DYNAMIC RESPONSE OF STRUCTURES SUBJECTED TO MISSILE IMPACT

Abstract

The area of missile impact has been drawing attention of engineers and scientists the world over, since World War I. Major fields for the study of impact response have been the accident analysis of automobiles and aircrafts; the design of Nuclear Power Plant (NPP) structure, underground power house, bunkers, space vehicles, battle ships, armoured vehicles etc. The area being vast, the present work encompasses the impact of missiles such as tornado borne debris and especially aircrafts upon concrete and reinforced concrete structures; missile penetration into soil and the impact of missiles upon metallic targets only. The reinforced concrete safety class structure of NPP has to withstand the impact of tornado missiles, internally generated missiles from the failure of pressure retaining systems or rotating machinery, and site proximity missiles due to offsite explosions or transportation accidents and aircraft crashes. Damage caused by these missiles may follow a number of consecutive hypothetically abnormal events. The consequences of any such incident are going to be far reaching and hazardous for the generations to come due to the leakage of nuclear radiations. The economic considerations, due to the low probability of impact loads but coupled with hazardous and far reaching consequences compels the designers to reduce the safety margins in the design of the structures required to withstand them. This requires that the actual response of structures to extreme loads, be predicted with a higher degree of confidence than is typically the case with conventional structures. On the basis of target or missile deformabi 1ity, the impacts can be classified as either hard or soft. In hard impact, the deformation of both the target and the missile is negligible. On the other hand soft impact may be due to soft missile or the soft target, or both. The missiles to be considered in the design of a structure are decided by the probabilistic analysis carried out for all postulated missiles. The safety design of NPP against aircraft crash requires the evaluation of crash probability. If the probability is smaller than the allowable value then the aircraft crash is neglected as design basis item. Otherwise adequate measures are taken to bring the release of radio active material within the permissible limit. The local impact response of concrete and reinforced concrete targets is characterised by intense dynamic stresses that produce crushing, cratering, shear failure, and tensile fractures of the target. The admissible local damage required from the point of view of security may be to prevent scabbing or just perforation. The emperical relations used in the prediction of local damage of concrete and reinforced concrete targets are applicable only within the range of parameter for which they were developed. Also, most of the relations are dimensionally nonhomogeneous. The prediction of local damage is critically reviewed and the theories of penetration and perforation are presented. Non dimensional emperical relations are proposed for predicting the penetration depth, scabbing thickness, perforation thickness and perforation velocity for- reinforced concrete targets. The prediction is better than the presently available approaches. Rectangular hyperbolic plotting is proposed for checking the scatter in the data with respect to a particular relation. The procedure of obtaining forcing function is dealt in this work for soft as well as hard impact. Three aircrafts namely Boeing 707-320, FB-111 jet fighter and Phantom F4 are considered in the present work. The reaction time response obtained on the basis of rigid target concept is not only unrealistic but also unconservat ive for some cases. The impact of target yielding is dependent both upon the characteristics of the target as well as the missile. The conclusion is based on the solution of the aircraft impact upon outer containment of NPP. The concept of confidence level has been investigated in relation to iv inclined targets also and the confidence curves are obtained for the aircrafts. The parameters influencing the forcing function are identified. Both, linear mass density as well as the crushing strength significantly affect the reaction time response depending upon the characteristics of the aircraft and the striking velocity. Though the past three decades have witnessed the development of many sophisticated models for the description of reinforced concrete, but only a few of the models have been employed in engineering analysis and most of the authors employed much less refined models for evaluating the overall response of the reinforced concrete targets. The three dimensional concrete models used by them does not simulate the response of concrete adequately whose three dimensional surface is noncircular on deviatoric plane. A material model developed for reinforced concrete suitable for transient dynamic analysis is presented. The proposed model accounts for most of the observed sources of material nonlinearity in triaxial stress state. The proposed strain rate sensitive elasto visco-plastic material model for reinforced concrete to simulate its transient dynamic behaviour is capable of properly representing the mechanical behaviour of the material. The proposed failure and yield surface is a five parameter model which is non circular as well as non-affine on deviatoric plane. The curve meridians of the model are described by cubic and the non circular trace in the deviatoric plane is represented by an ellipse. Unlike William Warnke's five parameter model, hydrostatic axis is normal to the yield surface. It meets the required characteristics of symmetry, smoothness and convexity. The failure criteria encompasses several earlier criteria as special cases giving it a definite edge over the others. Smeared crack approach with fixed crack angle is adopted for tensile cracking. Initiation of cracks depends upon maximum principal strain. Closing and reopening of cracks is allowed in the model following the secant path. The shear transfer across crack due to aggregate interlock and dowel action is incorporated by taking a reduced value of the shear modulus. Degradation in material strength due to accumulated damage is also included. Tensile strength is the most sensitive model parameter because it not only affects the cracking load but also the entire load displacement curve and the failure load. The fracture energy controls the tensile strain softening. When the model parameters required are not known then the average values can be given to the parameter's. To obtain the lower bound of failure load, conservative values of cracking strain and fracture energy should be employed. Some benchmark tests are analysed to assess the validity and accuracy of the model and to study the influence of various model parameters employed in the formulation. The practical utility of the program is demonstrated by analysing some medium sized numerical examples of aircraft impact analysis on 3D reinforced concrete structures. From numerical experiments performed throughout this work it can be concluded that the computational model developed and implemented in computer program is able to analyse the nonlinear behaviour of three dimensional reinforced concrete structures. It has been demonstrated that the computational model presented can be applied to the range of engineering problems under consideration with a reasonable degree of success. • Impact response calculations of reinforced concrete structures can be carried out without a priori knowledge of load time functions which is evaluated simultaneously. The present investigation has shown that the influence of nonlinearity in reinforced concrete material in the immediate vicinity of the point of impact on the vibration response is considerable. Linear elastic analysis of induced vibrations partly yield unrealistic results. A problem of axisymmetrlc impact of a metallic target by a flat ended cylindrical missile involving severe distortions is analysed considering vi triangular elements. The total Lagrangian formulation is employed to simulate the large deformation and distortion response. In this analysis perfect contact is assumed during the impact. The program developed for the purpose has been successfully employed to predict the penetration. An algorithm for the three dimensional searching is developed for the coupled analysis of the impact problem. Closed form solution is obtained for the impact of a hollow truncated cone upon a rigid target considering concertina type mode of collapse. The outward folding in this mode of collapse is disregarded on the basis of conservation of energy. This mode of collapse is found to be applicable for the missiles having thin membrane. Whereas for thicker membrane missiles like aircrafts, there will be gradual crushing. The demarcation is based on the principle of conservation of energy. Cylindrical cavity expansion model is developed for the penetration of missiles into the geological targets. vii