Discussion of “Impact of Solid Missiles on Concrete Barriers”

The author is to be congratulated for his work in addressing the difficult problem of missle impact on concrete barriers.The subject is very complicated and a complete theoretical treatment of the problem is not yet available.The author attempted to develop the theory in a crude and sometimes unjustified way, then tried to fit the relationship thus produced with the experimental results presently available using the Bayesian approach.Even in this type ofsemianalytical formulation, some basic and important areas need to be addressed properly.In developing the model, the author assumed that the strain energy can be estimated by considering a circle of radius ru (Eq.11).This is not a valid assumption.It has been observed in many experiments that cracks will be developed in the vicinity of the impact area in all directions (ll).The strain energy needs to be calculated by considering an area, definitely not along the periphery of a circle.The ultimate result (Eqs.15 and 16) may not be influenced by this assumption, but the aforementioned formulation is not correct.The scabbing and perforation thicknesses (Eqs.17 and 25) are developed while completely ignoring the effect of missile penetration in the target.Impact formulation for concrete structures without considering the penetration depth may not be adequate.To emphasize this statement, the penetration depths according to the NDRC equations and the impact areas for a given impact energy are plotted in Fig. 7.The penetration depth decreases as the impact area increases.This is expected.However, even when the impact area is large, i.e ., 140 sq in.(9,030 sq mm), the penetration depth for the given example is about 6.99 in.(177.5 mm), which is not negligible .In the Bayesian analysis section, a normal variable Y is introduced.The author assumed Y to be normal because "The chance that all worst conditions or all favorable conditions for the impact take place at the same time is small."This reasoning is not adequate according to this writer.The normal variable Y is a function of the product and division of three other random variables Ct> C2 , and C3 .When Ct> C2 , and C3 are independent lognormal variables, Y can be assumed as lognormal but not normal.The question of whether Y can take any value less than zero needs to be addressed.It appears that a lognormal distribution of Y may be a better choice.However, this will create problems for the Bayesian approach.The author estimated the prior mean and variance for Y, i.e. , £(1.1.)= 1.8 and E(a 2 ) = 0.04 without mentioning how many sample points he used in these estimations.However, the author updated the information by considering 8 additional sample points.The updated statistics of Y are found to be E(~.~o)