In this paper

the blasting vibration of rock is analyzed under the condition of multi-free surfaces

which is based on the excavation of a collapse cavity section in the extension of the existing tunnel. The effect of simulating blasting vibration on the reinforcement area of the collapse cavity and surrounding rock is investigated by a fully restarted numerical method and Lagrangian algorithm method. Furthermore

vibration velocities and the attenuation law of characteristic points are obtained. It is found that the maximum vibration velocities calculated by the numerical method are in accordance with the requirement of the safety of blasting vibration. It also verifies the feasibility of blasting design

and can be used a guide for the blasting construction. Meanwhile

the blasting vibration monitoring of collapse section excavation is also conducted. The obtained vibration velocities from field experiments with the numerical simulation are in a good agreement. The results indicate that numerical methods can be used to describe the rock fragmentation and blasting vibration well in the millisecond delay blasting. Therefore

the current study shows a good example for the similar engineering conditions.