Comparative assessment of impact analysis methods applied to large commercial aircraft crash on reinforced concrete containment

The precise evaluation of the potential damage caused by large commercial aircraft crash into civil structures, especially nuclear power plants (NPPs), has become essential design consideration. In this study, impact of Boeing 767 against rigid wall and outer containment building (reinforced concrete) of an NPP are simulated in ANSYS/LS-DYNA by using both force time history and missile target interaction methods with impact velocities ranging from 100 m/s to 150 m/s. The results show that impact loads, displacements, stresses for concrete and steel reinforcement, and damaged elements are higher in case of force time history method than missile target interaction method, making the former relatively conservative. It is observed that no perforation or scabbing takes place in case of 100 m/s impact speed, thus preventing any potential leakage. With full mass of Boeing 767 and impact velocity slightly above 100 m/s, the outer containment building can prevent local failure modes. At impact velocity higher than 120 m/s, scabbing and perforations are dominant. This concludes that in design and assessment of NPP structures against aircraft loadings, sufficient thickness or consideration of steel plates are essential to account for local failure modes and overall structural integrity. Furthermore, validation and application of detail 3D finite element and material models to full-scale impact analysis have been carried out to expand the existing database. In rigid wall impact analysis, the impact forces and impulses from FE analysis and Riera's method correspond well, which satisfies the recommendations of relevant standards and further ensure the accuracy of results in full-scale impact analysis. The methodology presented in this paper is extremely effective in simulating structural evaluation of full-scale aircraft impact on important facilities such as NPPs.

been studied by considering an aircraft crash upon the outer containment of an NPP. It has been observed in this investigation that the assumption of a rigid target is unconservative for some of the cases. It is usually assumed that variation in crushing strength has very little effect on the reaction from the target. However, the sensitivity analysis for reaction-time response indicates that both linear mass density and crushing strength are sensitive in affecting the reaction from the target, depending upon the characteristics of the aircraft and the striking velocity. The concept of confidence level has been investigated in relation to inclined targets also and confidence curves are obtained for aircraft.

INTRODUCTION
The outer containment of Nuclear Power Plants (NPP) is required to withstand the impact of crashing airplanes, aircraft debris, etc. in probabilistic considerations.
Its analysis therefore requires complete information on forces exerted upon the structure by these projectiles. The pioneering work in this direction was done by Riera [l] who uncoupled the problem of aircraft crashes by considering normal impact upon a rigid target leading to the impulse which has been later used by several others [2-61 for the analysis of structures. The assumption of a rigid target disregards the inertial and stiffness properties of the target structure. Although the assumption has been claimed to be conservative by various authors [3,7], the conclusion is based on the analysis of a rather stiff structure with insignificant local deformations. The effect of target yielding upon reaction time response has been studied in this paper by calculating the reaction simultaneously with the response of the target structure. The crashing of an aircraft upon a typical reinforced concrete (RC) outer containment of an NPP is considered for this investigation.
The subject of aircraft impact in relation to reaction-time curves is critically reviewed and drawbacks, if any, are pointed out. The probability density function for an aircraft striking an inclined surface is evaluated.
The sensitivity of the reaction time response of aircraft to the variation in crushing load and linear mass density of the aircraft is studied. In

