Hard missile impact on reinforced concrete

New penetration, scabbing and perforation formulae are derived for use in the design of reinforced concrete barriers to withstand impact by hard missiles. This is done by using dimensional analysis together with physical theories for the various impact processes. This leads to impact formulae with unknown coefficients which are then determined by an analysis of all available test data. The new formulae so derived are simple and, because of their parametric formulation, have a range of applicability easily definable in terms of impact parameters. The analysis indicates that some recently proposed impact formulae are not safe from the point of view of barrier design because the test data used for their derivation was affected by global movement of the barriers which reduced the measured local damage.     

Numerical studies of impact on reinforced concrete beam of hard missile

The safety design of concrete containment structures in nuclear power stations has thus far covered only accidents due to internal pressure, temperature loading and earthquake loading. Recently, designers and researchers have become interested in the important effects of the impact load of a projectile on nuclear power stations. This paper develops an FEM model for analyzing the collision of a hard missile against reinforced concrete structures and compares the results with impact tests conducted at our institute.     

Local response of reinforced concrete to missile impacts

An experimental and computational study was undertaken to determine the response of reinforced concrete walls to impacts from postulated tornado and other missiles. The study included laboratory-scale missile impacts, experiments to characterize concrete, computational model development, and two-dimensional simulations of missile impacts. Impact experiments with rods and pipes on small reinforced concrete walls showed crushing, cratering, spalling, radial cracking, and plug formation. The mechanisms governing this material response appear to be crushing, shearing, and tensile fracture. Static triaxial and dynamic plate impact experiments were used to determine the material properties. Dynamic strengths were higher than static; tensile strengths were ten times as high. A CAP constitutive model developed for concrete described compaction, Mohr-Coulomb yielding, and tensile separation following tensile strain accumulation. Model parameters were derived separately from the dynamic and the static data. Two-dimensional computational simulations were made of a rod impact experiment with threshold cracking using both static and dynamic parameters. The correct locations of fractures were predicted with the static parameters, but penetration and severity of failure were overpredicted. Penetration distance was correctly given with the dynamic parameters, but fracture was underpredicted. A model combining dynamic shaer and compaction properties with intermediate-rate tensile properties may be appropriate.     

Missile impact on a reinforced concrete structure

In this analysis an attempt was made to study the behaviour of a reinforced concrete structure under missile impact loading. The local deformations in all directions including the wall thickness, the plasticity and the stress waves at and surrounding the impact point were taken into consideration. The data of the impacting steel missile and the shape of the target concrete wall were given. As the impacting time is short in comparison to the fundamental eigenfrequency of the structure, it is possible to study the local deformation by isolating the impacted zone and its surroundings from the total structure. The boundaries of this region were considered as fully clamped. The results justified this assumption as the stresses at and near the boundaries were negligible in comparison to their counterpart at the impacting point. The PISCES 2 DL code was considered suitable for this type of calculation. Special routines defining the material and yield models for reinforced concrete were integrated in the program system.     

Local damage assessment of turbine missile impact on composite and multiple barriers

Fracture of rotary machines could result in turbine missiles, which are the irregularly shaped projectiles travelling at high velocities. The impact of such missiles on barriers in nuclear power plants has the potential to cause severe damages to the facilities, and endanger public safety. This paper applies the available damage assessment models for composite and multiple barriers to test data from experimental works of the past 2 decades. A method of analysis is used in which the missile's residual velocity after perforating each layer becomes the impact velocity for the next layer. The study indicates that composite action of dissimilar materials acting as a single unit improves the efficiency of the barrier. Recommendations are made as to the most accurate models and most appropriate parameters for barriers made of concrete and steel layers.     

Tangential shear tests of reinforced concrete containment elements

An experimental program to investigate the behavior of large scale reinforced concrete elements subjected to biaxial tension and shear forces is described. Six tests are being conducted on specimens 5 ft(1.52 m) square and 2 ft(0.61 m) thick, with no. 14 and no. 18 reinforcement. Program variables are level of biaxial tension, and monotonic vs. reversing shear load. Two monotonic tests have been completed to date. Behavior, strength, and deformations observed in these two monotonic tests are discussed.     

