Several correlations of experimental data are available for predicting the damage to simple reinforced concrete panels from the impact of hard flat-nosed cylindrical steel billets. Scabbing damage corresponds to dislodgement of a portion of the target’s rear face, and perforation has its usual connotation. More than 150 experimental results are available for comparison against these formulae. Neilson [286] estab­lishes that the revised NRDC correlation affords the most accurate predictions for missile penetration depth, and for the scabbing to perforation transition. Though the missile velocity for the onset of

Figure 6.10 Effect of Reinforcement Quantity on the Perforation

scabbing is accurate in 71% of cases, predictions of the perforation velocity are only 57% successful due to the lack of a reinforcement term in the correlation. During an attempted perforation steel reinforcement bars absorb energy by bending and shear, as well as by providing a net to retain broken concrete within the panel. Experimental results from Winfrith [286] in Figure 6.10 confirm a progressive increase in perforation velocity Vp with the amount of reinforcement, and they are correlated by

where

r — amount of square mesh reinforcement (% EWEF)

% EWEF — per cent of cross-sectional area occupied by the same square (EW) steel reinforcement just below the surface of each face (EF)

EW — “each way” (horizontal + vertical)

Other Winfrith experiments show that the perforation velocity for steel-faced concrete panels can be predicted by equation (6.5) if the thickness of a rear plate is converted to an equivalent reinforcement percentage. For example, a 1 mm thick rear plate on a 100 mm thick concrete panel corresponds to 1% EW. In the case of a front steel panel, the perforation energy of the composite is the sum of their individual perforation energies. The Ballistics Research Laboratory and Winfrith data are best correlated [286] especially for thicker steel panels by

E ‘ 1.44 x 109(hd)15 within ± 15% (6.6)

where

E — perforation energy (J); h — steel panel thickness (m) d — missile diameter (m); hd<3.4 x 10“3

Ohte et al. [287] confirm that conically-nosed hard missiles perforate targets more readily than flat-nosed ones. For specific missile-target combinations the perforation energy for a hard missile having a 45° half-angle nose is consistently about half that predicted by the BRL formula. With modification of panel thickness and missile diameter as a function of nose-angle in the BRL correlation satisfactory predictions of perforation energy are obtained.

Impacts of irregularly shaped fragments from a disintegrating steam turbine on reinforced concrete, metal panels or major pipe work are important safety issues especially for nuclear plants. Also of real concern is the perforation of a reinforced-concrete containment by aircraft whose geometries and crushing strengths are axially non­uniform. Though correlations are often sufficient for their specific physical situations having regular simple geometries, applications outside the experimental databases can lead to erroneous predictions. For example a linear extrapolation of the Canfield-Clator correlation [288] for steel projectiles impacting reinforced concrete wrongly suggests that no perforation would occur [289] at velocities less than 150 m/s. Empirical correlations for simple missile and target geometries are therefore inadequate for nuclear plants. Furthermore, the construction of complex replica models would not be cost — effective.

Accordingly the preferred option is the development of comprehensive physics-based computer simulations that are systematically validated by means of replica experiments with simple, but representative portions of the pertinent structures. Finite element techniques [290-293] were developed at Winfrith to pursue this strategy from about 1980.

In essence a finite element calculation divides the region for integrating a partial differential equation into sub-regions (finite elements) that are usually triangular or rectangular, though curved boundaries can be readily accommodated [293]. Values of the required solution at the elements corners constitute the “unknowns,” and for small enough elements the solution varies linearly across each element. However, higher-order numerical approximations can be formulated to allow larger mesh sizes [292]. Elliptic equations and the biharmonic equations of structural dynamics are both well suited to finite element techniques because their solutions are equivalent to the minimization of a quadratic functional (e. g., energy). In this form the required values become the unique solution of a linear equation having a positive definite matrix [115]. Galerkin’s method is equivalent, if applicable, to a variational approach but the resulting matrix is less sparse and has weaker numerical conditioning [115,292]. Early implementations of the finite element method involved a manual construction and labelling of the mesh that is evidently tedious, error prone and therefore a sizeable portion of the overall cost. Specific computer codes now automate data preparation and the interactive creation of a suitably graded mesh. However, considerable skill and experience are still required to achieve a successful outcome. Numerical solutions with finite elements are presently available for structures involving crushable materials, strain-rate dependent elasto-plastic materials and reinforced concrete with interfacial friction [296]. Dedicated software also assists the interpretation and presentation of computed

solutions. The following example illustrates the overall methodology for an aircraft crashing into a reinforced reactor containment.

