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.     

Analysis of aircraft impact to concrete structures

Analysis of aircraft impact to nuclear power plant structures is discussed utilizing a simplified model of a “fictitious nuclear building” to perform analyses using LS-DYNA software, representing the loading: (i) by the Riera force history method and (ii) by modeling the crash by impacting a model of a plane similar to Boeing 747-400 to the structure (i.e., “missile–target interaction method”). Points discussed include: (1) comparison of shock loading within the building as obtained from the Riera force history analysis versus from the missile–target interaction analysis, (2) sensitivity of the results on the assumed Riera force loading area, (3) linear versus nonlinear modeling and (4) on failure criteria.     

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.     

Integrated impact failure analysis of concrete slab structures with consideration of impact load characteristics

This paper describes a method of integrating a multi-mass model, which is applied to simulate the impact load characteristics for an impact collision, to a dynamic finite element analysis for concrete slab structures through an interactive procedure. Examples of the applicability and merit of the proposed linked procedure are then discussed.     

Research needs for design of concrete containment structures

Potential failure modes of reinforced concrete containment shells are outlined, especially those associated with pressure-induced cracking and seismic forces. A summary is given of experimental and analytical research needed to evaluate tangential shear capacity and stiffness, the interaction between liner and cracked concrete, peripheral (punching) shear capacity, radial shear behavior, and nonlinear dynamic analysis approaches.     

A study on dynamic impact of vertical concrete cask tip-over using explicit finite element analysis procedures

This work presents a study on dynamic impact of a vertical concrete cask (VCC) tip-over, using explicit finite element analysis (FEA) procedures. The VCC presented in this paper is made of reinforced concrete casted with a steel liner for accommodating a canister containing spent nuclear fuels. An explicit FEA code, LS-DYNA, is employed to treat the highly nonlinear problems encountered in postulated tip-over events. The plasticity and fragmentation of concrete are respectively treated by the pseudo-tensor material model and the element erosion technique. The interface de-bonding between VCC concrete and steel liner, contact/impact between VCC and target pad are all considered in order to investigate the reasonable impact load for cask design. Four cases with various analysis assumptions are respectively implemented and compared one another for ease of getting design load. The significance of interface de-bonding and concrete fragmentation in VCC to spent fuel cask design is highlighted in the reported numerical results.     

Verification of methods of analysis for soft missile impact problems

As part of a research project on the dynamic response of nuclear power plant structures subjected to impact loading, several computer programs have been developed to evaluate the reaction vs. time curve for ‘soft’ missiles impinging against fixed or moving targets. The mathematical-mechanical features of these computer programs are outlined, and reaction-time curves obtained by means of these programs are compared with experimental results. The influence of model discretization and of relevant input parameters is discussed, and areas in which further research is needed are indicated. It is shown that the mean reaction-time curve at the interface between missiles impinging against rigid or very stiff targets can be reliably predicted if the crushing strength of the missile is known.     

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.     

Research requirements for improved design of reinforced concrete containment structures

Reinforced concrete is a competitive material for the construction of nuclear power plant containment structures. However, the designer is constrained by limited data on the behavior of certain construction details which require him to use what may be excessive rebar quantities and lead to difficult and costly construction. This paper discusses several design situations where research is recommended to increase the designer's options, to facilitate construction, and to extend the applicability of reinforced concrete to such changing containment requirements as may be imposed by an evolving nuclear technology.     

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.     

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.     

Refined cracked concrete analysis of concrete containment structures subject to operational and environmental loadings

Recent commercial nuclear power plant containment concepts involve the use of large reinforced concrete structures to form pressure boundaries. Where these structures are not provided with an integral steel liner, excessive cracking of the concrete under loads could result in the loss of the pressure boundary integrity with the risk of over-pressurization of other structures. Cracking of concrete is a local phenomenon and considerable detail must be included in any analytical model to obtain sufficiently refined results for the prediction of crack size and propagation. This imposes severe limitations on the overall size of structures or structural components for which detailed cracking analysis can be considered directly. To overcome this restriction, a two step procedure was developed in which linear analyses were performed to obtain the gross response, and nonlinear cracking analyses were performed for selected portions of the structure to evaluate local cracking in detail. Through iteration, compatibility of behavior between the linear and nonlinear analyses was achieved with the gross response being used to extrapolate the local cracking results to predict cracking over the entire structure. This paper discusses the analysis procedures for the detailed evaluation of cracking in large reinforced concrete structures and components. Analyses performed for an actual unlined reinforced concrete containment structure using these procedures are discussed and results are presented.     

