A Post-Treatment of a Conventional Analysis to Represent Elastoplastic Behaviour of Piping Systems Under High Seismic Load

Abstract Following 2011 Fukushima earthquake event, the increase of the design seismic motions, compared to the initial ones considered for building nuclear power plants, lead to possible requirements of modified or additional pipe supports to satisfy the stress evaluation given in the design codes. Considering the highly favorable behavior of piping systems under seismic load both during earthquake events and laboratory tests, industrial less conservative analysis methods than the conventional linear dynamic analysis method, known as response spectrum analysis, have been sought for safe-side evaluation. Then the purpose of the paper is to propose and apply a simplified method to represent possible elastoplastic behavior of piping systems under high seismic loads. The rigorous analysis able to allow the most accurate prediction of the possible elastoplastic material behavior due to high seismic motions, especially localized in elbows, is the nonlinear time-history method. However, this type of simulation is not yet easily usable in industrial context, due to several reasons: low availability of floor accelerograms, requirement of more sophisticated model than beam elements, need of number of simulations from independent sets of accelerograms, sensitivity of results to simulation parameters and high computational time-consuming. Thus, the proposed so-called “Roche method” aims to conservatively evaluate, in comparison with nonlinear approach, resulting moments and stresses along the curvilinear piping abscissa, by representing local elastoplastic behavior, avoiding nonlinear analysis. Initially developed in case of static thermal expansion purpose, the method was then extended to dynamic seismic load, exploiting the spring effect in piping systems and by decomposing the piping response in amplified predominantly out-of-phase displacement-controlled part (secondary), and quasi-static in-phase force-controlled part (primary). The method consists in a projection of the linear stress, issued from response spectrum analysis, on a representative stress-strain curve of the material, by a slope depending on the spring factor. A reduction coefficient can thus be deduced, then applied but to the amplified part of the piping response, at frequencies below the input motion cut-frequency. Using code_aster open-source software, developed by Electricité de France company, comparative evaluations are performed on a 4-elbow piping system, with a diameter of approximately 0.17 m and a total mass about 600 kg, clamped at its two extremities. The seismic floor motion is represented either by 5 sets of tri-dimensional accelerograms, to be applied for reference nonlinear transient analyses, or corresponding rough pseudo-acceleration response spectra, to be applied for conventional response spectrum analysis followed by Roche method. The nonlinear model is composed of plastic straight pipe elements, combining beam and shell kinematics, whereas the linear model uses simple beam elements. The Rayleigh damping model is used for the transient analyses. Material tensile behavior is represented by a bilinear law with kinematic hardening both for nonlinear time history and Roche analyses. Reference quantities of interest are quadratic equivalent moments, based on bending and torsional moments, along the curvilinear piping abscissa, as the means of the temporal maxima relative to each set of accelerograms, associated with Student-Fisher interval estimation. By application of Roche method, a significant reduction of response spectrum quadratic equivalent moments can be obtained, especially at ending piping parts, in a conservative way compared with non-linear reference results. Fully validated on number of industrial complex piping systems, Roche method constitutes an easy and fast non-iterative post-treatment of a linear conventional analysis. It has been introduced in RCC-MRx French design code and can be used for safe-side justification of piping systems, when conventional linear analysis does not permit it.