Fragility assessment requires characterization of a component or system's performance through a performance function/limit-state equation. The exceedance of limit-state is representative of failure or damage state. For the purposes of evaluating piping fragility, characterizing the behavior of T-joints through an appropriate performance function is critical, as failures in piping are generally localized at the location of T-joints, elbows, and nozzles. Past studies have utilized a monotonic rotation-based performance function. However, the existing criteria does not account for the effect of cyclic behavior. As observed during prior experimental studies, the T-joint behavior under cyclic loading is different from that under monotonic loading, and therefore, it is important to include the effects of cyclic behavior while characterizing a performance function. Moreover, the monotonic rotation-based performance function could not replicate all the leakage locations observed during experimental studies on a full-scale two-story piping system. Therefore, it is important to develop a new limit-state for accurate piping fragility assessment. This paper presents the development of a new limit state which considers the cyclic behavior of a T-joint and quantifies the number of cycles to failure.

The recent advance of seismic metamaterials has led to various concepts for the attenuation of seismic waves, one of them being the locally resonant metamaterial. Based on this concept, the so-called metafoundation has been designed. It can effectively protect a fuel storage tank from ground motions at various fluid levels. In order to show the effectiveness of the proposed design, the response of the metafoundation is compared to the response of a tank on a traditional concrete foundation. The design process of conceiving the metafoundation, optimizing it for a specific tank, and its seismic response are described herein. Furthermore, the response of a tank during a seismic event can cause severe damages to pipelines connected to the tank. This phenomenon can be of critical importance for the design of a seismic tank protection system and must be treated with care. Since the coupled structure (tank + foundation + pipeline) exerts highly nonlinear behavior, due to the complexity of the piping system, a laboratory experiment has been conducted. More precisely, a hybrid simulation (HS) that uses the metafoundation and a tank as a numerical substructure (NS) and a piping system as a physical substructure (PS) was employed. To make the results relatable to the current state of the art, additional experiments were performed with concave sliding bearings (CSBs) as an isolation system in the NS. The metafoundation offered a clear attenuation of tank stresses and, in some cases, also reduced the stresses in the piping system.

A series of inelastic benchmark and parametric analyses was conducted on the tests of a pipe elbow and a piping system model made from carbon steel to investigate variabilities of elastic–plastic analysis results and clarify the factors affecting the analytical results. The analysis on the pipe elbow was the inelastic static analysis and the analysis on the piping system model included the inelastic dynamic analysis under the random input motion. From the benchmark analysis results, we found that setting the yield stress in the material property approximation had a significant influence on the inelastic analytical results, while the work hardening modulus in the bilinear approximation of the stress–strain curve had little influence. The parametric analysis was performed with the viewpoint to examine the influence of the yield stress and the work hardening modulus when the material property was approximated as the bilinear relation. The results also showed that the setting of the yield stress had larger impact on the analytical results than the setting of the work hardening modules. The parametric analysis results confirmed that the variation in the analytical results among different analysts would be reduced by using the same material property approximation.

To investigate the behavior of components and piping systems subjected to seismic loadings, the maximum restoring forces and maximum deformations of inelastic single-degree-of-freedom (SDOF) systems due to harmonic excitations and seismic floor motions are calculated and presented as diagrams. These systems have restoring forces characterized by a bilinear skeleton curve of a kinematic hardening rule. The diagrams show two types of characteristics, based upon which sinusoidal loadings can be categorized into force- and displacement-controlled loadings, and seismic loadings can be categorized into force- and displacement-dominant loadings, which are newly proposed herein. The characteristics of force- and displacement-dominant loadings are almost equal to those of force- and displacement-controlled loadings, respectively.

Buried pipelines are faced with and vulnerable to extreme hazards such as earthquakes, different types of faulting, and landslides. Generally, a buried pipeline is modeled as a beam on a series of springs, which represent the surrounding soil. To determine the specifications of these springs, the equations proposed by ASCE Guideline are usually used. Its accuracy was doubted by some recent studies. In this study, two full-scale tests simulating the effect of strike-slip faulting were initially carried out on 4 and 8-in. diameter steel pipes buried in compacted sandy soil. The displacement of the pipe was recorded directly at any moment, along its length. Then through optimization-based simulations, the specifications of the equivalent springs of the soil were calculated so that the deformation of the pipe along its length would be consistent with the experimental results. Then, based upon verified finite element models, a database of different parameters of buried pipes subjected to strike-slip faulting including the diameters and different burial depths was created. The results showed that the ASCE equations need modification at the condition of strike-slip faulting and so, based on the created database, a new form of the equations of lateral interaction between dense sandy soil and steel pipe in the presence of strike-slip fault was proposed.

