This paper addresses the influence of support gaps in the analyses of a piping system when subjected to a seismic hard rock high-frequency load. The system is located within the reactor containment building of a nuclear power plant and is assessed to be susceptible to high-frequency loads. The stress response of the pipe and the acceleration response of the valves are evaluated for different support gap sizes. It is shown that the inclusion of the support gaps in the analyses reduces the stress response for almost all pipe elements. On the other hand, the acceleration response of the valves is not necessarily reduced by the consideration of the gaps.

This paper presents a study on water filled pools within nuclear facilities subjected to seismic loads. The type of structure studied is an elevated rectangular concrete tank, supported by the reactor containment, which is a high cylindrical concrete structure. Seismic analysis is performed using finite element models, accounting for fluid-structure interaction (FSI) between the water and the concrete structure. The stresses in a concrete pool are calculated, also investigating the changes in stresses as additional cross-walls are added. The effects from earthquakes dominated by low and high frequencies are evaluated, representative for conditions at the West coast of North America and Northern Europe, respectively. It is shown that the coupled fluid-structure systems have more significant modes in the high frequency range compared to the models without water, that is, for frequencies at which the Northern European type earthquake has significant energy compared to the Western North American earthquake. The seismic analyses show that the relative increase of hydrodynamic pressure is higher when the outer walls of the pool are stiffened due to the inclusion of additional cross-walls. With the inclusion of additional cross-walls, modes with lower natural frequencies, although still relatively high, become more important for the hydrodynamic pressure response. Leading to a higher stress response in the outer walls of the pool for models including the additional cross-walls compared to models without cross-walls. The study indicates that the effect from fluid-structure interaction is of great importance also for seismic loads with relatively high-frequency content.

A concrete arch dam have been analyzed during seismic loading with a model based on acoustic elements to describe the water and infinite elements as quiet boundaries to prevent wave reflection. The results have also been compared with a simplified model based on Westergaards added mass approach. The simplified model is only used, in this study, for comparison with the more advanced model with acoustic elements. Therefore the results from this simplified model are just used as a rough estimate of the induced stresses and displacements. Despite this, the simplified Westergaard model gives similar results compared to the more advanced model with acoustic elements for the water and infinite elements for the boundaries. The largest difference between the models often occurs at the nodes in the base of the arch dam, which may be due to poor discretization. Generally, the Westergaard added mass gives higher maximum principal stresses at the base on the upstream side than the acoustic model, while often underestimating the min principal stresses at the base on the downstream side. Both models show high tensile stresses near the base of the arch dam that would result in cracks.

The objective of this paper is to evaluate different approaches to account for fluid-structure interaction (FSI) in seismic analyses of nuclear facilities. Different methods to account for FSI, from simplified to highly advanced numerical methods, are briefly reviewed and some important concepts are discussed. A benchmark example of a simple tank sloshing problem is included to evaluate the use of different FSI methods.

The main conclusion from the study is that it is of great significance to first of all include the effect of FSI. When considering the response of a tank subjected to a load of periodic nature, as in the benchmark example, the hydrodynamic effects are very important, since they increase the load effect on the structure. It is also observed that the simplified methods, in which the hydrodynamic effects are included as a mass-spring system, results in much higher stresses in the structure than if the fluid is included as continuum elements. However, the more advanced methods lead to extra computational time and also require more from the analyst. With the focus of this project being the global response of the structure, most methods describe the fluid unnecessarily complicated and phenomena such as splashing and turbulence are of little interest. The main aspects that influence the structure are the mass and inertia of the fluid along with the surface waves, the sloshing. Considering this, simplified methods such as elements with acoustic equations, and even mass-spring systems, to represent the fluid, often give results that are accurate enough.

Methods to describe the interaction between fluids and solids has been one of the biggest focus points for the research within the field of computationalengineering for the recent years. This area is of interest to a variety ofengineering problems, ranging from flow in blood vessels, aerodynamics andof course the interaction between water and civil engineering structures. Thetypical civil engineering application of fluid-structure interaction (FSI)encountered in a nuclear facilities is obtained at seismic loading, where the nuclear facilities consists of water filled pools of various sizes, for example the spent fuel and condensation pools. These water filled pools contribute with added mass to the structure, which lowers the natural frequency of thestructure as well as hydrostatic and hydrodynamic pressure that acts on thewalls of the pool due to wave propagation in the fluid. In addition, as the pools also have a free water surface towards the environment of thestructure, free surface wave propagation also has to be accounted for; i.e.sloshing. This introduces extra non-linearity to the problem, since a freesurface constitutes a boundary condition with an unknown location.

