Simplified seismic analysis methods in Belgium

Seismic design and analysis of nuclear plant systems, structures and components have requested huge effort and tremendous costs in the past two decades. The extended use of sophisticated, linear response type methods (modal analysis, spectral response) and the associated conservatism are responsible for the significant stiffening of the piping systems and the multiplication of supports and snubbers. The remedy used against the seismic risk seems worse than the pain itself, and safety might be impaired rather than improved. Indeed, system stiffening increases the average load level in normal operation (stresses, fatigue, nozzle loads, etc.); supports do not behave ideally as assumed (friction, rust, etc.) and snubbers are remarkably unreliable. On the other hand, experience with actual earthquakes shows that industrial facilities designed using very simplistic seismic techniques, or even no seismic requirement at all, suffer essentially no damage, even in the case of a large earthquake. This paradox challenges the traditional seismic design techniques, and appeals for revised seismic qualification methods of piping systems. When the assumption of the occurrence of an earthquake event is made in a plant in operation, which has not been designed against seismic criteria, the use of the standard seismic qualification techniques is still more questionable; simplified (quasi-static) techniques offer in this case a valuable and economically justified alternative. The paper describes the application of the quasi-static “modified load coefficient method” to the seismic assessment of the piping in a nuclear plant in operation, designed during the pre-seismic era.     

Comparative methods for analysis of piping systems subjected to seismic motion

The dynamic analysis of a three-dimensional piping system of a nuclear power plant is conveniently performed through a finite element method. When the modal analysis is used, only the first few modes of vibration are computed for practical purposes. In this paper is proposed a method of residues which evaluates the neglected modes and combines them with the first calculated modes to estimate the total seismic response of the piping. This methods emphasizes the importance of the selected modes. When the approach is made through a time history input function, this latter is usually characterized by a combination of several recorded accelerograms, e.g. El Centro, San Francisco and Taft. The response of a particular piping has been evaluated by means of these two methods: the use of the modal approach will be strongly recommended due to its inherent advantage of economy and also computation time and reliability.     

Response spectrum analysis of piping systems with elastic-plastic gap supports

A new seismic support device and its application in piping systems is described. The device, E-BAR (patented), can be cost effectively used for snubber replacement programs, mitigation of hydraulic transients, pipe whip and as a thermal stop. The device has pre-set gaps to allow free thermal movement. During a seismic or other dynamic load event, if the pipe movement exceeds the gap dimension, the device acts as an elastic or elastic-plastic restraint. The device also has a unique design feature for not exceeding the restraint force beyond a specified limit design value. To analyze piping systems with gap supports having elastic-plastic characteristics, modal analysis procedures for both response spectrum and time history methods are developed. The comparison of responses obtained from the procedures with nonlinear time history analysis and test results available in the literature shows excellent correlation. A pilot program conducted for snubber replacement with E-BARs demonstrates that the limit force feature of E-BAR makes them very attractive for snubber replacement. This is because a particular E-BAR with a specified limit design force can be selected, such that, the E-BAR replacing the snubber does not require any modifications be made to the existing support steel and hardware.     

Automated analysis of multiple-support excitation piping problems

An automated solution algorithm is presented for the treatment of multiple-support excitation piping problems. The method is an extension of the well-known response spectrum analysis method which is routinely used for seismic analysis of structural systems. The new algorithm was incorporated in Kraftwerk Union's proprietary computer code KWUROHR for static and dynamic analysis of piping systems.In this paper the numerical results from the use of envelope and multiple-support acceleration input spectra are presented for two typical piping systems in nuclear power plants. From the comparison of these results it becomes obvious that the multiple-support excitation method should be recommended as standard analysis procedure for systems attached to support points which are subjected to different acceleration spectra. The additional computer cost is negligible.     