Some Japanese nuclear power plants have experienced several large earthquakes beyond the design basis ground motion. In addition, cracks resulting from long-term operation have been detected in piping systems. Therefore, to assess the structure integrity and to evaluate the fragility of cracked pipes taking the occurrence of large earthquakes into account, it is very important to establish a crack growth evaluation method for cracked pipes that are subjected to large seismic cyclic response loading. In our previous study, we proposed an evaluation method for crack growth during large earthquakes through experimental study using small size specimens and investigation using finite element analyses. In the present study, to confirm applicability of the proposed method to pipe, crack growth tests were conducted on both stainless and carbon steel pipe specimens with a circumferential through-wall crack, considering large seismic cyclic response loading with complex waveforms. The predicted crack growth values are in good agreement with the experimental results and the applicability of the proposed method was confirmed.

A procedure is described for risk-based seismic performance assessment of pressurized piping systems considering ratcheting. The procedure is demonstrated on a carbon steel piping system considered for OECD-NEA benchmark exercise on quantification of seismic margins. Initially, fragility analysis of the piping system is carried out by considering variability in damping and frequency. Variation in damping is obtained from the statistical analysis of the damping values observed in earlier experiments on piping systems and components. The variation in ground motion is considered by using 20 strong motion records of the intraplate region. Floor motion of a typical reactor building of a nuclear power plant under these actual earthquake records is evaluated and applied to the piping system. The performance evaluation of the piping system in terms of ratcheting is carried out using a numerical approach, which was earlier validated with shake table ratcheting tests on piping components and systems. Three limit states representing performance levels of the piping system under seismic load are considered for fragility evaluation. For each limit state, probability of exceedance at different levels of floor motion is evaluated to generate a fragility curve. Subsequently, the fragility curves of the piping systems are convoluted with hazardous curves for a typical site to obtain the risk in terms of annual probability of occurrence of the performance limits.

The behavior of aboveground storage tanks subjected to seismic excitation was investigated using numerical methods by taking flexibility of foundation into account. The hydrostatic load due to stored liquid has an axisymmetric distribution on the tank shell and base. However, during seismic events, the hydrodynamic load originating from the seismic acceleration of liquid in the tank starts to act in the direction of the earthquake motion. This leads to a nonaxisymmetric loading distribution, which may result in buckling and uplifting of the tank structure. Finite element models were created having nonlinear material properties and large deformation capabilities. Three different tank geometries with liquid height to tank radius aspect ratios of 0.67, 1.0, and 3.0 were selected representing broad, nominal, and slender tanks. These tanks were subjected to two different hydrodynamic loading based on Housner's and Jacobsen–Veletsos' pressure distributions, which forms the basis of design provisions used in American Petroleum Institute API 650 and Eurocode 8, respectively. These pressure distributions were formulated under the assumption of rigid tank wall and base. Furthermore, each tank for a given geometry was subjected to two different foundations: (1) representing a rigid foundation and (2) representing a flexible foundation. The flexible foundation was created using a series of compression-only elastic springs attached to tank base having equivalent soil stiffness. Static analysis corresponding to maximum dynamic force was performed. The finite element results for circumferential and longitudinal stress in the shell were compared with the provisions of API 650. It was found that the effect of foundation flexibility from the practical design point of view may be neglected for broad tanks, but should be considered for nominal and slender tanks.

Although acceleration and cumulative absolute velocity (CAV) are used as seismic indexes, their relationship with the damage mechanism is not yet understood. In this paper, a simplified evaluation method for seismic fatigue damage, which can be used as a seismic index for screening, is derived from the stress amplitude obtained from CAV for one cycle in accordance with the velocity criterion in ASME Operation and Maintenance of Nuclear Power Plants 2012, and the linear cumulative damage due to fatigue can be obtained from the linear cumulative damage rule. To verify the performance of the method, the vibration response of a cantilever pipe is calculated for four earthquake waves, and the cumulative fatigue damage is evaluated using the rain flow method. The result is in good agreement with the value obtained by the method based on the relative response. When the response spectrum obtained by the evaluation method is considered, the value obtained by the evaluation method has a peak at the peak frequency of the ground motion, and the value decreases with increasing natural frequency above the peak frequency. A higher peak frequency of the base leads to a higher value obtained by the evaluation method.

