Abstract: Based on the two-dimensional plane sliding instability mechanical model of rock slope with bedding intermittent joints,the cusp catastrophe theory model of the instability of jointed slope under gravity stress was established.According to the catastrophe model,the effects of the lengths of intermittent joints (joint connection rate),the inclination angle of joints,the friction angle and cohesion of joints on slope stability were discussed,and the critical instability height of slope was deduced. Then,the criterion conditions of slope instability were put forward. Finally,the finite difference method (FLAC^3D) was used to simulate the failure form of rock slope with intermittent joints under the conditions of different joint connection rates and inclination angles. The results show that the greater the joint connection rate and the inclination angle of joint,and the smaller the friction angle and cohesion of joint and the friction angle and cohesion of rock,the higher the possibility of the slope instability. When the connectivity of the joints is small,the rock friction angle and cohesion are the main factors affecting the slope stability. However,with the continuous increase of the connectivity of the joints,the effects of joint friction angle and joint cohesion on slope stability become more and more significant and gradually become the main factors to control the slope stability. Sliding-block toppling mixed progressive failure of the rock slope with bedding intermittent joints occurs under gravity stress and the penetration failure of the joint rock bridge is caused by the propagation of the shear cracks formed at the tip of joints and existing joints. The failure of the lower rock bridges first occurs and the formed shear cracks gradually extend upward,and then form a local or integral sliding surface. By comparing the results of theoretical calculation and numerical simulation,it is found that it is applicable to evaluate the stability of the kind of slope by using the proposed theoretical instability criterion,which provides some theoretical supports for the rock mass stability evaluation and instability prediction of jointed rock slope.