Evaluation of calculational and material models for concrete containment structures

A computer code utilizing an appropriate finite element, material and constitutive model has been under development as a part of a comprehensive effort by the Electric Power Research Institute (EPRI) to develop and validate a realistic methodology for the ultimate load analysis of concrete containment structures. A preliminary evaluation of the reinforced and prestressed concrete modeling capabilities recently implemented in the ABAQUS-EPGEN code has been completed. This effort focuses on using a state-of-the-art calculational model to predict the behavior of large-scale reinforced concrete slabs tested under uniaxial and biaxial tension to simulate the wall of a typical concrete containment structure under internal pressure. This paper gives comparisons between calculations and experimental measurements for a uniaxially-loaded specimen. The calculated strains compare well with the measued strains in the reinforcing steel; however, the calculations gave diffused cracking patterns that do not agree with the discrete cracking observed in the experiments. Recommendations for improvement of the calculational models are given.     

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.     

Experimental investigations of pressure and temperature loads on a containment after a loss-of-coolant accident

For the design of an LWR containment one of the important conditions to be considered is the rapid rise of internal pressure and temperature caused by a loss-of-coolant accident (LOCA) of the primary cooling system. The phenomena occurring within a containment during a LOCA are currently investigated through experiments with a model containment. The experimental results are compared with the results of model calculations to improve the calculational methods.An experimental facility was built, consisting of a primary coolant circuit and a special model containment. The model containment, built in conventional reinforced concrete, has a diameter of 12 m, a height of 12.5 m, a capacity of 580 m³ and is designed for an internal pressure of 6 bar. The interior is divided by concrete walls and removable partitions into several compartments, which are interconnected through openings with adjustable cross sections. By exchanging the removable partitions it is possible to modify the interior of the containment and to simulate different containment shapes. For the first experiments a PWR configuration with nine compartments has been installed. The model scales of the compartment volumes and the overflow areas are about 1:64 compared to the 1200 MW PWR plant Biblis A.Up to now the test facility has been used for four trial runs and nine PWR LOCA experiments with single- and double-ended pipe ruptures of 100 mm dia. in a steam generator compartment and in the nozzle compartment. The initial conditions of the pressurized water in the coolant circuit before rupture were 140 bar and 290°C. About 0.1 sec after the rupture the flow rate at the site of rupture reaches its maximum of about 400 kg/sec (single-ended rupture) and 800 kg/sec (double-ended rupture). From the compartment where the rupture takes place a water-steam-air mixture streams through openings into the other compartments of the containment. Differential pressures between the compartments were measured with maximums of up to a few bar 0.15–0.5 sec after rupture, depending on the positions of rooms and transducers.Approximately 30–40 sec after rupture the blowdown has finished and the pressure in the containment has reached about 4–5 bar. The maximum pressure in a model containment is lower and the decrease of the pressure by condensation is faster than in a full-scale containment, due to the greater ratio of inner surface area to volume of a model containment. During blowdown the temperature of the containment atmosphere rises to about 150°C. Several minutes later the temperature of the concrete walls has increased non-uniformly causing considerable stress in the walls. Approximately 30 min after rupture measurements on the outside of the outer containment wall show a temperature-caused strain of about 30–60% of the maximum pressure-caused strain. A comparison between experiments and calculations shows discrepancies indicating the need for further development of calculational methods.     

Recent results on the evaluation of the overpressure response of concrete and steel containments

Analytical studies have been performed for the evaluation of the ultimate load capacity of concrete containment structures. In addition, analyses of steel containment models were carried out to validate computer codes for the analysis of steel containment structures. This paper reports on some of the results of these analyses, dealing first with the global ultimate load behavior of typical prestressed and reinforced concrete containment structures. The results of these analyses are described, with particular attention given to identifying local effects and failure mechanisms of concrete containment structures. On the basis of the global analysis results, local effects analyses were carried out which show clear evidence of large strain concentrations in the liner. The utility of the ABAQUS-EPGEN code is also demonstrated for three steel containment small-scale models tested by Sandia National Laboratory. The basic geometry of the models consisted of a thin cylindrical shell with a hemispherical dome. One of the models included ring stiffeners in the cylinder, and the other model included penetrations without ring stiffeners. The results of these calculations are presented without test data comparisons.     

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.     

