Abstract: In this study, a multi-degree of freedom model method was proposed to construct the differential equation for similar dynamic responses of complex stereoscopic goaf of metal ore under blasting load excitation. The correction factor matrix λ of the shear effect and the action coefficient matrix B were also introduced to describe the shearing effect of surrounding rock under external loads. The Newmark-β method was applied to solve the differential equation for similar dynamic responses in the goaf. The self-contained Matlab program was used to realize the fast calculation, which solved the problems of low efficiency and poor accuracy of the dynamic responses of the multi-degree of freedom goafs. An example of the 3×3 unit goaf in a metal mine was compared with the numerical simulation method. The results show that this method can directly reflect the dynamic response laws of the particles in the stereoscopic goaf group, and the displacement and velocity curves are basically consistent with the numerical simulation results. The maximum displacement is the area with the application of the blasting load. The comparison between the calculation results of the multi-degree of freedom model method and the field displacement monitoring results reveals that their displacement changes are similar, their peak values are at the same order of magnitude, and the latter displacement is slightly delayed. This research provides a new way to study the dynamic responses of the complex stereoscopic goaf group.

Key words: multi-degree of freedom model method, dynamic response, stereoscopic goaf group, blasting load, Newmark-β method