Comportement local des enceintes en beton sous l'impact d'un projectile rigide: Local behaviour of reinforced concrete walls under missile impact

Since 1974 CEA and EDF have developed in France a large programme with the aim to work out a means of computation reliable enough for the knowledge of the behaviour of reinforced concrete walls under missile impacts. The shots were performed on reinforced concrete slabs, the thickness of which were chosen to represent in a realistic way the thickness of the wall of a reactor containment. The scales used in this modeling were mainly one-half and one-third. The following parameters were kept constant: the properties of the concrete and the geometric shape of the missile (flat nose). Also studied were the effects of variation of parameters like missile velocity (25–450 m/s), its mass (20–300 kg), ratio of the missile diameter to the thickness of the slab (0.24–2.9) and characteristics of the steel reinforcement.The results of these tests may be summarized in a homogeneous perforation formula in the case of a velocity lower than 200 m/sec: where Vc is the minimum velocity for perforation, ø diameter of the missile, M its mass, σ the ultimate compressive strength of the concrete, its density and ρ its thickness.     

Application of an impact analysis code to reinforced concrete structures

A numerical constitutive model representing the behavior of concrete material is proposed in this paper. The stress-strain relations are kept in accordance with the updated information, such as stress, strains, strain rates in the principal directions of stress, crack states, yield states, rupture states. The algorithm of the constitutive model was implemented to the explicit impact analysis code DYNA3D. The experimental tests were also held, in which a 100 kg weight with 8 m/s velocity drops onto a reinforced concrete structure. The results of the DYNA3D analysis were compared with those of the tests and show a good agreement.     

Research status and needs for shear tests on large-scale reinforced concrete containment elements

Reinforced concrete containments at nuclear power plants are designed to resist forces caused by internal pressure, gravity, and severe earthquakes. The size, shape, and possible stress states in containments produce unique problems for design and construction. A lack of experimental data on the capacity of reinforced concrete to transfer shear stresses while subjected to biaxial tension has led to cumbersome if not impractical design criteria. Research programs recently conducted at the Construction Technology Laboratories and at Cornell University indicate that design criteria for tangential, peripheral, and radial shear are conservative.This paper discusses results from recent research and presents tentative changes for shear design provisions of the current United States code for containment structures. Areas where information is still lacking to fully verify new design provisions are discussed. Needs for further experimental research on large-scale specimens to develop economical, practical, and reliable design criteria for resisting shear forces in containment are identified.     

Probabilistic methodology for turbine missile risk analysis

A methodology has been developed for estimation of the probabilities of turbine-generated missile damage to nuclear power plant structures and systems. Mathematical models of the missile generation, transport, and impact events have been developed and sequenced to form an integrated turbine missile simulation methodology. Probabilistic Monte Carlo techniques are used to estimate the plant impact and damage probabilities. The methodology has been coded in the TURMIS computer code to facilitate numerical analysis and plant-specific turbine missile probability assessments. Sensitivity analyses have been performed on both the individual models and the integrated methodology, and probabilities have been estimated for a hypothetical nuclear power plant case study.     

Local damage of reinforced concrete slabs by impact of deformable projectiles

This study is to get informations about the local damage of reinforced concrete slabs by the impact of deformable projectiles. Five types of projectiles with different magnitudes of axial strength were employed for the impact tests. The target specimen were 0.6 m square reinforced concrete slabs with different thickness ranging from 7.0 to 15.0 cm. The striking velocity was kept at 200 m/s in all tests. And the effects of the projectile nose shape on the extent of local damage were also investigated experimentally.     

Effect of reinforcement ratio on the resistance of reinforced concrete to hard projectile impact

This paper discusses the effect of the reinforcement ratio on the perforation resistance of reinforced concrete elements, and proposes a way to evaluate it quantitatively. A review of the works that refer to the reinforcement effect on the perforation resistance, is followed by a theoretical quantitative evaluation of this effect. This theoretical expression is then used to modify existing perforation formulae, such that they include the reinforcement ratio as a variable. The theoretical results are compared to experimental results of tests that were planed to observe the resistance of concrete plates with different reinforcement ratios, to hard projectile impact.     

