Abstract: The numerous non-penetrating intermittent joints in rock slopes play an important role in controlling the strength and failure mode of rock mass under excavation disturbance. In order to determine the meso-influence laws of intermittent joint interaction in the slope under the action of excavation, using the superposition principle and the Kachanov method, the stress intensity factor of parallel offset double cracks at the tip in rock mass under unloading conditions is calculated, the influences of many factors on the interaction between cracks are theoretically analyzed, and the unloading tests on rock-like specimens with parallel offset cracks are conducted. The results show that: (1) The interaction at the crack tips becomes more severe and sensitive if the length of the main crack larger or the staggered distance between the cracks or the length of rock bridge is shorter. (2) As the inclination angle of cracks increases, the tensile failure gradually increases but shear failure weakens. (3) The sensitivity of the amplification factors of the stress intensity factor affected by the angle is positively correlated with the length of rock bridge. In addition, the axial-initiation stresses of cracks in different specimens theoretically calculated under unloading conditions are compared with the measured ones by tests, and it is found that the relative error between them are all less than 4.7%, revealing that the proposed theoretical formula is a reasonable and feasible method to calculate the axial-initiation stresses of cracks. The propagation laws of the offset parallel cracks in rock under unloading conditions are revealed and are conducive to the studies on meso-failure mechanism of jointed rock slopes in open-pit mines under the action of excavation.