Predictions of displacements and stresses in cracked reinforced concrete containment vessels subjected to seismic loads

A three dimensional, nonlinear finite element analysis capability for analysis of cracked reinforced concrete nuclear containment vessels is described. A bilinear shear stress-shear strain model, based on experiments, is used to study the distribution of radial and tangential shear produced by horizontal seismic loading. Results show substantial redistribution of tangential shear, and significant increases in radial shear, peak bending stress, and vessel displacement, as compared to conventional linear analysis results.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Ultimate analysis of BWR Mark III reinforced concrete containment subjected to internal pressure

Numerical analyses are carried out by using the ABAQUS finite element program to predict the ultimate pressure capacity and the failure mode of the BWR Mark III reinforced concrete containment at Kuosheng Nuclear Power Plant, Taiwan, R.O.C. Material nonlinearity such as concrete cracking, tension stiffening, shear retention, concrete plasticity, yielding of reinforcing steel, yielding of liner plate and degradation of material properties as a result of high temperature effects are all simulated with proper constitutive models. Geometric nonlinearity as a result of finite deformation has also been considered. The results of the analysis show that when the reinforced concrete containment fails, extensive cracks take place at the apex of the dome, the intersection of the dome and the cylinder and the lower part of cylinder where there is a discontinuity in the thickness of the containment. In addition, the ultimate pressure capacity of the containment is 23.9 psi and is about 59% higher than the design pressure 15 psi.     

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.     

Nonlinear dynamic response of cracked reinforced concrete nuclear containment vessels

In the design of reinforced concrete nuclear vessels horizontal cracks are assumed to exist as a result of pressurization. Seismic shear forces must be transmitted across these cracks. The nonlinear dynamic response of cracked vessels is studied. The force-displacement relationship across the cracks are taken from the experimental investigation that included the shear transferred by the concrete but not by dowel action of the vertical steel. The stiffness is highly nonlinear, hysteretic, and degrading. A modal analysis technique, based on an eigenvalue reanalysis procedure, is developed and it is compared with a direct numerical integration solution. Only typical response values are given for particular values of the variables and for one particular earthquake input.     

Numerical modeling of reinforced concrete containment walls under cyclic shear

This paper provides an overview of research in numerical modeling of reinforced concrete containment walls subjected to cyclic shear. Bases for the development of the model are discussed, and application of the model is shown. Further research needs and interests are suggested for improved analysis capabilities and design.     

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.     

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.     

Conceptual design and analysis of a semi-passive containment cooling system for a large concrete containment

An internal evaporator-only (IEO) concept has been developed as a semi-passive containment cooling system for a large dry concrete containment. The function of this system is to keep the containment integrity by maintaining the internal pressure not to exceed ultimate design pressure, i.e. 0.83 MPa (120 psia) in the absence of any other containment cooling following a severe accident, which postulates core damage and hydrogen combustion. The ability of the concept to protect the containment was evaluated for the design basis accident (DBA) large break loss of coolant accident (LB LOCA) and severe accident scenarios (LB LOCA without Emergency Core Cooling System (ECCS) and containment spray flow, 100% zirconium oxidation and complete hydrogen combustion). All were modeled using the GOTHIC computer code. It was concluded that a practical system requiring four IEO loops could be utilized to meet design criteria for severe accident scenarios.     

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.     

Shell finite element of reinforced concrete for internal pressure analysis of nuclear containment building

This paper describes a 9-node degenerated shell finite element (FE), an analysis program developed for ultimate pressure capacity evaluation and nonlinear analysis of a nuclear containment building. The shell FE developed adopts the Reissner-Mindlin (RM) assumptions to consider the degenerated shell solidification technique and the degree of transverse shear strain occurring in the structure. The material model of the concrete determines the level of the concrete stress and strain by using the equivalent stress-equivalent strain relationship. When a crack occurs in the concrete, the material behavior is expressed through the tension stiffening model that takes adhesive stress into account and through the shear transfer mechanism and compressive strength reduction model of the crack plane. In addition, the failure envelope proposed by Niwa is adopted as the crack occurrence criteria for the compression-tension region, and the failure envelope proposed by Yamada is used for the tension-tension region. The performance of the program developed is verified through various numerical examples. The analysis based on the application of the shell FE developed from the results of verified examples produced results similar to the experiment or other analysis results.     

Research related to buckling design of nuclear containment

This paper discusses the recent experimental and analytical studies related to buckling design of fabricated steel shells. The effects of initial imperfections and residual stresses on buckling are under investigation. The test programs include ring and stringer stiffened as well as ring stiffened cylinders subject to combinations of axial compression and external pressure. Proposed modifications to ASME Code Case N-284, “Metal Containment Shell Buckling Design Methods,” as well as the need for additional research, are discussed.     

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.