Prediction of dynamic response of rock under impact loads

The existing dynamic response diagram of marble to shock waves is used to verify the applicability and rationality of prediction model and prediction formula for the nonlinear dynamic response of rock under low velocity loading. The applicable conditions of the loading rate waveform function are proposed. Based on the study of the apparent elastic modulus of the fitting coefficient,the impact compaction coefficient a and the impact initial elastic modulus b,as well as the compaction action a₁ and slip action a₂ of the fractured voids in a rock sample, are proposed, and a=a₁+a₂,a₁>0,a₂<0. When it is subjected to the action of loads, the compaction degree of the rock sample and slip action exist simultaneously. In the loading section,|a₁|<|a₂|,and in the unloading section, |a₁|>|a₂|. That causes a<0 in the loading stage and a>0 at the unloading section. The loading-unloading rate response ratio β,which represents the ratio of the average tangent modulus of the unloading section to the average tangent modulus of the loading section, is defined. As the value of β increases, the degree of rock damage is also greater. At different frequencies, the sandstone has β≈2 in the loading mode of triangular waves and sine waves. The measured values of strain, deformation rate and energy value of each strain gauge are in good agreement with the calculated ones. It is proved that the nonlinear dynamic response prediction model and prediction formula for rock under low velocity loads have good applicability and rationality in the case of high-speed shock waves with millisecond time variation, which broadens the application range of the prediction formula and model. It is helpful to the design and construction of the project with strict displacement control.