strain softening properties of fault softening section. A rheological constitutive model is constructed based on the fractional derivative according to fractional calculus. A slope instability criterion is proposed within catastrophe analysis. The influences of the fault medium length, stiffness ratio, and different orders of the fractional derivative on slope stability are discussed. The critical height and critical safety factor of the dynamic slope instability are derived, and the catastrophe instability time is predicted. The results show that longer softening stages are associated with smaller stiffness ratio values, higher fractional orders, and a greater possibility of slope instability. Slope stability is dynamic under the rheological action of the fault medium.