Mechanism underlying dynamic size effect on rock mass strength

• We used Maxwell type model for modeling mechanical behavior of rock mass.
• We obtained the relationship between strength, sample size and strain rate.
• Together with static size effect we predicted the dynamic fragmentation size well.
• We succeeded also in predicting the characteristic transition strain rate.
• We showed that our model complies with that of Grady.

This paper presents the research on mechanism of dynamic size effect on rock mass strength based on structural hierarchy. Relaxation model of Maxwell type for rock mass is used to obtain the relationship between strength, sample size and strain rate. This model is used to analyse the experimentally observed laws of dynamic size effect on rock mass strength. 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 completely. The larger the sample size is, the more time is required for cracks to propagate through the sample, and the higher the applied stresses are before the macro-fractures of samples occur. On the other hand because of the static size effect the higher dynamically applied stresses will initiate the cracking at smaller scale levels of rock sample, and the fragment size is smaller. The developed model succeeded in explaining the main features of dynamic and static size effect and the apparent controversy in experimental data, and in predicting the dynamic fragmentation size, the characteristic transition strain rate and characteristic sample size.