The uniform response spectrum (URS) analysis method is generally used to seismic qualification of piping systems in nuclear power plants (NPPs). This method can reasonably not only compute dynamic responses of the piping systems exposed to different seismic motions from the building but also tend to overestimate the responses due to an assumption while conservatively considering a variety of the characteristic among input loadings. Increases of design seismic motions for NPPs in Japan by 2–3 times due to the 2011 off Pacific Coast of Tohoku Earthquake resulted that structures, systems, and components such as piping systems are subject to numbers of additional supporting structures to meet the design code requirements. Use of multiple-input analysis methods (independent support motion methods) is expected to bring high degree of precision in dynamic responses than the URS method. However, existence of a handful of experimental tests prevents from utilizing the method in the design process for NPPs in Japan. In order to practically utilize the multiple-input analysis methods in the plant design, this paper provides validation analyses and results for the multiple-input analysis methods for piping by conducting excitation tests and validation analyses. Some recommendations were also found in the study for seismic design of NPPs.

The accident at the Fukushima Dai-ichi Nuclear Power Plant (NPP) resulting from the 2011 Great East Japan Earthquake raised awareness as to the importance of considering Beyond Design Basis Events (BDBE) when planning for safe management of NPPs. In considering BDBE, it is necessary to clarify the possible failure modes of structures under extreme loading. Because piping systems are one of the representative components of NPPs, an experimental investigation was conducted on the failure of a pipe assembly under simulated excessive seismic loads. The failure mode obtained by excitation tests was mainly fatigue failure. The reduction of the dominant frequency and the increase of hysteresis damping were clearly observed in high-level input acceleration due to plastic deformation, and they greatly affected the specimens’ vibration response. Based on the experimental results, a procedure is proposed for calculating experimental stress intensities based on excitation test so that they can be compared with design limitations.

This article presents the experimental and numerical studies of fatigue-ratcheting in carbon steel piping systems under internal pressure and earthquake load. Shake table tests are carried out on two identical 6 in pressurized piping systems made of carbon steel of grade SA333 Gr 6. Tests are carried out using similar incremental seismic load till failure. Wavelet analysis is carried to evaluate frequency change during testing. The tested piping systems are analyzed using iterative response spectrum (IRS) method, which is based on fatigue-ratcheting and compared with test results. Effect of thickness variation in elbow on strain accumulation is studied. Excitation level for fatigue-ratcheting failure is also evaluated and the details are given in this paper.

In this paper, performance criteria for the seismic design of industrial liquid storage tanks and piping systems are proposed, aimed at introducing those industrial components into a performance-based design (PBD) framework. Considering “loss of containment” as the ultimate damage state, the proposed limit states are quantified in terms of local quantities obtained from a simple and efficient earthquake analysis. Liquid storage tanks and the corresponding principal failure modes (elephant's foot buckling, roof damage, base plate failure, anchorage failure, and nozzle damage) are examined first. Subsequently, limit states for piping systems are presented in terms of local strain at specific piping components (elbows, Tees, and nozzles) against ultimate strain capacity (tensile and compressive) and low-cycle fatigue. Modeling issues for liquid storage tanks and piping systems are also discussed, compared successfully with available experimental data, and simple and efficient analysis tools are proposed, toward reliable estimates of local strain demand. Using the above reliable numerical models, the proposed damage states are examined in two case studies: (a) a liquid storage tank and (b) a piping system, both located in areas of high seismicity.

Many recent studies have emphasized the need for improving seismic performance of nonstructural systems in critical facilities in order to reduce the damage as well as to maintain continued operation of the facility after an earthquake. This paper is focused on evaluating system-level seismic fragility of the piping in a representative high-rise building. Piping fragilities are evaluated by incorporating the nonlinear finite-element model of a threaded Tee-joint that is validated using experimental results. The emphasis in this study is on evaluating the effects of building performance on the piping fragility. The differences in piping fragility due to the nonlinearities in building are evaluated by comparing the fragility curves for linear frame and nonlinear fiber models. It is observed that as nonlinearity in the building increases with increasing value of peak ground acceleration, the floor accelerations exhibit a reduction due to degradation/softening. Consequently, the probabilities of failure increase at a slower rate relative to that in a linear frame. It is also observed that a piping located at higher floor does not necessarily exhibits high fragilities, i.e., the fundamental building mode is not always the governing mode. Higher order building modes with frequencies closest to critical piping modes of interest contribute more significantly to the piping fragility. Within a particular building mode of interest, a good indicator of the amplification at different floor levels can be obtained by the product of mode shape ordinate and modal participation factor. Piping fragilities are likely to be higher at floor levels at which this product has a higher value.

