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.     

Numerical modeling of concrete under thermal loads

The formulation needed for the conductance of heat by means of explicit integration is presented. The implementation of these expressions into a transient structural code, which is also based on explicit temporal integration, is described. Comparisons of theoretical results with code predictions are given both for one-dimensional and two-dimensional problems. The coupled thermal and structural solution of a concrete crucible subjected to a sudden temperature increase predicts the history of cracking. The extent of cracking is compared with experimental data.     

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.     

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.     

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.     

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.     

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.     

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.     

Effect of high explosive detonations on concrete structures

A numerical method to calculate the damage caused to concrete structures by surface charges is presented. The effect of the detonation on the concrete has been modelled in the case of high explosives, positioned and detonated on the surface of a concrete structure.     

Creep prediction of concrete for reactor containment structures

Since the biggest time-dependent prestress loss of a prestressed concrete nuclear reactor containment structure is due to the creep of concrete, creep is one of the most important structural factors to be considered for the safety of a reactor containment structure during design, construction and maintenance. Creep in concrete has also recently been considered in evaluation of the crack resistance of concrete at an early-age in the durability examination of massive concrete structures like reactor containment structures. Existing empirical formulas on creep prediction show errors in their predictions due to simplified consideration of mixture proportions, and they also show large discrepancy among their predictions. In addition, they do not consider early-age behaviors of concrete and thus are mainly for the prediction of long-term creep at hardened concrete. In this paper, the creep characteristics of the reactor's both early-age and hardened reactor concrete made of type V cement are examined by carrying out both early-age and long-term creep tests. Then, the creep of the reactor concrete is predicted by using major creep-prediction equations of the AASHTO LRFD design specification, the Japanese standard specification for concrete structure, the ACI Committee 209 and the CEB/FIP model code and the Bazant and Panula's model, and the predicted results are compared with the test results. From the comparison, the applicability of the creep-prediction equations for the concrete of a reactor containment structure at both early-age and hardened stages is 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.     

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.     

Seismic fragility of reinforced concrete structures in nuclear facilities

The failure and fragility analyses of reinforced concrete structures and elements in nuclear reactor facilities within the Seismic Safety Margins Research Program (SSMRP) at the Lawrence Livermore National Laboratory are evaluated. Receiving special attention are uncertainties in material modeling, behavior of low shear walls, and seismic risk assessment for nonlinear response. Problems with ductility-based spectral deamplification and prediction of the stiffness of reinforced concrete walls at low stress levels are examined. It is recommended that relatively low damping values be used in connection with ductility-based response reductions and that static nonlinear force-deflection curves be studied for better nonlinear dynamic response predictions.     

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.     

Reliability-based assessment of integrity of bonded prestressed concrete containment structures

The main function of a nuclear containment structure is to prevent the leakage of radioactive materials from the reactor in the event of a serious failure in the process system. To maintain a high level of leak integrity, prestressed concrete is widely utilized in containment construction. In bonded prestressing systems, excessive prestressing losses caused by unexpected material deformations and degradation of tendons could result in the loss of leak integrity under an accident. To safeguard against this, the Canadian Standard, CSA N287.7 (1995), recommends periodic inspection and evaluation of prestressing systems of CANDU containments. As bonded tendons are not amenable to direct inspection, the evaluation is based on the testing of a set of beams with features identical to the containment. The paper presents a quantitative reliability-based approach to evaluate the containment integrity in terms of the condition of bonded prestressing systems. The proposed approach utilizes the results of lift-off, destructive, and flexural tests to update the probability distribution of prestressing force, and to revise the calculated reliability against through-wall cracking of containment elements. An acceptable criterion for the results of beam tests is established on the basis of maintaining adequate reliability throughout the service life of the containment.     

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.     

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.     

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.     

Design of reinforced concrete structures subjected to three components of earthquake

The effects of three earthquake components are usually combined using the square root of the sum of the squares (SRSS) method. In this paper, strength criteria have been developed for reinforced concrete structures subjected to three earthquake components using the SRSS method of combining the effects as the basis.     

Modeling and code development for concrete structures: An overview

The present status of efforts to model concrete behavior under projected extreme loadings suitable for finite element formulation is presented. The difficulties in modeling introduced by problems associated with quality control of the concrete mix and dependency of test results on a number of variables are pointed out. A variety of modeling schemes which attempt to take into account such peculiarities of concrete behavior are discussed, and advantages and shortcomings of each scheme are mentioned. Future analytical and experimental research needs are indicated, especially with regard to reinforced concrete element modeling. The present paper constitutes a state-of-the-art report on computer modeling of plain and reinforced concrete behavior and contains appropriate recommendations from the authors.