Structural hierarchy and dynamic size effect of rock strength

The mechanism of dynamic size effect of strength of rock is studied from the viewpoint of structural hierarchy. Relaxation model of Maxwell type for rock is used to obtain the relationship between strength, sample size and strain rate. It is shown that because of the finiteness of crack propagation velocity, when the strain rate is well above certain characteristic strain rate, dynamic loading process takes predominant role, the stresses in sample have not enough time to relax, the larger the sample size is, the more time is needed for cracks in sample to go through the sample, the ultimate applied stresses before macrofracture are greater and the strength is higher. From other hand because of the size effect the higher dynamically applied stresses will activate the cracking at smaller scale levels of rock sample, and the fragment size is smaller. Based on the presented model the characteristic strain rate separating the predominant diapasons for static and dynamic size effect is determined, and the fragment size is predicted satisfactorily.