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.     

Model tests of turbine missile impact on reinforced concrete

The results of 25 impact tests on 1/11-scale models of reinforced concrete nuclear plant walls are presented. These tests determined experimentally the maximum velocity at which postulated turbine missiles are contained by typical reinforced concrete walls. The parameters varied were missile weight, velocity, orientation, and impact angle, as well as target design and thickness. The results showed that the NDRC perforation formula used extensively in current practice is overly conservative, whereas a newer empirical formula (CEA-EDF) gave reasonably conservative predictions of the test results. All but the most energetic postulated missiles are stopped by containment wall models, and steel liners on these walls are effective in suppressing backface concrete scabbing.     

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.     

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.     

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.     

Non-linear response of reinforced concrete containment structure under blast loading

The paper demonstrates the effect of an external explosion on the outer reinforced concrete shell of a typical nuclear containment structure. The analysis has been made using appropriate non-linear material models till the ultimate stages. The generation and the propagation of blast wave and its effect on a cylindrical structure are discussed. Parametric studies have also been performed for surface detonations of different amount of blast charges at a distance of 100 m from a nuclear containment shell. Critical distances have been evaluated for different amount of blast charges for nuclear containment shell.     

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.     

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.     

Concept study for a combined reinforced concrete containment

A variety of different types of steel and concrete containments have been designed and constructed in the past. Most of the concrete containments had been pre-stressed, offering the advantage of small displacements and a certain leak-tightness of the concrete itself. However, considerable stresses in concrete as well as in the tendons have to be maintained during the whole lifetime of the plant in order to guarantee the required pre-stressing. The long-time behaviour and the ductility in the case of beyond-design-load cases must be verified. Contrary to a pre-stressed containment a reinforced containment will only be significantly loaded during test conditions or when needed in case of an accident. It offers additional margins which can be used especially for dynamic loads such as impacts or for beyond-design events.The aim of this paper is to show the feasibility of a so-called combined containment which means a containment capable of resisting both severe internal accidents and external hazards, mainly the aircraft crash impact as considered in the design of nuclear power plants in Germany.The concept is based on a lined reinforced containment without pre-stressing. The mechanical resistance function is provided by the reinforced concrete and the leak-tightness function is provided by a so-called composite liner made of non-metallic materials. Some results of tests performed at Siemens laboratories and at the University of Karlsruhe which show the capability of a composite liner to bridge over cracks at the concrete surface will be presented in the paper.The study shows that the combined reinforced concrete containment with a composite liner offers a robust concept with high flexibility with respect to load requirements, beyond-design events and geometrical shaping (arrangement of openings, an integration of adjacent structures). The concept may be further optimized by partial pre-stressing at areas of high concentration of stresses such as at transition zones or at disturbances around large openings.     

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.     

Numerical simulation of a high velocity impact on fiber reinforced materials

Whereas the calculation of a high velocity impact on isotropical materials can be done on a routine basis, the simulation of the impact and penetration process into nonisotropical materials such as reinforced concrete or fiber reinforced materials still is a research task.

We present the calculation of an impact of a metallic fragment on a modern protective wall structure. Such lightweight protective walls typically consist of two layers, a first outer layer made out of a material with high hardness and a backing layer. The materials for the backing layer are preferably fiber reinforced materials. Such types of walls offer a protection against fragments in a wide velocity range.

For our calculations we used a non-linear finite element Lagrange code with explicit time integration. To be able to simulate the high velocity penetration process with a continuous erosion of the impacting metallic fragment, we used our newly developed contact algorithm with eroding surfaces. This contact algorithm is vectorized to a high degree and especially robust as it was developed to work for a wide range of contact-impact problems. To model the behavior of the fiber reinforced material under the highly dynamic loads, we present a material model which initially was developed to calculate the crash behavior (automotive applications) of modern high strength fiber-matrix systems. The model can describe the failure and the postfailure behavior up to complete material crushing.

A detailed simulation shows the impact of a metallic fragment with a velocity of 750 m s⁻¹ on a protective wall with two layers, the deformation and erosion of fragment and wall material and the failure of the fiber reinforced material.     

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.     

Synopsis of the results from overpressurizing a reinforced concrete containment model

Sandia National Laboratories completed the testing of a 1:6-scale containment building for a light water reactor in July 1987. Results from this and other containment model testing are being used by the US Nuclear Regulatory Commission to benchmark analytical techniques. The validated techniques can then be used to predict the behavior of actual nuclear power plant containments to a variety of hypothesized severe accidents.The most recent containment building tested was made of reinforced concrete and had many of the features found in full-size containments. Testing consistent of a structural integrity test, and integrated leak rate test, and concluded with an overpressurization test of the structure. Highlights of the results from the overpressurization of the containment model are presented.     

Penetration resistance of reinforced concrete containment structures

Containment structures not only provide a leak tight barrier, but also play a role in ensuring that the structures can withstand the impact load from projectile impacts or internal plant accidents. In assessing the containment structures of nuclear power plants, predicting the characteristics of impact resistance in relation to design and safety considerations is relevant. This investigation proposes a simple but effective method of performing numerical analysis on perforation resistance of reinforced concrete containment structures. In this work, normal and oblique impacting is considered to examine the residual velocity and impact phenomena of an ogive-nose steel projectile with various impact velocities against a reinforced concrete slab. Additionally, a phase diagram is devised to describe the ballistic terminal phenomena of projectile and target. This model could assess the resistance to penetration to results in the optimum design of the containment structures in nuclear power plants.     