Long-term tests of reinforced concrete beams loaded by temperature gradient or settlement of a support

The creep of concrete has a considerable influence on the relaxation of the restraint effects and restraint stresses; particularly if the temperature of the concrete is higher than normal. The risk of cracking, for example, caused by the settlement of supports, is also diminished owing to creep; particularly if the rate of restrained displacement (settlement of a support) is slower than the rate of creep. It is difficult to consider the effect of relaxation from a calculational point of view, because the time dependences of several factors cannot be reliably modelled.In this research the relaxation of the restraint effects, due to both sudden and slow settlement of a support, was examined as a function of time; the relaxation of the restraint effect due to a thermal gradient was also investigated. In particular, was observed that the relaxation was fairly rapid in a heated beam. The relaxation of restraint effects caused by the settlement of supports was also considerable.     

A review of procedures for the analysis and design of concrete structures to resist missile impact effects

Concrete containment walls and internal concrete barrier walls are often required to withstand the effects of missile impact. Potential missiles include external tornado generated missiles (steel rods, steel pipes, wooden poles, and automobiles), aircraft crash, and internal accident generated missiles (turbine blade, and steel pipe missiles resulting from pipe break). Impacting missiles can be classified as either ‘hard’ or ‘soft’ depending upon whether the missile deformability is small or large relative to the target deformability. This paper only deals with the effects of ‘hard’ missile impact. Missile velocities between 100 and 1500 ft/sec are emphasized. ‘Hard’ missile impact results in both local wall damage and in overall dynamic response of the target wall. Local damage consists of spalling of concrete from the front (impacted) face and scabbing of concrete from the rear face of the target together with missile penetration into the target. If damage is sufficient the missile may perforate or pass through the target. This paper reviews the various empirical procedures commonly used for determining penetration depth, perforation thickness, and scabbing thickness for concrete targets subjected to ‘hard’ missile impact. Results obtained from these procedures are compared with test data results for low velocity impacts (200–1500 ft/sec). Design recommendations to prevent detrimental local wall damage are presented. Overall dynamic response of the target wall consists of flexural deformations and a potential flexural or shear failure if the strain energy capacity of the wall does not exceed the kinetic energy input to the wall by the striking ‘hard’ missile. Simplified procedures are defined for determining the dynamic response of the target wall and for preventing overall failure of the wall. Included are procedures for defining the effective target mass to be used in determining the fraction of the total missile kinetic energy which is transferred or ‘input’ into the target wall. Also included are procedures for defining the total strain energy capacity of the target wall as determined from the moment and rotational capacities of flexural yield hinges and the yield line deformation pattern of the wall. Lastly, criteria for preventing a premature shear failure are presented.     

Response of buried pipes to missile impact

This paper presents the methodology and results of the analyses carried out to determine an effective layout and the dynamic response of safety related cooling water pipes, buried in backfill, for the Alto Lazio Nuclear Power Plant in Italy, subjected to missile impact loading at the backfill surface. The pipes are composed of a steel plate encased in two layers of high-quality reinforced concrete.The methodology comprises three steps. The first step is the definition of the ‘free-field’ dynamic response of the backfill soil, not considering the presence of the pipes, through a dynamic finite element direct integration analysis utilizing an axisymmetric model.The second step is the pipe—soil interaction analysis, which is conducted by utilizing the soil displacement and stress time-histories obtained in the previous steps. Soil stress time-histories, combined with the geostatic and other operational stresses (such as those due to temperature and pressure), are used to obtain the actions in the pipe walls due to ring type deformation.For the third step, the analysis of the beam type response, a lumped parameter model is developed which accounts for the soil stiffness, the pipe characteristics and the position of the pipe with respect to the impact area.In addition, the effect of the presence of large concrete structures, such as tunnels, between the ground surface and the pipe is evaluated.The results of the structural analyses lead to defining the required steel thickness and also allow the choice of appropriate embedment depth and layout of redundant lines. The final results of the analysis is not only the strength verification of the pipe section, but also the definition of an effective layout of the lines in terms of position, depth, steel thickness and joint design.     

Analytical studies on local damage to reinforced concrete structures under impact loading by discrete element method

This paper proposes a new analytical approach for assessing local damage to reinforced concrete structures subjected to impact load, by applying the discrete element method (DEM). It first outlines the basis concept and analytical formulation of the DEM. Next, it discusses the results of simulation analyses of concrete material tests, uni-axial compression tests and tensile splitting tests conducted to determine appropriate analytical parameters such as material constants, failure criteria and strength increase factors depending on strain rate. Finally, the adaptability of the DEM to local damage to reinforced concrete structures impacted by rigid and deformable missiles is verified through simulation analyses of various types of impact tests. Furthermore, the various impact response characteristics and failure mechanisms, such as impact forces, penetration behavior, reduction in missile velocity and energy transfer process, which are difficult to obtain experimentally, are analytically evaluated by the DEM.     

