Through the application of SHPB (split Hopkinson pressure bar) test

this research firstly analyzed the law of damage under the cyclical impact on grey sandstone samples with the condition of static load. After that

to obtain the sample failure mode and speculate the relationship between dynamic stress and strain

the static-dynamic loading experiments on pre-damaged rock samples were also performed. Finally

based on the principle of strain equivalence

the total damage variable under the condition of static-dynamic loading was analyzed to derive the damage evolution equation to explain the relation of damage constitutive. Based on above tests

the research suggests: (1) the damage variable of rock sample can be divided into three stages during the process of cyclical impact

which are rapid increase

low-speed development and high-speed development

meanwhile

a higher axial pressure will lead to a lower damage variable in the stage of low-speed development; (2) compared with pre-damaged sample

the effect of strain rate enhancement on intact samples is more significant under the same condition; (3) the joint impact of pre-damaged variable ( ) and static-load damage variable ( ) might be negative

which therefore explained the fact that the dynamic strength increases with the static pressure under the condition of static-dynamic loading; (4) the constructed constitutive relation is also in perfect agreement with the curve of test value

which can in turn show a consistency between the macro- and micro- damage of the rock and then reflect the nonlinear influence of cyclical impact and static loading on total damage development.