塑性变形对管系地震动力响应的影响

在评述线弹性分析方法的基础上,阐明了在管系特别是核管系动力响应分析中考虑塑性变形影响的重要性,介绍了现有考虑塑性影响的方法及其存在的问题.指出要降低现行规范的保守性,提出合理的管系抗震设计方法,     

Comparison of multiple support excitation solution techniques for piping systems

Design and analysis of nuclear power plant piping systems exposed to a variety of dynamic loads often require multiple support excitation analysis by modal or direct time integration methods. Both methods have recently been implemented in the computer program KWUROHR for static and dynamic analysis of piping systems, following the previous implementation of the multiple support excitation response spectrum method (see papers K6/15 and K6/15a of the SMiRT-4 Conference).The results of multiple support excitation response spectrum analyses can be examined by carrying out the equivalent time history analyses which do not distort the time phase relationship between the excitations at different support points.A frequent point of discussion is multiple versus single support excitation. A single support excitation analysis is computationally straightforward and tends to be on the conservative side, as the numerical results show. A multiple support excitation analysis, however, does not incur much more additional computer cost than the expenditure for an initial static solution involving three times the number, L, of excitation levels, i.e. 3L static load cases. The results are more realistic than those from a single support excitation analysis.A number of typical nuclear plant piping systems have been analyzed using single and multiple support excitation algorithms for: (1) the response spectrum method, (2) the modal time history method via the Wilson, Newmark and Goldberg integration operators and (3) the direct time history method via the Wilson integration operator. Characteristic results are presented to compare the computational quality of all three methods.     

Impact of structural steel flexibility and restraints gaps on the dynamic behaviour of piping

The effect of gaps present in the seismic supports of nuclear piping systems and of the flexibility of the steel structure to which intermediate supports are attached, is studied in this paper. An actual piping system is used to investigate the impact of structural steel and mechanical snubber gaps on the dynamic behaviour of piping. An evaluation is thus performed of the finite element modeling techniques employed by the designers in the dynamic analysis of piping systems.     

Effects of ductility on seismic response of piping systems and their implication on design and qualification

This study is concerned with the inelastic seismic response of nuclear power plant piping systems. Two systems are examined. The first one is an idealized four-equal-span pipe run and the second one consists of two configurations modified from an existing pipe run. Detailed finite element seismic time history analyses are performed using the computer program. By varying the various geometrical and physical parameters, calculations are made for a total of 76 cases. The results show that ductility generally contributes to reducing the response of piping systems. An empirical relation between the support load reduction factor and support ductility demand is given and a chart and simple procedures are suggested for the design and qualification of piping supports taking ductility into consideration.     

Consideration of uncertainties in seismic analysis of coupled building piping systems

In this paper, we present an analytical study for incorporating the effect of uncertainties in modal properties of uncoupled primary and secondary systems in the seismic analysis of non-classically damped coupled systems such as building piping by response spectrum method. Monte Carlo simulation is used to illustrate that the secondary system design response when defined at a non-exceedence probability of 0.84 over the individual responses obtained from multiple response spectrum analyses by considering uncertainties in modal parameters is excessively higher than the design response specified at the same non-exceedence probability over the responses obtained from multiple time history analyses. This is so because the earthquake input in a response spectrum method is characterized by a design spectrum which by itself is specified at a non-exceedence probability of 0.84 over the multiple time histories with normalized peak ground acceleration. Accurate evaluation of design response at a non-exceedence probability of 0.84 in the response spectrum method requires that the individual modal responses be defined at appropriate probability levels that may be different than the conventionally used non-exceedence probability value of 0.84. The required probability values are evaluated by using first order reliability method. It is shown that the modal responses, when defined at a non-exceedence probability of 0.84, would give relatively accurate values of design response only if the individual modes are perfectly correlated or a single mode contributes to the particular response quantity of interest. For all other cases, the design response would be excessively high. The accurate probability values needed to specify each modal response evaluated using the first order reliability method cannot be incorporated directly in a response spectrum analysis due to computational inefficiency. Two simplified methods, based on total probability theorem, are developed in this paper to overcome this limitation. It is shown that these methods give design response values that are very close to the true values obtained from multiple time history analyses.     

