Study on the Coupling Effect of Sample Size and Strain Rate on Rock Compressive Strength

Deformation and failure of rock have size and strain rate effects. However, the coupling effect of sample size and strain rate on strength of rock is not well studied. At present, the experimental research in this area has accumulated definite experimental data, but there is a lack of theoretical model with solid theoretical basis. Therefore, in the present paper the coupling effect of sample size and strain rate on compressive strength of rock is studied theoretically. In the quasi-static loading regime, the formula for the coupling effect of sample size and strain rate on rock strength is obtained by combining the thermally activated mechanism and the static size effect law of rock strength. In the dynamic loading regime, the formula for the coupling effect of sample size and strain rate on the rock compressive strength is determined by using the Weibull’s activation law of rock defects and the shortest time condition of propagation and coalescence of cracks at different scale levels. Based on the conclusion that the strain rate sensitivity of the strength of rock is the result of competition between the coexisting thermally activated and macro-viscous mechanisms, which dominate at different ranges of strain rates, the formulae for the coupling effect of sample size and strain rate in static and dynamic regimes are superposed to obtain an unified formula for the coupling effect of strain rate and sample size effect on rock compressive strength. The critical strain rate for given sample size and the critical sample size for given strain rate are determined. The comparison with the existing theoretical models and experimental results shows that the present theoretical model is consistent with the existing theories and experimental results, indicating that the proposed model is reasonable. The present model is applicable to rocks of laboratory scale levels.