We demonstrate a comprehensive earthquake response analysis method for improving the seismic input force estimation of buried pipelines by combining ground motion and soil amplification analyses. Using this method, the seismic input force of an actual pipeline was estimated and its seismic performance was checked for a largest assumed seismic fault scenario. Three-dimensional inhomogeneity of ground and surface topography is known to greatly affect the results of ground motion and soil amplification analyses. To consider these effects, a linear wave propagation analysis using a 10 × 10 9 degree-of-freedom three-dimensional finite element model was conducted for the ground motion analysis, and a nonlinear wave propagation analysis using an 80 × 10 6 degree-of-freedom three-dimensional finite element model was conducted for the soil amplification analysis. The application example showed that three-dimensional inhomogeneity of ground and surface topology caused complex seismic input forces to buried pipelines, and demonstrated the effectiveness of the comprehensive seismic analysis method proposed in this study.

The need of enhanced seismic analysis and design rules for petrochemical piping systems is widely recognized, where the allowable stress design method is still the customary practice. This paper presents an up-to-date performance-based seismic analysis (PBSA) of piping systems. The concept of performance-based analysis is introduced and a link between limit states and earthquake levels is proposed, exemplifying international code prescriptions. A brief review on seismic design criteria of piping systems is then provided by identifying the main critical issues. Finally, the actual application of the performance-based approach is illustrated through nonlinear seismic analyses of two realistic petrochemical piping systems.

With a purpose of identifying the failure mode and associating the ultimate strength of piping components against seismic integrity, many kinds of failure tests have been conducted for thick wall piping for light water reactors (LWRs). However, there are little failure test data on thin wall piping for sodium cooled fast reactors (SFRs). In this paper, a series of failure tests on thin wall elbows for SFRs is presented. Based on the tests, the failure mode of a thin wall piping component under seismic loads was identified to be fatigue. The safety margin included in the current design methodology was clarified quantitatively.

The minimum wall thickness required to prevent seismic buckling of a reactor vessel (RV) in a fast reactor is derived using the system based code (SBC) concept. One of the key features of SBC concept is margin optimization; to implement this concept, the reliability design method is employed, and the target reliability for seismic buckling of the RV is derived from nuclear plant safety goals. Input data for reliability evaluation, such as distribution type, mean value, and standard deviation of random variables, are also prepared. Seismic hazard is considered to evaluate uncertainty of seismic load. Minimum wall thickness required to achieve the target reliability is evaluated, and is found to be less than that determined from a conventional deterministic design method. Furthermore, the influence of each random variable on the evaluation is investigated, and it is found that the seismic load has a significant impact.

Dynamic loads in piping systems are mainly caused by transient phenomena generated by operating conditions or installed equipment. In most cases, these dynamic loads may be modeled as harmonic excitations, e.g., pulsating flow. On the other hand, when designing piping systems under dynamic loads, it is a common practice to neglect strong nonlinearities such as shocks and friction between pipe and support surfaces, mainly because of the excessive cost in terms of computational time and the complexity associated with the integration of the nonlinear equations of motion. However, disregarding these nonlinearities for some systems may result in overestimated dynamic amplitudes leading to incorrect analysis and designs. This paper presents a numerical approach to calculate the steady-state response amplitudes of a piping system subjected to harmonic excitations and considering dry friction between the pipe and the support surfaces, without performing a numerical integration. The proposed approach permits the analysis of three dimensional piping systems, where the normal forces may vary in time and is based in the hybrid frequency–time domain method (HFT). Results of the proposed approach are compared and discussed with those of a full integration scheme, confirming that HFT is a valid and computationally feasible option.

This paper deals with the effectiveness of two isolation systems for the seismic protection of elevated steel storage tanks. In particular, the performance of high damping rubber bearings (HDRB) and friction pendulum isolators (FPS) has been analyzed. As case study, an emblematic example of elevated tanks collapsed during the Koaceli Earthquake in 1999 at Habas pharmaceutics plant in Turkey is considered. A time-history analysis conducted using lumped mass models demonstrates the high demand in terms of base shear required to the support columns and their inevitable collapse due to the insufficient shear strength. A proper design of HDRB and FPS isolator according to the EN1998 and a complete nonlinear analysis of the isolated tanks proved the high effectiveness of both isolation systems in reducing the response of the case tank. Actually, the stability conditions imposed by the code and a reduced level of convective base shear obtained with the second isolation typology suggests the use of FPS isolators rather than HDRB devices.