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

Abstract

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.