Similarity law of global and local responses of reinforced concrete beams subjected to impact loading

In the experiment of scaled models to dealing with the impact of reinforced concrete large structures, the strain rate hardening effect can lead to significant differences between the dynamic responses of prototype and model. In the present study, this thorny problem is solved by adjusting the impact velocity. Based on the mechanisms of different dynamic responses, the similarity laws for the global and local responses of reinforced concrete beams subjected to impact loading are proposed by considering the strain-rate effect of materials through Buckingham Π-theorem, where constitutive models of different materials are employed for inferring dynamic stress. In dimensional analysis, multiple control factors need to be considered simultaneously, such as the strain-rate effects of steel and concrete, since reinforced concrete components are typical composite structures. The similarity law cannot be unified when considering multiple control factors. In view of this, it is recommended to estimate the dynamic response of reinforced concrete components subjected to impact loading through the upper and lower bounds of similarity law. The upper bound of similarity law is based on the strain-rate effect of concrete, while the lower bound of similarity law is based on the strain-rate effect of steel bar. The numerical models of reinforced concrete beams are established based on the experimental background. The numerical simulations with different scaling factors indicate that the model modified by the lower bound of similarity law can better predict the global response of prototype, while the model modified by the upper bound of similarity law can more accurately predict the local response of prototype. In addition, the influence of dynamic elastic modulus of reinforced concrete on the similarity law is discussed through comparative analysis.