The underground concrete silo, designed as a hollow cylinder with a large aspect ratio and thin walls, is highly susceptible to failure caused by intentional or accidental soil explosions. To enhance its protection, this study investigates the dynamic tensile responses and failure mechanisms of underground concrete silos subjected to high-yield soil explosions. The concept of nominal crack width is proposed to quantitatively describe the degree of overall bending-induced tensile responses and failure of the concrete silo. The influences of explosive weights, standoff distances, and the aspect ratios and thicknesses of the underground concrete silo are quantitatively explored first. On this basis, a dimensionless number combining these major influencing factors is derived using dimensional analysis. The derived dimensionless number has a clear physical meaning, reflecting three aspects: the inertia of the blast loading, the resistance ability of concrete material to bending responses and failure, and the resistance ability of silo structure to bending responses and failure. The results demonstrate that the proposed dimensionless number effectively correlates with the overall bending-induced tensile responses and failure of silo structures across various geometries and explosion scenarios, exhibiting a good linear relation with the dimensionless nominal crack width of the concrete silo. With its solid physical foundation, the dimensionless number offers practical applications in scaling analysis and fast damage assessment. Specific examples of these applications are presented and discussed in this study.