Progress in development of acceptance criteria for local thinned areas in pipe and piping components

Over the last 30 years there has been a considerable amount of research conducted on the effect of corrosion on the burst strength of buried gas and oil transmission pipelines. The results of numerous burst tests on artificial flaws and corroded pipe removed from service were used to validate an empirical analysis that was essentially the limit–load solution for an axial crack in a pipe under pressure loading. This basic concept led to acceptance standards in ANSI B31G, and a more recent modified B31G criterion using the RSTRENG computer program developed at Battelle. This program takes into account variable flaw depths rather than the parabolic flaw shape assumed in the original B31G criterion. Since that time, more fundamental research has been conducted to develop a more accurate and theoretically based failure criterion. The Battelle/Pipeline Research Committee International PCORR computer program is an example of a special purpose shell-element based, finite element, PC criterion for the evaluation of local thinned area (LTA) flaws. This program has evolved with time from linear-elastic to elastic-plastic stress with provisions for axial as well as hoop stresses. The development and new insights into blunt flaw behavior resulting from this program will be one aspect covered in this paper. In the nuclear industry erosion-corrosion, or flow-accelerated corrosion, in single-phase liquid lines has become a major problem. Computer programs, such as the EPRI Checworks program, have been developed to assist the plant operators with deciding where to focus their inspections. However, to date no generally validated acceptance criteria have been developed for the plant piping. Plant piping, whether in nuclear power plants, fossil power plants, or petrochemical plants, have several differences from buried pipelines which need to be considered. The buried pipelines typically have low longitudinal stresses that frequently are compressive, and have no pipe fittings such as tees, elbows, and reducers except at compressor stations. Plant piping needs to consider hoop stresses and axial tension loads from the pressure, as well as, bending stresses from dead-weight loads, thermal expansion stresses, and seismic loads. In an effort to develop flaw acceptance criteria for Section XI of the ASME Boiler and Pressure Vessel Code, the criteria in Code Case N-480 have been revised and implemented into a new code case (the number has not yet been assigned). These criteria essentially use either the ANSI B31G approach for axial flaws, or the ANSI B31.1 or ASME Section III stress analysis rules to show that the residual strength of the thinned region meets the initial design stress limits. This paper presents some of the validation efforts recently undertaken to determine the inherent margins in the design stress equation approach compared with the applied safety factors in the axial and circumferential flaw limit–load solutions in: (i) the gas and oil pipeline industries; (ii) the proposed criteria in Belgium for the nuclear industry and other criteria, and (iii) the preliminary criteria from a recently proposed ASME Code Case on erosion/corrosion acceptance criteria and the ASME Appendix H criteria for flawed ferritic nuclear pipe.     

Crack stability evaluation of nuclear main steam pipe considering load reduction effect

The objective of this paper is to evaluate the crack stability of a nuclear main steam pipe, considering load reduction effect due to the presence of circumferential through-wall crack. Also, optimization techniques are adopted to simulate the crack effect on the elbow component of piping systems. By using a general beam element that contains a discontinuous cross-section, piping analysis is performed to obtain the reduced load. Considering this reduced load, LBB design concept is applicable to the nuclear main steam pipe system. Also, by combining an optimization program and a general finite element analysis software, the appropriate dimensions are simplified and an equivalent beam element representing the effect of crack in the elbow could be successfully obtained.     

Structural evaluation of a piping system subjected to thermal stratification

Piping systems in nuclear power plants are often designed for pressure, mechanical loads originating from deadweight and seismic events and operating thermal transients using the equations in the ASME Boiler and Pressure Vessel Code, Section III. In the last few decades a number of failures in piping have occurred due to thermal stratification caused by the mixing of hot and cold fluids under certain low flow conditions. Such stratified temperature fluid profiles give rise to circumferential metal temperature gradients through the pipe leading to high stresses causing fatigue damage. A simplified method has been developed in this work to estimate the stresses caused by the circumferential temperature distribution from thermal stratification. It has been proposed that the equation for the peak stress in the ASME Section III piping code include an additional term for thermal stratification.     

