Dynamic statistical damage constitutive model based on the Hoek–Brown criterion at high strain rates

Dynamic damage constitutes a significant factor influencing engineering safety. Constitutive models predicated on statistical distribution demonstrate a capability in accurately representing the dynamic failure process of rocks. This study employs the high-strain-rate Hoek–Brown criterion to delineate the strength characteristics of rock microelements, subsequently establishing a novel dynamic statistical damage constitutive model based on statistical damage theory. Firstly, the model’s validity was corroborated using test data from different rocks (sandstone, granite, and marble) under varying confining pressure conditions. Subsequently, the influence of parameters F₀ and m on the stress–strain curve was discussed. Finally, the relationships between the Hoek–Brown criterion parameters ( \(\sigma_{{c\dot{\varepsilon }}}\) ${\sigma }_{c\dot{\epsilon }}$ , \(m_{{\dot{\varepsilon }}}\) $m_{\dot{\epsilon }}$ ) and the strain rate for different rocks were analyzed. The findings suggest that the model effectively characterizes the stress–strain relationship during the dynamic failure process.