The mechanical characterization of dynamic direct damage in brittle rock under pre-tension stress is crucial for evaluating the safety and stability of deep rock engineering. However

due to the harsh experimental conditions associated with dynamic direct tension of pre-tensioned rocks

experimental studies in this area are relatively scarce

and theoretical investigations into the macro-micro mechanisms are even rarer. Based on the wing crack extension model under quasi-static direct tensile loading

the static and dynamic fracture toughness relationship models

and the dynamic-static coupling function of strain rate and strain

a constitutive relationship model for dynamic direct tensile damage of brittle rock under pre-tension is proposed by introducing the fracture toughness modification parameter  related to pre-tension stress. The relationship between the enhancement of dynamic crack fracture toughness and dynamic direct tensile strength in pre-tensioned rock is established. The dynamic direct tensile strength increases with pre-tension stress

provided that the pre-tension stress does not exceed the crack initiation stress in rocks. By comparing the magnitude of axial pre-tension stress 1pre with the crack initiation stress 1ci

the expansion of wing cracks is categorized into three cases

each corresponding to a different constitutive relationship. The effects of pre-tension stress on the mechanical properties of brittle rock are analyzed

along with the influence of the rock’s initial state (initial damage

crack size

density

and angle) on the mechanical properties of pre-tensioned brittle rock. The findings provide theoretical references for the construction and design of deep underground engineering.