Development of Effective Applied Moment Formulations for Integrity Assessment of Nuclear Piping Systems under Static and Dynamic Loading Conditions

Abstract

Attentions to the beyond design basis earthquake have been increased following the Fukushima Daiichi nuclear accidents on March 11, 2011. Especially, the refinement of the current analysis methodologies has emerged as one of high priority issues for the piping integrity evaluation. In this dissertation, a set of generalized formulations has been developed to take into account the effect of pipe restraint for consistent analysis of the crack opening displacement and crack stability of nuclear piping containing a postulated circumferential crack in order to enhance the confidence in the Leak-Before-Break (LBB) characteristics. For the current LBB analysis procedure, evaluation models for the crack opening displacement as well as those for crack stability analysis have been derived from the assumption that both ends of the pipe under analysis are free to rotate. In reality, however, the behavior of pipe with a crack can be restrained by connected components or structures. These aspects of restrained boundary conditions can make a significant favorable influence on the crack instability prediction and unfavorable impact on the prediction of leakage size crack by an underestimation of crack opening displacement (COD). In this regards, there have been attempts to evaluate the combined results of the restraint effects from the above two aspects. First, the equations to determine the onset of a crack extension were developed for various piping systems and loading conditions case by case. But generalized formulations which can be employed as the unified practical method has not been derived. Recently, the analytical expressions to evaluate the restraint effect on COD were proposed for both linear elastic and elastic-plastic analysis, with its applicability limited to a straight pipe with fixed ends subjected to pressure induced bending. Although significant efforts have been made in earlier studies to deal with the restraint effect on the calculation of COD and crack stability analysis separately, these are simultaneous phenomena caused by the decreases in the applied moment at the cracked section due to the pipe restraint. Therefore, it is desired to develop a unified formulation to determine the effective applied moment at a postulated cracked section considering the boundary conditions that can be utilized to a balanced analysis of both COD and flaw stability. This dissertation mainly serves to the aims for the development of generalized solutions that readily enable balanced evaluations of the restraint effect starting from the following questions:

i) How can we analytically evaluate the effective applied moment at the cracked section taking into account the pipe restraint effects? ii) Can the generalized formulations be applicable to various types of the piping geometries and loading conditions including dynamic loads including earthquake effect? iii) Can the developed formulations be verified against both finite element analysis and experimental results under static and dynamic loading conditions? iv) What is the impact of new formulations developed in this dissertation on pipe integrity analysis and future LBB designs?

The first new formulation has been derived for a one-dimensional pipe subjected a pressure induced bending that is considered in the earlier studies. Based on the compliance approach, the formulation was then extended to the three-dimensional piping system and other types of loading conditions including the distributed load and relative displacement of supports. To verify the developed formula, a series of finite element analysis was conducted for the static and dynamic loading conditions. The static analyses were performed to evaluate the amount of restraint considering the anticipated loads of the normal operating conditions. In addition, the crack stability analysis assumes the faulted dynamic loading condition in which the seismic load is considered. Furthermore, the dynamic analysis using cracked pipe model accompanying the comparisons with experimental data also conducted to demonstrate that restraint coefficient is also available for transient loading conditions. As results, it is confirmed the generalized analytical formulations, finite element analysis and experimental data agree with each other very well in all examined conditions. Finally, using the developed formula, the effect of restraint on the LBB evaluation was investigated. All the analysis results of this dissertation indicated that the restraint effect on the applied moment has more significant influence on the crack stability evaluation than on COD. Therefore, the current LBB evaluation procedure, with no attention to the pipe restraint effect, can predict conservative results compared to the case in which the restraint effect is considered for the conditions examined herein. The developed formulation has two implications of the practical significance. First, if the restraint effect is implemented into the current practice of deterministic LBB analysis using the developed formulations, the piping system can be shown to possess greater safety margins. Second, the time history analysis of the piping system for various crack length can be replaced with a single uncracked pipe system analysis with the restraint coefficient without sacrificing accuracy at the significant saving in time and cost. Therefore, the generalized formulations developed in this dissertation can greatly help improve the applicability of the probabilistic fracture mechanics analysis and/or seismic fragility analysis that otherwise require a significant number of time-consuming calculations.