Cusp catastrophe theory models of the rock slope instability under open blasting load were built based on the two-dimensional mechanical instability model considering the factors of blasting dynamic load. According to the established model

the influences of the amplitude and frequency of blasting dynamic load on the slope stability were discussed

and the dynamic critical instability height of the slope was derived

the criterion of the slope instability was also proposed. The result reveals that the possibility of slope instability increases with the increase of amplitude of the dynamic load

the decrease of frequency and the increase of trailing edge crack depth; the stability of slope is dynamic

and with the increase of incident angle of stress wave

the possibility of slope failure is increasing under blasting load. Taking two slopes in Dagushan Open-pit Mine as examples

the dynamic safety factor and the dynamic self-stability critical height of the slope are calculated

and the rationality of the proposed slope instability criterion is verified by the actual stability of the slope at present. It provides a certain theoretical support for preventing the dynamic instability of slope rock mass in the process of blasting excavation in open-pit mine.