Response of piping system on friction support to bi-directional excitation

Installation of friction devices between a piping system and its supporting medium is an effective way of energy dissipation in the piping systems. In this paper, seismic effectiveness of friction type support for a piping system subjected to two horizontal components of earthquake motion is investigated. The interaction between the mobilized restoring forces of the friction support is duly considered. The non-linear behavior of the restoring forces of the support is modeled as an elastic-perfectly plastic system with a very high value of initial stiffness. Such an idealization avoids keeping track of transitional rules (as required in conventional modeling of friction systems) under arbitrary dynamic loading. The frictional forces mobilized at the friction support are assumed to be dependent on the sliding velocity and instantaneous normal force acting on the support. A detailed systematic procedure for analysis of piping systems supported on friction support considering the effects of bi-directional interaction of the frictional forces is presented. The proposed procedure is validated by comparing the analytical seismic responses of a spatial piping system supported on a friction support with the corresponding experimental results. The responses of the piping system and the frictional forces of the support are observed to be in close agreement with the experimental results validating the proposed analysis procedure. It was also observed that the friction supports are very effective in reducing the seismic response of piping systems. In order to investigate the effects of bi-directional interaction of the frictional forces, the seismic responses of the piping system are compared by considering and ignoring the interaction under few narrow-band and broad-band (real earthquake) ground motions. The bi-directional interaction of the frictional forces has significant effects on the response of piping system and should be included in the analysis of piping systems supported on friction supports. Further, it was also observed that the velocity dependence of the friction coefficient does not have noticeable effects on the peak responses of the piping system.     

Analysis and test correlation of flexible and stiff piping systems

An in situ pipe test program was conducted to provide a basis for evaluating piping analysis methodologies and design philosophies. In this program, a 20.3-cm boiler feedwater line with two fundamentally different support systems was tested and analyzed. One system employed hanger supports and was very flexible. The second system employed strut and snubber supports and was relatively stiff. Snapback and forced vibration tests were performed on the piping systems. The test results were used to determine piping damping values and to correlate with analyses. These analyses were used to evaluate current piping analysis methodologies and their analytical models. Also, parametric studies were performed with the analytical models to evaluate the effect of different support systems on the pipe behavior for thermal and seismic loads. In addition, the seismic analysis results were compared to quantify the differences between direct time integration and response spectra analysis methods.     

Pipe rupture and steam/water hammer design loads for dynamic analysis of piping systems

The design of restraints and protection devices for nuclear Class I and Class II piping systems must consider severe pipe rupture and steam/water hammer loadings. Limited stress margins require that an accurate prediction of these loads be obtained with a minimum of conservatism in the loads. Methods are available currently for such fluid transient load development, but each method is severely restricted as to the complexity and/or the range of fluid state excursions which can be simulated. This paper presents a general technique for generation of pipe rupture and steam/water hammer design loads for dynamic analysis of nuclear piping systems which does not have the limitations of existing methods. Blowdown thrust loadings and unbalanced piping acceleration loads for restraint design of all nuclear piping systems may be found using this method. The technique allows the effects of two-phase distributed friction, liquid flashing and condensation, and the surrounding thermal and mechanical equipment to be modeled. A new form of the fluid momentum equation is presented which incorporates computer generated fluid acceleration histories by inclusion of a geometry integral termed the “force equivalent area” (FEA). The FEA values permit the coupling of versatile thermal-hydraulic programs to piping dynamics programs. Typical applications of the method to pipe rupture problems are presented and the resultant load histories compared with existing techniques.     