Prior to unification the large number of military overflights led the Federal German Government to legislate that a nuclear reactor containment must withstand the impact of a Phantom RF-4E aircraft at 215 m/s. However, no such prescriptive requirements apply in the United Kingdom where each site must be separately assessed. Two principal safety concerns are

i. whether a crashing aircraft can perforate the secondary con­tainment or cause unacceptable damage

ii. the nature of vibrations transmitted to the rest of the structure.

Because the crushing strength of an impacting aircraft is so much less than the collapse loading of a reinforced concrete containment, it is therefore a soft missile and deformation of the concrete structure can be neglected in calculating the imposed transient loading. Riera [67] first quantified the situation as part of a safety assessment for the Three Mile Island installation near Harrisburg Airport. His principal assumptions are that an impact produces a region of compacted stationary debris and that the undistorted portion of an airframe continues on towards the target. By Newton’s second and third laws of motion the total reaction force R(t) on the building is

R(t) = — (mV) = mV + m V (6.7)

where m and V denote respectively the instantaneous mass and velocity of the undistorted portion of the aircraft. If a structure is slowly crushed in a hydraulic press, the involved mass remains constant throughout so the term mV is termed the crushing force Fc of the intact portion. With this nomenclature, equation (6.7) becomes

R(t) = Fc(t) + mV2 (6.8)

where Fc(f)now contains an allowance for strain-rate enhancement and m denotes the instantaneous mass per unit length of the residual airframe. By further assuming that impact velocities remain constant at the approach velocity, the aircraft manufacturer’s drawings then

Figure 6.11 Reaction Loadings for Typical Aircraft

provide data for a conservative evaluation of the transient reaction loading on a building. A refinement of the above analysis represents each structurally different longitudinal section of an aircraft, and the loss of mass by dispersed fragmentation should its ultimate compressive

Figure 6.12 Replica Aircraft Model

strength be exceeded [294,295]. These reaction loadings [289] for the impacts of a Boeing 707, Phantom RF-4E, and a Tornado on a rigid structure are graphed in Figure 6.11.

Replica 1/25th scale experiments were performed at Winfrith for an aircraft impacting a proposed reactor containment at around 220 m/s. The aircraft model is shown in Figure 6.12, and the curved reinforced containment was simulated by a flat panel with a massive circumferen­tial ring-beam to provide an edge restraint representative of the remain­ing structure. Axial mass and stiffness distribution of the model aircraft were engineered to reasonably match the design reaction loading like that in Figure 6.11 The scaled reaction loading in Figure 6.13 formed

the input to a DYNA-3D finite element code as a transient pressure on the impact zone of the experimental reinforced concrete barrier. A computer simulation then predicted its crack formation etc allowing for interaction between the concrete and its reinforcement. Code validation was as usual sought by comparison with the replica experi­ments. Though cracking was generally over-predicted [289], good agreement was achieved with regard to transient deflections [296]. Moreover, though model experiments indicated the perforation of a 1 m thick prototype barrier and severe damage at 1.5 m thickness, a 2 m thick containment appeared to be essentially undamaged.

To conclude, the range of Winfrith replica experiments have extensively validated the DYNA-3D code modules for crushable mate­rials, strain-rate-dependent elasto-plastic materials and reinforced con­crete with interfacial friction. Nuclear safety assessments can now be confidently implemented with regard to the impact of disintegrating plant items or crashing aircraft on concrete buildings, steel panels or pipe work.