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, Dcs, which accurately reflects the overall bending-induced tensile response and failure mechanism of concrete silos. The correction strategy involves maintaining an equal Dcs 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.

中文翻译：

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用于缩放土壤爆炸下地下混凝土筒仓动态拉伸响应和破坏的速率依赖相似性理论


从尺寸分析中得出的传统相似性理论与众所周知的比例模型和原型之间的材料应变率效应不可扩展性问题作斗争。这种限制极大地阻碍了按比例模型测试的应用，特别是小规模离心模型测试，在抗爆炸载荷结构的研究中的应用。为了克服这一挑战，本研究提出了一种速率依赖性相似性理论，用于缩放大型地下混凝土筒仓（46 m 高）在大产土爆炸下的动态拉伸响应和失效。所提出的理论包括一种源自经过验证的无量纲数 Dcs 的校正方法，该方法准确反映了混凝土筒仓的整体弯曲诱导拉伸响应和失效机制。校正策略包括通过调整缩放模型中的炸药重量和混凝土的静态抗拉强度来解释应变率效应的差异，从而在缩放模型和原型之间保持相等的 DCS。为了验证该理论，设计了一系列几何相似的筒仓模型，比例因子β = 1、1/2、1/5、1/10、1/20、1/50 和 1/100。使用包含炸药-土壤-筒仓系统的全耦合数值模型进行高保真数值模拟。结果表明，在传统的基于尺寸分析的相似性理论中，缩放筒仓模型的拉伸损伤和失效与原型模型明显不同。 然而，根据所提出的速率相关相似性理论，β = 1 ∼ 1/100的筒仓模型的失效模式几乎相同，表明所提出的理论可以有效解决缩放模型和原型之间材料应变率效应不同的棘手问题。这种相似性理论为设计准确反映原型行为的缩放模型提供了坚实的理论基础，从而推动了比例模型测试在抗爆炸载荷结构研究中的应用。