Early-age behaviour of concrete nuclear containments

A numerical model has been developed to predict early-age cracking for massive concrete structures. Taking into account creep at early-age is essential if one wants to predict quantitatively the induced stresses if autogenous or thermal strains are restrained. Because creep strains may relax internal stresses, a creep model which includes the effects of hydration and temperature is used. For the prediction of cracking, a simple elastic damage model is used. Numerical simulations are performed in order to predict the behaviour of a massive wall and a concrete containment of a nuclear power plant. They show that significant relaxation of stresses (due to creep) occurs only after about 10 days, after cracking occurs. Moreover, since temperature in concrete may reach important values in massive concrete structures, it appears that effect of temperature on creep must be taken into account for an accurate prediction of cracking.     

Design considerations for concrete nuclear containment structures subjected to simultaneous pressure and seismic shear

Improvements in design code provisions for tangential shear in secondary concrete nuclear containment vessels are needed. This paper presents a brief summary of an experimental research program conducted at Cornell University on tangential shear. Six inch thick reinforced concrete panels were subjected to combined in-plane tension and shear as a behavioral model of a section of the wall of the containment under the combined loading of internal pressurization and seismic shear. Approximately 50 panels were tested. Parameters studied included: tension level and direction (biaxial or uniaxial), shear level and type (monotonic, cyclic, or a combined mode), sequence of applied loading, and reinforcing ratio and orientation.The results of the research indicate that current code provisions are overly conservative with regard to the amount of tangential shear to be carried by the orthogonally reinforced concrete. By increasing the allowable stress, the required amount of diagonal reinforcing would be reduced. This would result in savings in fabrication costs and construction time, and improved structural reliability through improved concrete placement. The research also indicates a need for a more exact consideration of containment displacements. Shear stiffnesses for the panels were extremely low, indicating that containment displacements may be larger than anticipated. The code provisions in this area are limited and unsubstantiated.     

Plastic analysis of concrete containment structure

Overpressure capacity of a box type concrete containment structure is evaluated. Plastic analysis of the finite element model is performed using a quadrilateral plate element of homogeneous material. A special approach is used to represent nonlinear properties of reinforced concrete, such as concrete cracking and crushing and steel yielding. Those properties are represented by a set of idealized stress-strain curves of equivalent homogeneous sections.The analysis allows for a better estimate of the overpressure capacity of the containment structure while keeping the computer cost low by avoiding the use of the more expensive reinforced concrete brick element.     

Containment vessel design and practice

This paper attempts to review the state of the art of methods of analysis and design of the concrete containment vessels required for BWR and PWR. A step-by-step critical appraisal of the existing work is given. Elastic, inelastic and cracking conditions under extreme loads are fully discussed. Problems associated with these structures are highlighted. A three-dimensional finite element analysis given by the author is included to cater for service, overload and dynamic cracking of such structures. Missile impact and seismic effects are included in this work. The second analysis is known as the limit state analysis, which is given to design such vessels for any kind of load.Two existing vessels in reinforced and pre-stressed concrete are examined. Substantial calculations are given in order to assess their behaviour. Both these original analyses were developed by the author and are given in the appendices. They have been fully tested on four other vesels and two models. Due to limitations of space, some of these details could not be revealed. A brief explanation is given regarding the computer programs supporting the above analysis.     

Construction of a concrete containment model

This paper discusses the features and construction of a reinforced-concrete containment model that has been built at Sandia National Laboratories in Albuquerque, New Mexico. The model Light-Water-Reactor (LWR) containment building was designed and built to the American Society of Mechanical Engineers (ASME) code by United Engineers and Constructors, Inc. The containment model will be tested to failure to determine its response to static internal overpressurization. The results from testing the heavily instrumented containment will be used to assess the capability of analytical methods for predicting the performance of containments subject to severe accident loads as part of the US Nuclear Regulatory Commission's program on containment integrity.The scaled dimensions of the cylindrical wall and hemispherical dome are typical of a full-size containment. Features representative of a prototypical containment and included in the heavily reinforced model are equipment hatches, personnel airlocks, several small piping penetrations, and a thin steel liner attached to the concrete by headed studs.     

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.     

Leakage potential of LWR containment penetrations under severe accident conditions

This paper is an overview of a Sandia National Laboratories, Albuquerque (SNLA) study of the performance of mechanical penetrations in light-water reactor (LWR) containment buildings that are subjected to severe accident environments. The study is concerned with modes of failure as well as the magnitude of leakage. The following tests have been completed, are under way, or are planned: (a) seals and gaskets have been tested to register the effects of radiation aging, thermal aging, seal geometry, and squeeze on seal and gasket materials in severe accident environments; (b) the performance of a full-scale airlock will be evaluated at severe accident temperature and pressure levels; (c) personnel airlock and equipment hatch tests were made on a model of a steel containment building; and (d) tests of mechanical penetrations are planned as part of a test on a model of a reinforced concrete building. This program is part of an overall US Nuclear Regulatory Commission (USNRC) effort to evaluate the integrity of LWR containment buildings.     

