Similarity Relationship for Brittle Failure Dynamic Model Experiment and Its Application to a Concrete Dam Subjected to Explosive Load

This paper suggests that the idea of the breaking strength of the brittle material scale being equal to the length scale was abandoned in the dynamic model brittle failure experiments. The concept of the failure load intensity scale, and that the breaking strength of the brittle material scale is equal to the failure load intensity scale, was put forward for the first time. This paper proposes an equivalent dynamic failure model test for a concrete dam subjected to strong underwater shock waves caused by explosions to illustrate the use of the similarity relationship. Based on the differential equation of motion for an elastic medium, similarity constraints on the time and Poisson’s ratio for elastic motion are obtained. Moreover, the constraints on the concrete’s strength and load are selected to simulate damage that is approximately the same. The equivalent test is based on drop-hammer equivalent impact models and empirical formulas that describe underwater explosions for four types of explosives, and the maximum pressure, impulse, elastic modulus, and strength of the model and prototype materials are similar. Finally, the numerical simulation is performed with a FEM to test with reliability the similarity relationship. By comparing the failure mode and pressure from the model test and numerical simulation, it can be considered that the experimental theory and method are partially validated. The similarity relationship proposed in the present paper provides more options for the selection of the material in the model. The proposed prediction method makes pollution-free, cost-effective, and easily operated simulations available.