Critical thickness calculation for concrete shelter subjected to projectile penetration followed by charge explosion

The earth penetrating weapon (EPW) employs a precision guidance system to achieve accurate emplacement at a predetermined depth, after which a cylindrical explosive charge is detonated to induce damage and failure to the protective structure. Within a layered protective structure, the concrete shelter serves as a sacrificial layer; consequently, the critical perforation thickness, i.e., the minimum thickness required to prevent complete penetration followed by catastrophic failure under combined projectile impact and subsequent charge detonation, constitutes the primary design control parameter. To enable engineering-level prediction, the coupled penetration-explosion process induced by EPW was rationally idealized as a pre-drilled charge explosion. Building upon this simplification, a computational method for predicting the penetration depth of the penetrator prior to detonation was first formulated; then, the calculation formula for the peak stress of the blast wave in the concrete beneath the cylindrical charge and the analytical model for the wavelength of the blast wave were established, respectively; on this basis, corresponding calculation methods for the crushed depth and spall depth of the concrete shelter induced by the charge explosion of EPW were proposed; finally, a practical and iterative calculation framework for determining the critical perforation thickness of the concrete shelter subjected to projectile penetration followed by charge explosion was developed and rigorously validated against a comprehensive database of controlled blast experiments. Variations in striking velocity, depth of burial, charge mass, charge length-to-diameter ratio, concrete compressive strength and shelter thickness were encompassed by the validation. Results demonstrate strong agreement between model predictions and experimental measurements across all test configurations, confirming the method’s reliability and broad applicability. Leveraging the validated framework, critical perforation thicknesses were systematically determined for five representative EPWs impacting concrete shelters across a compressive strength range of 30–150 MPa and initial striking velocities of 300–400 m/s. The research results can provide an important reference for the design of protective structures against EPWs.