Tension tests of concrete containment wall elements

Tension tests of concrete containment wall elements were conducted as part of a three-phase research program sponsored by the Electric Power Research Institute (EPRI). The objective of the EPRI experimental/analytical program is twofold. The first objective is to provide the utility industry with a test-verified analytical method for making realistic estimates of actual capacities of reinforced and prestressed concrete containments under internal over-pressurization from postulated degraded core accidents. The second objective is to determine qualitative and quantitative leak rate characteristics of typical containment cross-sections with and without penetrations. This paper covers the experimental portion the the EPRI program.The testing program for Phase 1 included eight large-scale specimens representing elements from the wall of a containment. Each specimen was 60-in (1525-mm) square, 24-in (610-mm) thick, and had full-size reinforcing bars. Six specimens were representative of prototypical reinforced concrete containment designs. The remaining two specimens represented prototypical prestressed containment designs.Various reinforcement configurations and loading arrangements resulted in data that permit comparisons of the effects of controlled variables on cracking and subsequent concrete/reinforcement/liner interaction in containment elements.Subtle differences, due to variations in reinforcement patterns and load applications among the eight specimens, are being used to benchmark the codes being developed in the analytical portion of the EPRI program.Phases 2 and 3 of the test program will examine leak rate characteristics and failure mechanisms at penetrations and structural discontinuities.     

Analysis of an ice-condenser containment building anchorage system

A 3-D non-linear finite-element analysis of an ice-condenser steel containment anchorage system, which considers the parameters that affect this complex system, was performed. The model included a portion of the containment shell, knuckle plate, base plate, reinforced concrete mat, anchor bolt, anchorage system, soil foundation material, and a portion of the containment shield building. The results showed the early formation of conical failure surfaces within the concrete that are associated with the brittle failure mode. However, these surfaces were not completely developed to the top of the containment basemat. No high strains were recorded in the anchorage system or the containment shell. Hence, failure of the containment anchorage system was not hypothesized.     

Structural response of fast breeder reactors to hypothetical core disruptive accidents

Liquid metal-cooled fast breeder reactors (LMFBRs) so far have been analyzed for the consequences on the plant and the environment for hypothetical core disruptive accidents (HCDAs). To provide the appropriate analytical tools for this effort, analysis and codes are currently under development in several countries. They combine the hydrodynamics and solid mechanics (and more recently the bubble dynamics) phenomena to gage stresses, strains, and deformations of the important components of the system, and the overall adequacy of the primary and secondary containments. The effort is partitioned into the structural analysis of (a) the core components, and (b) the primary system components beyond the core.The core mechanics effort covers the structural response of fuel pins, hexcans, fuel elements, and fuel element clusters to transient pressures and thermal loads. Two- and three-dimensional finite element codes are under development for these core components. The results of these analyses would permit evaluation of the adequacy of the heat removal process to continue following severe core component deformations. Also, these analyses are currently being combined with neutronics, for the core transition phase, to allow for the mass movements for realistic neutronic calculations.The primary system and containment program treats the structural response of the components beyond the core, starting with the core barrel. Combined hydrodynamics-solid mechanics codes provide transient stresses and strains and final deformations for components such as the reactor vessel, reactor cover, cover holddown bolts, as well as the pulses for which the primary piping system is to be analyzed. Both, Lagrangian and Eulerian two-dimensional codes are under development, which in their combined form provide greater accuracy and longer durations for the treatment of HCDAs. More recently the codes are being augmented with bubble migration capability pertaining to the latter stages of the HCDA, after slug impact. This step will permit treatment of the instabilities following slug impact, the ultimate reversal of the sodium slug with the rising bubble, the bubble break-up, and the calculations of sodium splillage and radioactive gases, if any, in the secondary containment. The extent of sodium spillage and sodium fires should be known for evaluation of the secondary containment. The mechanics of bubble migration are needed for radiological study of post-accident phenomena. More recently dynamic fracture mechanics considerations are being incorporated to remove arbitrary failure criteria imposed on components such as the core barrel and vessel.Most recent developments involve the adaptation of the 2-D Eulerian primary system code to the 2-D elastic-plastic treatment of the primary piping. The pulses are provided at the vessel primary piping interfaces of the inlet and outlet nozzles. The calculation includes the elbows and pressure drops along the components of the primary piping system. Pressures larger than the ones used as input at the inlet and outlet nozzles were observed. As expected, they occur far from the nozzles, in the pipe, where the pulses meet.Recent improvements to the primary containment codes include introduction of bending strength in materials, Lagrangian mesh regularization techniques, and treatment of energy absorbing materials for the slug impact. A further development involves the combination of a 2-D finite element code for the reactor cover with the 2-D finite-difference hydrodynamic code for continuous monitoring of stresses, strains, and deformations in the cover, as well as pressure changes in the hydrodynamic code. Substantial experimental effort is in progress in various countries on the response to energy releases of vessels and internals, piping systems, subassemblies, and subassembly clusters. These experimental results are being utilized for the verification or modification of the analyses and codes under development.     

