Rock Deformation And Failure With Consideration Of Dynamic Interaction Of Multiscale Cracks

Rock-like materials contain numerous cracks whose interaction affects the macroscopic mechanical properties of the materials significantly.A mechanical model of cracks of three scale levels is proposed to investigate the pattern of crack propagation and possible failure modes produced.For modelling crack interaction between different scale levels,the unloading domain of influence of a single crack is considered approximately on average as the sphere with the diameter being the crack size drawn around the crack center.With the consideration of interaction between cracks of the same and different scale levels and degradation of their mechanical property caused by propagation of cracks,the total axial stress and additional inertia induced stresses time-history,the crack tip stress intensity factor time-history and the motion equation of the crack are solved simultaneously by numerical method,and the variation of the crack propagation initiation time,the coalescence time of cracks and variation of crack length with time are obtained.The main conclusions are listed as follows:(1)The propagation mode of a single wing-crack under impact loading is revealed.A wing-crack propagates in a discrete pulse-type way at the initial stage before the stage of continuous crack propagation.(2)Propagation and coalescence of cracks of different scale levels for different initial crack concentration result in different patterns of cracks propagation and failure.For relatively lower initial crack concentrations,the interaction of cracks of the first scale level dominates,producing failure due to the coalescence of cracks of the first scale level.With the increase of the initial crack concentration,the coalescence of cracks of the third scale level dominates leading to failure at a higher initial concentration.With the further increase of the initial crack concentration,the failure is produced by the coalescence of cracks of the second scale level.At even higher initial crack concentrations the failure is again produced by the coalescence of cracks of the first scale level.The dynamic strength decreases with the increase in the initial crack concentration.(3)Inertia effect occurring in samples under dynamic loading affects the deformation and fracture of samples.This paper is also devoted to the nonuniformity of inertia effect on crack propagation and failure of rock specimen under dynamic loading.The formulae for calculation of inertia effect were deduced in rectangular parallelepiped rock-like samples under axial dynamic loading,which shows that the inertia induced stresses has a parabolic distribution across the specimen cross-section.The proposed model containing cracks of three scale levels is also used to investigate the dynamic propagation of cracks and inertia effect of rock-like materials,and the variation of the crack propagation initiation and coalescence times of cracks at different positions in the specimen are obtained.It is found that because of the inertia effect,the cracks near the edge of the specimen will propagate and coalesce earlier than the cracks in the center of the specimen,which will lead to the failure of the specimen in the sequence from outside to inside.