Analysis of reinforced concrete containment vessels considering concrete cracking

Cracking of concrete influences the stress analysis of concrete containment vessels. If cracking is ignored, the resulting shell analysis can be unconservative in some cases and extremely conservative in others. A cracked concrete shell is a structurally orthotropic one. That is, it does not have the same properties in membrane action and bending action. Closed form equations are presented for cracked concrete shells using the split rigidity concept. The equations cover symmetrically loaded cylindrical shells, effects of concentrated forces and moments on spherical shells, and effects of openings and concentrated forces and moments on cylindrical shells. In addition, methods are discussed that can be applied to cracked concrete shells by using finite element techniques.     

Pipe-to-pipe impact tests

Existing licensing criteria express what damage shall be assumed for various pipe sizes as a consequence of a postulated break in a high energy system. The criteria are contained in Section 3.6.2 of the Standard Review Plan, and the purpose of the program described with this paper is to evaluate the impact criteria by means of a combined experimental and analytical approach.A series of tests has been completed. Evaluation of the tests showed a deficiency in the range of test parameters. These deficiencies are being remedied by a second series of tests and a more powerful impact machine.A parallel analysis capability has been developed. This capability has been used to predict the damage for the first test series. The quality of predictions has been improved by tests that establish post-crush and bending relationships.Two outputs are expected from this project:

• - data that may, or may not, necessitate changes to the criteria after appropriate value impact evaluations.

• - an analytic capability for rapidly evaluating the potential for pipe whip damage after a postulated break.

These outputs are to be contained in a value-impact document and a program final report.     

Equivalent loading due to airplaine impact taking into account the non-linearities of impacted reinforced concrete buildings

The airplane impact loading condition applied to a nuclear power plant building usually leads to very large excitations locally around the impact point and in the overall structure. This excitation is also characterized by a wide frequency content (up to 100 Hz). The state of the art of assessing the effect of an airplane impact was to apply a widely recognized rigid load function (RLF) impact force determined with Riera's Method to a linear elastic structure model and to perform calculations in order to obtain time histories and acceleration spectra. Because the real response of the building is not only governed by the elastic behaviour but also by the non-linear behaviour of the cracked and damaged concrete around the impact point the results obtained by this procedure are very conservative for the main part of the structure. The object of the paper is to present a numerical method of determining the dynamic response at characteristic points of the building taking into account the non-linear behaviour of locally impacted cracked damaged concrete.The method is based on the determination of a verified load function (VLF) which, applied to a linear elastic model of the structure, leads to the same response of the building (far from the impact point) as that due to the RLF impact force applied to a more realistic non-linear model of the reinforced concrete building. The practical advantage of using this procedure is that it avoids long and costly non-linear time integration of a full structural model.In order to obtain the VLF one only performs non-linear explicit calculations locally which include the main physical phenomenon occurring in an impacted reinforced concrete structure.     

Tests of spinning turbine fragment impact on casing models

Ten 1/11-scale model turbine missile impact tests were conducted at a Naval spin chamber test facility to assess turbine missile effects in nuclear plant design. The objective of the tests was to determine the effects of missile spin, blade crush, and target edge conditions on the impact of turbine disk fragments on the steel casing. The results were intended for use in making realistic estimates for the initial conditions of fragments that might escape the casing in the event of a disk burst in a nuclear plant. The burst of a modified gas turbine rotor in a high-speed spin chamber provided three missiles with the proper rotational and translational velocities of actual steam turbine fragments. Tests of bladed, spinning missiles were compared with previous tests of unbladed, nonspinning missiles. The total residual energy of the spinning missiles, as observed from high-speed photographs of disk burst, was the same as that of the nonspinning missiles launched in a piercing orientation. Tests with bladed missiles showed that for equal burst speeds, the residual energy of bladed missiles is less than that of unbladed missiles. Impacts of missiles near the edge of targets resulted in residual missile velocities greater than for central impact.