Rate-dependent similarity theory for scaling the dynamic tensile responses and failure of underground concrete silos under soil explosions

The conventional similarity theory derived from dimensional analysis struggles with the well-known issue of non-scalability of material strain-rate effects between scaled models and prototypes. This limitation has significantly hindered the application of scaled model tests, particularly small-scale centrifugal model tests, in the study of structures against blast loading. To overcome this challenge, this study proposes a rate-dependent similarity theory for scaling the dynamic tensile responses and failure of large-scale underground concrete silos (46 m in height) subjected to large-yield soil explosions. The proposed theory includes a correction method derived from a verified dimensionless number, D_cs, which accurately reflects the overall bending-induced tensile response and failure mechanism of concrete silos. The correction strategy involves maintaining an equal D_cs between the scaled model and the prototype by adjusting the explosive weight and the concrete’s static tensile strength in the scaled model to account for differences in strain-rate effects. To verify the theory, a series of geometrically similar silo models with scaling factors β = 1, 1/2, 1/5, 1/10, 1/20, 1/50, and 1/100 were designed. High-fidelity numerical simulations were performed using a fully coupled numerical model encompassing the explosive-soil-silo system. The results demonstrate that, with the conventional dimensional analysis-based similarity theory, the tensile damage and failure of the scaled silo models differ significantly from those of the prototype. However, with the proposed rate-dependent similarity theory, the failure patterns of the silo models with β = 1 ∼ 1/100 are almost identical, indicating that the proposed theory can effectively address the troublesome issue of dissimilar material strain-rate effects between scaled models and prototypes. This similarity theory offers a solid theoretical foundation for designing scaled models that accurately reflect prototype behavior, thereby advancing the application of scaled model tests in the study of structures against blast loading.