Design of rock-rubble concrete shield against the combination of penetration and explosion of warheads

Aiming at the resistance evaluation and engineering design of the rock-rubble concrete shield under the combination of penetration and explosion of Earth Penetrating Weapons, firstly, this paper proposed a finite element modeling method for rock-rubble concrete shields. By conducting numerical simulations of quasi-static and penetration tests on ultra-high performance concrete targets containing different coarse aggregate types (corundum and basalt), particle sizes (5-15 mm, 5-20 mm, 35-45 mm, and 65-75 mm), and volume fractions (15% and 30%), the reliability of the modeling method, material constitutive models and corresponding parameters, as well as finite element analysis approach was thoroughly verified. Then, using the semi-infinite rock-rubble concrete shield penetrated by the SDB as a case study, the quantitative influence of type (corundum, basalt, and granite) and dimensionless particle size of rock-rubble (ranging from 0.3 to 2.2 times the projectile diameter) on the penetration depth was analyzed, and optimal design recommendations were determined. Furthermore, the penetration analyses of three typical prototype warheads, i.e., SDB, WDU-43/B, and BLU-109/B, were carried out, and the corresponding penetration resistances of normal strength concrete (NSC), ultra-high performance concrete (UHPC), and corundum rubble concrete (CRC) shields against the above three warheads were quantitatively compared. Finally, the engineering design method for the CRC shield under the combined effects of penetration and explosion of prototype warheads was proposed. The results indicate that the CRC shield containing the particle size of 1.3 to 1.7 times the projectile diameter exhibits the most excellent penetration resistance. Under the penetration of three types of warheads, the penetration depths in CRC shield were 0.29 m, 0.78 m, and 0.68 m, respectively, which are reduced by 61.8%-64.1% and 43.3%-58.0% compared to those in NSC and UHPC shields. Under the combined effects of penetration and explosion, the perforation limits of the CRC shield are 0.52 m, 1.22 m, and 1.50 m, while the scabbing limits are 1.11 m, 2.26 m, and 3.17 m. Compared with NSC and UHPC shields, the perforation limits are reduced by 60.5%-64.0% and 43.3%-58.0%, respectively, and the corresponding scabbing limits are reduced by 61.8%-69.1% and 34.7%-40.5%, respectively.