LITERATURE REVIEW
The pioneering work in the area of aircraft impact on nuclear shielding structures was done by Riera [ 11.
In an attempt to improve upon Riera's formulation, Hornyik [5] considered energy balance as well by assuming rigid perfectly plastic behaviour of the missile material. Rice and Bahar [8] presented an alternative derivation for calculating reaction-time history. The pitfall of their approach appears to be admitting a continuous velocity distribution throughout the control volume, in conjunction with the assumption that the thickness of the deformation zone is mathematically zero, which results in a finite jump of velocity at the missile-target interface. In fact the thickness of  the deformation zone may be expected to be negligible in comparison with the length of the missile, but need not be mathematically null. In reality they found the lower limit to the reaction-time curve for Riera's model.
An attempt was made by Lange and Laue [9] to improve the material model by modelling it up to failure in a rational way. However, these refinements are questionable due to the general lack of information about the material behaviour at very high strain rates and the structural layout, etc. The hydrodynamic model used to determine the velocity of wreckage pieces does not yield conservative results [2]. An approach that involves significantly more computing effort was proposed by Drittler and Gruner [2]. This procedure was applied in [3] by the same authors to determine the reaction-time curve for a fast flying military aircraft, which was adopted as a design criterion in the Federal Republic of Germany. Bilinear elasto-plastic material behaviour and geometric linearity were assumed. The influence of the model discretisaion on the results deserves additional research.
In the most comprehensive study published to date, Wolf et al. [7] show that the reaction-time curve for a large commercial aircraft as obtained by Riera is practically indistinguishable form that obtained by modelling the aircraft with lumped masses interconnected by elasto-plastic springs. Gardner [4] showed clearly that the effect of gravitational forces upon the reaction is negligible. He found the reaction-time curves for an oblique impact upon a vertical or horizontal target with different confidence levels. Kinsella and Jowett [lo] presented a rather crude linear scaling procedure to group a range of military combat aircraft and determined the reaction response for normal impact upon a rigid target.

BASIC FORMULATION FOR NORMAL IMPACT
As a projectile strikes a target, a part of it close to the target gets crushed and the remaining portion of the projectile undergoes elastic deformation, which, from the point of view of deformation, may be regarded as rigid with not much error. So, consider a soft missile to consist of a thin deformation zone S, and a rigid zone S, within control volume S as shown in Fig. 4. The following assumptions have been made in the The aircraft is assumed as a one-dimensional model. Therefore, this model can yield only total force; it will not give variation of force on the contact area. It is assumed that the projectile axis and its flight trajectory coincide and the impact is normal. The aircraft is assumed to be soft. This assumption is justified because the impulse obtained for the aircraft usually lies close to the elastic projectile [4].
Assuming no torn-off wreckage pieces, no momentum crosses the boundary of the control volume.
centre of mass is the reaction from the target. If the mass entering the deformation zone remains confined without any further change, we can write where P,[x(t)] is the load necessary to crush or buckle the projectile. If the target is assumed to be rigid, the reaction from the target as given by eqn (3) reduces to Fig. 7. Probability density function for trajectories striking a target inclined at an angle 0 with horizontal.

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The assumption of a rigid target leads for most cases to conservative results. However, if it happens that a flexible wall deforms in such a way that rebound motion of the wall occurs during a time interval when the load function passes through its maximum, then higher maximum values for the load are to be expected than in the case of the rigid target. Now, let us apply the principle of conservation of energy to the control volume S at times t and t + dt.
Loss of kinetic energy of the rigid portion in time dt is equal to the sum of work done in plastic deformation of the missile and the residual kinetic energy of the mass after crushing.
where t). = yield strain; P,[x (r)]c, = work done in plastic deformation of unit length at coordinate x(t)=e (say); Jf = constant of proportionality between velocity of rigid portion V and residual velocity V' of mass after crushing. From this expression, we obtain The value of t,. has been taken as unity because complete crushing of missile length dx is considered. The value offwill lie between 0 and 1. If it is assumed that the missile after crushing gets deflected by 90.' (i.e. f = I), this expression becomes the same as  obtained in the conservation of momentum approach.
The rigid target assumption is claimed to be conservative and eqn (4) is usually followed for the determination of reaction time response. However, the claim is based on a rather stiff target. Therefore, the effect of target yielding has been investigated in a subsequent section.

