Considering explosive charge shape and embedded depth in the design of concrete shelter thickness

Cost and safety are important considerations when designing the thickness of a protective reinforced concrete shelter.The blast perforation limit(BPL)is the minimum concrete shelter thickness that resists perforation under blast loading.To investigate the influence of the depth of embedment(DOE)and length-to-diameter ratio(L/D)of an explosive charge on the BPL,the results of an explosion test using a slender explosive partially embedded in a reinforced concrete slab were used to validate a refined finite element model.This model was then applied to conduct more than 300 simulations with strictly controlled variables,obtaining the BPLs for various concrete slabs subjected to charge DOEs ranging from0 to∞and L/D values ranging from 0.89 to 6.87.The numerical results were compared with the experimental results from published literature,further verifying the reliability of the simulation.The findings indicate that for the same explosive charge mass and L/D,the greater the DOE,the larger the critical residual thickness(Rc,defined as the difference between the BPL and DOE)up to a certain constant value;for the same explosive charge mass and DOE,the greater the L/D,the smaller the Rc.Thus,corresponding DOE and shape coefficients were introduced to derive a new equation for the BPL,providing a theoretical approach to the design and safety assessment of protective structures.