Analytical expressions for forces on structures due to spherical blast waves

The blast-resistant design of structures is becoming important due to the enhanced security requirements. The estimation of net forces and moments is essential to proportioning the design section of homogeneous structures such as blast-walls. The current design procedures consider the planar wave assumption, which is true when the structure is either small compared to the shock front or located very far from the explosion. Furthermore, due to the reflections of the shock waves, the structures experience reflected overpressure, which depends on the angle of incidence and incident overpressure of the shock wave front on the exposed structural surface. Under the planar wave assumption, the angle of incidence will always be normal, however, it will be significantly different from normal for spherical blast waves. Therefore, this study investigates the interaction of an unyielding straight structural surface with spherical blast waves and develops an exact solution for the blast pressures and net forces on the rigid surface. For direct design applications, the approximate closed-form approximations are also developed and compared with the exact solutions. The detailed discussions indicate that below a certain scaled distance, the planar wave solutions significantly overestimate the forces, and in those cases, the proposed closed-form approximations can be conveniently used. The applicability and limitations of the developed solution are illustrated through respective examples.