OBLIQUE IMPACT
Although normal impact is likely to be the most unfavourable condition for the target structure, the same is not true for floor response spectra. Moreover, normal impact rarely occurs in real life and the conditional probability of normal impact is very small. Also, the orientation of the target structure may be such that the normal impact may not occur at a particular location on the target. It is for these reasons that oblique impact has also been considered in the present work.
Let tl be the inclination of the aircraft to the normal and 4 be the angle of friction between the target and the missile, which is assumed to be reliably estimated. If a < $, the impact point will be stationary and the normal F,, and tangential F, reaction can be found from the relations F,,= F[x(t)]coscr and F,= F[x(t)]sina.
On the other hand, when a > 4, an unbalanced tangential force 6F, appears at the target-missile interface and causes the contact point to move and rotates the missile, 6F, being given by Since a changes with time, for this particular case a has been replaced by a (t ). The application of classical dynamics for the rotation of the missile (Fig. 5) leads to 2 dI d% Ims+$df

=F[x(t)]L,,cosa(t)
x (sin 4 -sin a (t )), (9) where 0 is the change in the angle of inclination at time t such that GL (t ) = a (0) + 8; L, is the distance of the centre of mass of the rigid portion of the missile from the instantaneous point of impact and Z, is the mass moment of inertia of the uncrushed portion of the aircraft with respect to the centre of mass. The expression (9) has been used for calculating the change in the angle of inclination 0.

CONFIDENCE LEVEL FOR IMPACT REACTION
Considering the position of a flying aircraft as a random variable in three-dimensional space, the probability density function p(p) for an aircraft crash striking the structure may be defined by N'(P) P(P)=-N '(n PI N(a) = number of trajectories striking the target between 0 and a (11) Therefore, the probability P of an aircraft striking the structure at an angle less than or equal to fi is It is believed that an isotropic trajectory distribution is most relevant to the air crash problem. The consideration of a hemisphere by Reira [Ill and Gardner [4] is true only for aircraft striking a horizontal or vertical surface. However, we shall consider a segment of a sphere for an aircraft striking an inclined target (Fig. 6). The probability density function for such a case has been evaluated as explained below.
The area of a hypothetical segment of a sphere from which the trajectories can come is between the angles /I and #I + d@ to the target whose normal is inclined at an angle 0, with the horizontal. The probability density function for an isotropic trajectory distribution upon a structure is obtained as (Fig. 7) N'(a) = 2 sin u 2 -cos 0, for a ,< 0, sin a =2-cost?, for a > 0,.
If c% trajectories have an angle greater than an angle a, then the normal component of the reaction curve corresponding to a, will envelope c% of the normal reaction curves (see Fig. 8 whereas, for u, 2 0, The values of a,. for different confidence levels and inclinations of the target have been worked out and are given in Table 1. The most severe normal impact for c % confidence occurs when 0, = a, and it is given by the relation (%)"I," = &. (1-J) Equation (17) gives the values of (cI,),,,~~ for 50, 90 and 95% confidence levels as 48"11'23", 18"40'18" and 13"0'10", respectively. For a given value of LX,, c will be maximum when 0, = 90", whereas, for a given value of 8,, c will be maximum when a, = 0".

NUMERICAL SOLUTION
Numerical finite difference approach has been employed for determining the reaction from the target using the above described equations.
The impact process continues until any one of the following conditions are met: (i) velocity of aircraft diminishes to zero; (ii) angle of inclination of aircraft from normal to the target surface reaches 90' limit; (iii) missile gets completely crushed.
The variations of peak reaction and impact duration for the normal impact of three aircraft upon an unyielding target are shown in Figs 9 and 10. It is seen from these figures that the peak reaction increases with increase in velocity. However, the rate of increase for the Boeing and FB-111 aircraft is nearly the same, whereas it is much slower in case of the Phantom F4. Impact duration of the Boeing and FB-111 usually decreases but it is nearly constant for the Phantom F4. This behaviour for the Phantom F4 may be attributed to the sharp variations in crushing strength and linear mass density.
The horizontal and vertical components of the reaction-time curves for the three aircraft under study striking a horizontal or vertical target at 100 m/set velocity for the 90% confidence level are shown in Figs 11-13. The change in inclination due to the rotation of the aircraft is also shown in these figures. As an aircraft strikes at an inclination c1 to the target, its angle of inclination remains more or less constant until such time when the missile velocity reduces significantly. Beyond this, the inclination increases at a faster rate which results in a faster rate of reduction of the reaction for all three cases.

