In this paper

the influence of unloading time（unloading rate）on the cracking

radial stress wave propagation

and radial stress evolution in a circular tunnel surrounding rock was studied by use of the continuum-discontinuum method proposed by the authors.This method was based on the Lagrangian element method

deformational discrete element method

and fictitious crack model.The influence of unloading time on the cracking

radial stress wave propagation

and radial stress evolution of the surrounding rock was investigated successively.A shorter unloading time was accompanied by more cracks

and a greater and more intense fluctuation of the maximum unbalanced force in the surrounding rock.The crack near the excavation boundary changed from a continuous distribution to a discontinuous distribution with the increase of the unloading time.When the unloading time was short

the crack distribution in the surrounding rock was continuous

which was because that the maximum principal stresses at these locations exceeded the tension strength.When the unloading time was moderate

the crack distribution in the surrounding rock was similar to V-shaped notches

which may be related to the presence of shear stresses at these locations.At a shorter unloading time

the number of radial stress rings in the disturbed zone（i.e.

the decreasing zone of radial compressive stresses）was greater and clearer

the fluctuation of radial stresses in the surrounding rock was more evident

and the maximum radial tensile stresses（or minimum radial compressive stresses）were larger（respectively

smaller）.