Failure and fracturing analysis of concrete structures

Some aspects of fracture analysis of concrete structures are discussed in this article. In particular it is shown that when localized failure occurs (by macrofracture propagation or localization of strain) structural size effects come into play. Mesh dependent finite element solutions are then observed unless size effects are correctly accounted for.Tensile fracture is examined first. The “classical” discrete and smeared crack approaches are reviewed and their extension to nonlinear fracture models like the fictitious crack model and the crack band model is illustrated. The smeared crack approach coupled first with a tensile strength criterion, second with a linear elastic fracture mechanics criterion is then applied to the failure mode analysis of a PCRV.Plastic fracturing with localization into shear bands, strain softening, mesh dependence and its correction are examined next. The use of plasticity for tensile fracture simulation is also discussed.Finally numerical difficulties inherent to the modeling of softening behavior are investigated.     

Local effects of impactors on concrete structures

Available formulae for predicting the penetration depth, scabbing thickness, and perforation thickness of concrete structures impacted by solid missiles are summarized, reviewed, and compared. Based on quadratic and cubic regression analysis of existing data, two new formulae have been proposed for predicting the penetration depth of concrete due to the impact by solid missiles. The new penetration equations are compared statistically with NDRC penetration formula and two other recent penetration formulae. Also, new simple formulae have been proposed for predicting the scabbing thickness and perforation thickness of concrete walls.     

Serviceability design load factors and reliability assessments for reinforced concrete containment structures

A reinforced concrete nuclear power plant containment structure is subjected to various random static and stochastic loads during its lifetime. Since these loads involve inherent randomness and other uncertainties, an appropriate probabilistic model for each load must be established in order to perform reliability analysis. The current ASME code for reinforced concrete containment structures are not based on probability concepts. The stochastic nature of natural hazard or accidental loads and the variations of material properties require a probabilistic approach for a rational assessment of structural safety and performance. The paper develops probability-based load factors for the limit state design of reinforced concrete containment structures. The purpose of constructing reinforced concrete containment structure is to protect against radioactive release, and so the use of a serviceability limit state against crack failure that can cause the emission of radioactive materials is suggested as a critical limit state for reinforced concrete containment structures. Load factors for the design of reinforced concrete containment structures are proposed and carried out the reliability assessments.     

On three-dimensional nonlinear analysis of concrete structures

Solution capabilities for three-dimensional geometric and material nonlinear finite element analysis of concrete structures are presented. The concrete material is modeled including triaxial nonlinear stress-strain behavior, tensile cracking, compression crushing and strain-softening. The objective in this work was the development of a practical nonlinear concrete analysis capability. The material model can also be employed to represent some rock materials. The results of various sample analyses are given, in which the stability and accuracy of the finite element representations have been studied.     

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.     

Application of the distinct element method to the analysis of the concrete members under impact

In this paper, the distinct element method is applied to the analysis of the behavior of a structure under impact. At first, this method is applied to the one-dimensional wave propagation problem by comparing with the experimental results and the theoretical results. The effectiveness of this method is confirmed by including not only elastic behavior but also the fracture of a structural member. Second, this method is developed to two-dimensional problems to simulate the behavior of a simply supported beam under an impact load. Finally, it could be shown that this method is effective to simulate wide phenomena from elastic behavior to a fracture under impact.     

Research and development of inelastic analysis procedures for reactor component design in Japan

The paper presents a survey of the activities taken by the JSME Subcommittee on Research and Development of Methods for Inelastic Structural Analysis to promote inelastic analysis procedures for high temperature reactor component design. An overview of benchmark test problems for the qualification of computer programs is given.