INFLUENCE OF VARIATION IN BUCKLING LOAD AND LINEAR MASS DENSITY
The sensitivity of the reaction time responses of an aircraft to the variation in crushing load and linear mass density of the aircraft has been studied. The crushing strength is magnified and reduced by a factor of two and linear mass density is varied by 10%. The response of this variation for the three aircraft under study is shown in Figs 1419. The contribution of buckling load towards total reaction can be seen in Figs 20-25 for the three aircraft under study for two velocities, 50 and 100 mjsec. It is seen from these plots that for stiffer aircraft the contribution of crushing strength towards reaction is greater, which further increases with decrease in velocity.
The influence of the buckling load for 50% variation and the linear mass density for 10% variation are also shown in Table 2.
It has been reported by others [5] that the precision required in the measurement of crushing strength is not so important.
This statement may be true for some cases (as seen above) but cannot be generalised. It is clearly seen from the above discussion that the mass density and the crushing strength are equally

EFFECT OF TARGET YIELDING
The effect of target yielding is studied by simultaneously calculating the reaction following relation (3). Outer containment of a typical NPP (Fig. 26) analysed by Rebora et al. [12] for the horizontal impact of the Boeing 707-320 at 230mph, has been considered in the present study.
The geometry of the containment shell, reinforcement details and corresponding mesh discretisation are shown in Fig. 26 of 40mm diameter bars spaced at a c/c distance of 80 mm (1.1%) placed circumferentially and meridionally in the cylindrical shell as well as in the spherical top dome. The material properties used in the analysis are taken from [12].
The shell is discretised into 52, 20-noded isoparametric brick elements with a total of 342 nodes leading to 1100 degrees of freedom of the structure. The horizontal impact of a Boeing 707-320 with a striking velocity of 102.82 mjsec (230 mph) on the RC containment is analysed. The area of impact is assumed to be 28 m2.
The reaction-time responses for the rigid target and the yielding target for the horizontal crashing of the three aircraft are plotted in Fig. 27. It is seen from these plots that reaction-time response is almost unaffected initially. However, when the peak reaction is reached, the response of the target becomes more pronounced, thereby affecting the reaction-time response. When the decline in the reaction is sharp, the target response will still be high but the velocity of the missile is considerably reduced, as a result of which the effect on the reaction becomes more pronounced, as in the case of the Boeing 707-320. In the case of the Phantom F4, the decline in the reaction is not so sharp, therefore the variation is not so noticeable. It is further noticed that the reaction-time response obtained on the basis of a rigid target is not even conservative.
In the case of a slender target, the effect of target response upon the reaction may be even more pronounced.
It is therefore undesirable to use the reaction-time response obtained on the basis of a rigid target concept as is the usual practice. It is noticed that the reaction-time response obtained on the basis of a rigid target is not only unrealistic but also unconservative. In the case of a slender target, the effect of target response upon the reaction will be more pronounced. The effect of target yielding is dependent upon both the characteristics of the target and those of the missile. It is therefore undesirable to use the reaction-time response obtained on the basis of a rigid target concept as is the usual practice. 3.
The concept of confidence level has been investigated in relation to inclined targets also and confidence curves have been obtained for the aircraft. Linear mass density and crushing strength significantly affect the reaction-time response, depending upon the characteristics of the aircraft (linear mass and crushing strength) and the striking velocity. 7. a.

Acknowledgements-The
first author wishes to thank his parent institute, Aligarh Muslim University, for granting leave to pursue a Ph.D. under the Quality Improvement Program (QIP) scheme of the University Grants Commission (UGC), India.