Preliminary evaluation of aircraft impact on a near term nuclear power plant

For the assessment of the safety and durability of a nuclear power plant (NPP), the containment building behaviour shall be evaluated, under various service and extreme conditions, both natural or produced by natural accident or vicious man activities, like September 2001 jet aircraft crashes.The aim of this paper is to preliminary evaluate the effects and consequences of the energy transmitted to the outer containment walls (according to the international safety and design code guidelines, as NRC or IAEA ones) due to a military or civil aircraft impact into a nuclear plant, considered as a ‘beyond design basis’ event.To perform reliable analysis of such a large-scale structure and determine the structural effects of the propagation of this types of impulsive loads (response of containment structure), a realistic but still feasible numerical model with suitable materials characteristics were used by means of which relevant physical phenomena are reflected. Moreover a sensitivity analysis has also been carried out considering the effects of different containment wall thickness and reinforced/prestressed concrete features. The obtained results were analysed to check the NPP containment strength margins.     

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.     

Pneumatic pressure tests of steel containment models — Recent developments

This paper describes the results of recent pneumatic pressure tests of steel containment models. These tests are part of the Containment Integrity Program whose objective is the qualification of methods for predicting containment response during severe accidents and extreme environments. Sandia National Laboratories is conducting this combined experimental and analytical program for the U.S. Nuclear Regulatory Commission (NRC). The long-range plans for the program include the following three containment loading conditions: static internal pressurization, dynamic internal pressurization, and seismic loadings. Steel, reinforced concrete, and prestressed concrete containment types are being considered.In the present experimental effort, models of steel containment structures are being subjected to static internal pressurization. The first set of models are about the size of hybrid-steel containments. Tests of these models are nearly finished. Testing of a large steel model, about of full size, will complete the static pressure experiments with steel models. Analysis of the models is paralleling the experimental effort.The Containment Integrity Program is being coordinated with other NRC programs on potential leakage of penetrations in containments. The results from all of the programs should provide a basis for predicting the structural and leakage behavior of containments during temperature and internal pressure loadings.     

The COVA program—Validation of the fast reactor containment code seurbnuk

Extensive studies are underway in the UK and elsewhere to investigate the consequences of a hypothetical core disruptive accident in a fast reactor. Within these studies there is a continuing need to determine the response of the primary containment system to loads generated by such a major release of energy. A number of fast reactor containment codes are currently being developed for this purpose.The COVA (COva VAlidation) program of experiments is being undertaken to provide high quality data against which the codes can be validated. The tests progress from simple bare vessel assemblies to tests incorporating the main axisymmetric features of loop and pool reactor designs.A companion paper in this journal discusses recent developments in the containment code SEURBNUK which is being jointly developed by the UKAEA and JRC Ispra. This paper describes the status of the validation of SEURBNUK against data from the COVA experiments. Considerable progress has been made in the application of the code to the more complex configurations of the later tests which are more representative of reactor geometries and it is concluded that SEURBNUK has reached a stage where it provides a useful calculational capability for containment analysis. Nevertheless, further work is needed to improve the predictions of vessel deformations and roof loadings in some geometries.     

Early-age behaviour of concrete in massive structures, experimentation and modelling

This study is focused on the behaviour of concrete at early-age in massive structures, in relation with the prediction of both cracking risk and residual stresses, which is still a challenging task. In this paper, a 3D thermo-chemo-mechanical model has been developed, on the basis of complete material characterization experiments, in order to predict the early-age development of strains and residual stresses, and in order to assess the risk of cracking in massive concrete structures. The parameters of the proposed model were identified on two different concretes, High Performance Concrete and Fibrous Self-Compacted Concrete - from simple experiments in the laboratory: uniaxial tension and compression tests, dynamic Young's modulus measurements, free and autogenous shrinkages, semi-adiabatic calorimetry. The proposed model has been implemented in a Finite Element code, and the numerical simulations of the laboratory tests have proved the model consistency.Furthermore, early-age experiments conducted on massive structures have also been simulated, in order to investigate the predictive capability of the model, and to assess the model performance in practical situations where varying temperatures are involved.