Abstract
Many analytical and numerical models exist that can describe the effect of single projectile impacts on steel targets. These models are not adequate for the evaluation of live fire shoot house containment systems, which are subjected to repeated impact loading from small caliber projectiles over the lifetime of the structure. Models assuming perfectly rigid projectiles over-predict penetration depths. Models assuming rigid targets cannot predict any penetration, and hydrodynamic models are best suited to high velocity impacts well above the ranges of conventional ordinance. Development of sufficient analytical or numerical tools using traditional techniques would be either intractable, empirically based and unique to a given scenario, require unique material properties that are not commonly available, or require significant computational effort. Due to the limited amount of empirical data on multiple impact failure, classical reliability methods are not suitable for assessing the probability of containment system perforation. Using existing experimental results of .223 caliber ammunition against AR500 steel panels with 2-inch ballistic rubber, a commonly found protective system in these facilities, the cumulative effects of multiple projectiles were quantified to estimate the number of impacts required to perforate the target material. Impacts were simulated from normal distributions of the x and y coordinates describing the impact point using a cartesian coordinate plane. The impact resistance of the steel was also simulated from a triangular distribution to account for the variability of the experimental results. Monte Carlo Simulation was then used to estimate the expected number of impacts to cause failure at a single point on the target. Using this collective model, it was possible to determine that the distribution of the number of rounds to cause target failure approached a normal distribution. The results indicated that the mean impacts at failure was 11800 with a standard deviation of 800 impacts. Finally, targeting the allowable risk level for structural failure from the JCSS probabilistic model code from the simulated normal distribution, it was determined that the safe number of impacts was approximately 7996. Decision makers can utilize the safe number of impacts to inform training guidance for the future use of facilities and to develop effective inspection requirements. This model can also be adapted to evaluate similar training facilities and to assess how other small caliber projectile impacts would affect live fire shoot house containment systems, providing a useful tool for the design and analysis of future and the assessment of existing facilities for use with ammunition that did not exist during its design.
Risk Evaluation on China Government Bonds with EWMAVaR and SVM Methods