Research on modeling shear transfer in reinforced concrete nuclear structures

This paper provides an overview of research in modeling the mechanisms of shear transfer in reinforced concrete nuclear structures. Bases for the development of analytical models are discussed. Preliminary analysis results are presented for the wall specimens to study the behavior of a containment wall portion under biaxial tension and tangential shear loading. Further research needs and interests are suggested for improved analysis capabilities and design.     

Dynamic rupture analysis of reinforced concrete shells

Extreme dynamic loading conditions often require the rupture analysis of reinforced and prestressed-concrete structures. The study presented in this paper extends a method of analysis of dynamic loading conditions which has proven efficient for short- and long-time loads. Another aim is to adapt the method to thin-walled structures. It is not sufficient to work only with plastic rupture and yield surfaces locally which are compared to the elastic distribution of the stress resultants; it is essential to account for the redistribution of the latter. The method proposed consists of discretizing the structure into isoparametric three-dimensional elements with 20 nodes for the concrete and one-dimensional bar elements with three nodes for the steel. The latter can also be handled with a ‘smeared’ two-dimensional membrane element. In compression a three-dimensional non-linear elastic constitutive law is introduced for the concrete, and a triaxial failure surface expressed in the stress invariants is used, determining cracking and crushing. Two- and three-dimensional cracking surfaces in which no components of stress are transmitted are accounted for. The possibility exists that, during the history of loading, cracks can close up again. For steel, a yield criterion is selected. The non-linear analysis is based on the concept of initial stress. Residual loads are calculated using information in Gauss integration points. The ultimate load is reached when the algorithm does not converge. The corresponding failure modes can be interpreted as those for which a state of equilibrium is no longer possible. The equations of motion are discretized in time, using an extension of the linear acceleration method. As in the static case, several iterations are necessary to reduce the residual load vector to a negligible quantity. A built-in circular plate is analyzed for an evenly distributed load.The results with one and several isoparametric elements in width are compared to the solution determined with the classical yield line theory. Cracks in the concrete and yielding of the steel in both directions are properly represented. In the non-linear domain moment redistribution is observed which allows for a substantial increase in the ultimate load. All states of material behaviour are observed in the final stage. A thin-walled shell consisting of a cylinder and a sphere is also examined for a non-symmetric loading involving the interaction of membrane and bending behaviour. A dynamic non-linear analysis is performed for this load, which represents the impact of an airplane on the external shield building of a nuclear power plant. The non-linear analysis does allow for a substantial saving of reinforcement steel compared to the standard design procedure. Conclusions which include pitfalls, shortcomings and suggestions for future research are specified.     

Reliability assessment of reinforced concrete containment structures

A reliability analysis method for seismic category I structures subjected to various load combinations is developed and numerical examples are worked out under various assumptions and idealizations. The method falls generally within the so-called level III category within the framework of reliability analysis and design.     

Nonlinear dynamic analysis of reinforced concrete structures

Dynamic ultimate load calculations mainly for reinforced concrete beams and plates, are discussed. Starting from the corresponding differential equations, the calculations also include the rotational inertia of single beam or plate elements as well as the shear deformations. With actual structural dynamic problems in nuclear power plants, the shear behaviour of reinforced concrete beams and plates is more important than it is usually, as is shown by examples. The finite propagation velocity of bending and shear waves are taken into account. Solution of the equations of motion is obtained by numerical intergration using finite time and space intervals. The calculations are performed using time dependent bending and shear laws for reinforced concrete up to the point of failure with realistic deformations. These latest scientific developments are of great significance for dynamic ultimate load analysis in practice.Elastic-plastic examples of application are compared with corresponding linear-elastic solutions. It is shown that the design of construction members based on elastic-plastic dynamic stress calculations in general is economically advantageous. This important conclusion is proven by numerical results. Also the relation to the approximation of a one-degree-of-freedom dynamic system, including or excluding the plastic ductility of the structural member, is demonstrated.Finally, lumped-mass multi-degree systems calculated by integrating numerically the corresponding equations of motion, are dealt with briefly. A nonlinear dynamic calculation of a foundation of a recently built reactor building is presented as an example for blast resistant analysis.     

Study on a concrete filled structure for nuclear power plants

The feasibility of a new structural system for nuclear power plant buildings utilizing concrete filled steel structures, termed ‘SC structural system' was studied. SC wall test specimens (1/5 scale) were manufactured and compressive loading tests were carried out to determine how to prevent buckling. Also, bending shear tests were performed using H-section wall specimens to determine the shear and bending characteristics of SC walls. This paper presents an outline of the feasibility study, and the various structural properties resulting from the experiments.     

Material equations for steel fibre reinforced concrete members

The application of steel fibre reinforced concrete is a supplement to existing methods used in concrete constructions. In combination with conventional or prestressed reinforcement, structural members made of steel fibre reinforced concrete display high load bearing capacity, reliability and durability, making them well suited to withstand high dynamic forces (impact, vibration). Steel fibre reinforced concrete is an expensive material. Its use can only prove economical if its favourable properties are taken into account in design. In this contribution suitable material equations and results of selected tests and presented.