Performance of a piping system and equipment in the HDR simulated seismic experiments

This paper describes a portion of the analysis and results of the United States Nuclear Regulatory Commission/Idaho National Engineering Laboratory (USNRC/INEL) participation in the SHAG (Shakergebaude) Seismic Research Program conducted by Kernforschungszentrum Karlsruhe (KfK) at the Heissdampfreaktor (HDR), a decommissioned nuclear reactor. The program analyzed the responses of a piping system and associated line-mounted equipment when subjected to various seismic and hydraulic loadings. Of interest was to evaluate the influence that piping support system flexibility has on piping system responses. The results of the studies will contribute to the technical basis for assessing the responses of light water reactor (LWR) piping and fine-mounted equipment to earthquakes.     

Enhanced seismic criteria for piping

In situ or laboratory experiments have shown that piping systems exhibit satisfactory seismic behavior. Seismic motion is not severe enough to significantly damage piping systems unless large differential motions of anchorage are imposed. Nevertheless, present design criteria for piping are very severe and require a large number of supports, which creates overly rigid piping systems. CEA, in collaboration with EDF, FRAMATOME and IRSN, has launched a large R&D program on enhanced design methods which will be less severe, but still conservative, and compatible with defect justification during operation. This paper presents the background of the R&D work on this matter, and CEA proposed equations.Our approach is based on the difference between the real behavior (or the best estimated computed one) with the one supposed by codified methods. Codified criteria are applied on an elastically calculated behavior that can be significantly different from the real one: the effect of plasticity may be very meaningful, even with low incursion in the plastic domain. Moreover, and particularly in piping systems, the elastic follow-up effect affects stress distribution for both seismic and thermal loads.For seismic load, we have proposed to modify the elastic moment limitation, based on the interpretation of experimental results on piping systems. The methods have been validated on more industrial cases, and some of the consequences of the changes have been studied: modification of the drawings and of the number of supports, global displacements, forces in the supports, stability of potential defects, etc.The basic aim of the studies undertaken is to make a decision on the stress classification problem, one that is not limited to seismic induced stresses, and to propose simplified methods for its solution.     

安全壳外挂水箱结构强度分析

我国自主设计的第3代核电站安全壳外挂水箱用于超设计基准事故下内层安全壳的长期排热,这是确保安全壳完整、核电厂安全的重要设施。因此,有必要对外挂水箱在极限安全地震动与温度异常工况组合作用下的结构强度进行分析。建立带有外挂水箱的外层安全壳有限元模型,开展网格敏感性分析,并通过模态分析研究结构的振动特性。采用时程分析法,对结构同时施加温度和地震动载荷,基于流固耦合方法分析水体与结构的相互作用,研究外挂水箱结构的地震动响应以及水箱内水体振荡特性。研究表明,水体在水箱凹沉处水面振荡幅度较大,在EL Centro地震动、人工合成地震动和长周期地震动工况下外挂水箱的最大拉应变和最大压应变绝对值均小于C60混凝土许用应变值。     

Reliability-based load and resistance factor design for piping: an exploratory case study

This paper presents an exploratory case study on the application of Load and Resistance Factor Design (LRFD) approach to the Section III of ASME Boiler and Pressure Vessel code for piping design. The failure criterion for defining the performance function is considered as plastic instability. Presently used design equation is calibrated by evaluating the minimum reliability levels associated with it. If the target reliability in the LRFD approach is same as that evaluated for the presently used design equation, it is shown that the total safety factors for the two design equations are identical. It is observed that the load and resistance factors are not dependent upon the diameter to thickness ratio. A sensitivity analysis is also conducted to study the variations in the load and resistance factors due to changes in (a) coefficients of variation for pressure, moment, and ultimate stress, (b) ratio of mean design pressure to mean design moment, (c) distribution types used for characterizing the random variables, and (d) statistical correlation between random variables. It is observed that characterization of random variables by log-normal distribution is reasonable. Consideration of statistical correlation between the ultimate stress and section modulus gives higher values of the load factor for pressure but lower value for the moment than the corresponding values obtained by considering the variables to be uncorrelated. Since the effect of statistical correlation on the load and resistance factors is relatively insignificant for target reliability values of practical interest, the effect of correlated variables may be neglected.