The main part of this report constitutes as a state-of-the-art summary whereconcepts important for FSI analyses are presented and important differencesare discussed. Due to the different interests of the numerous disciplinesengaged in this research area, a large number of methods have been developed, where each has different strengths and weaknesses suited for the problem in mind when developing the method. The focus of this report havebeen to describe the most important numerical techniques and the categories of methods that or of most interest for civil engineering problems, such as simplified analytical or mass-spring models, Acoustic Elements, ArbitraryLagrangian-Eulerian (ALE) and coupled Eulerian-Lagrangian (CEL).

Thereafter two benchmark examples are presented, intended to highlightdifferences between the different methods. In the first study, sloshing of aliquid tank is studied where the numerical methods are compared toexperimental results, regarding the movement of the free water surface. In addition, the hydrodynamic (fluid) pressures on the walls of the tanks arecompared between the different numerical methods. It was shown that mostanalysis methods give accurate results for the sloshing wave height whencompared with the experimental data. It should however be mentioned that the tank was only excited by a simple harmonic motion with a frequency thatdo not give rise to any resonance waves in the water body.

Also when it comes to fluid pressure good agreement between the differentanalysis methods was found, although no experimental data was available forthis parameter. It was also noticed that for the sloshing tank, most of the change in pressure occurred close to the free surface of the water, which indicates that it mainly consists of a convective pressure, i.e. from the sloshing. Thereby, finite element programs that account the impulsive mass incivil engineering FSI problems should not be used for this type of analysis. In the second study, the numerical methods are compared based on differenttypes of seismic input, such as a large earthquake with mainly low frequencycontent typically like an earthquake on the US west coast and one smallerearthquake with relatively higher degree of high frequency content typicallylike a Swedish type of earthquake. One important observation was that the relative increase in induced stresses in the structure, with and withoutconsideration of the water was significantly larger for the Swedish earthquakethan for the US earthquake. One possible reason for this may be that the Swedish earthquake is not large enough to excite the relatively stiff structurewithout any water, but it will induce significant dynamic effects in the waterwhich give rise to higher stresses in the concrete as well. However, this shows that it is very important to include water in seismic analyses.

Metoder för att beakta interaktionen mellan fluider och strukturer har varit ettav de främsta forsknings- och utvecklingsområdena inom numeriska metoderunder de senaste åren. Detta område tillämpas inom en rad olika tekniskaproblem, så som flöde i blodkärl, aerodynamik och naturligtvis interaktionenmellan byggnader och vatten. En typisk tillämpning av fluid-strukturinteraktion(FSI) inom konstruktionsanalyser av kärntekniska anläggningar, uppstår vid seismisk belastning där anläggningen inkluderar vattenfylldabassänger i olika storlekar, så som bränsle- och kondensationsbassänger. Vattnet i dessa bassänger har en stor inverkan på strukturens verkningssätt,där det dels bidrar med en ökad massa som sänker strukturensegenfrekvenser, dessutom ger vattnet upphov till hydrostatiskt och hydrodynamiskt tryck på bassängens väggar p.g.a. vågutbredningen i fluiden. Dessutom, eftersom bassängerna har en fri vattenyta så måste även den friaytans vågutbredning beaktas, d.v.s. sloshing. Detta medför ytterligare enicke-linjäritet i problemet, eftersom en fri yta utgör ett okänt randvillkor. Huvuddelen av denna rapport utgör en state-of-the-art sammanställning, där de begrepp som är väsentliga för FSI analyser presenteras och viktiga skillnader diskuteras. På grund av alla olika tekniska tillämpningar av FSI hosolika discipliner inom forskningsområdet, så har en stor mängd metoderutvecklats. Varje metod har sina styrkor respektive svagheter beroende påvilken tillämpning som den har utvecklats för. Fokus i denna rapport har varit att beskriva de numeriska metoder samt de kategorier av metoder som är avstörst intresse för konstruktionsanalyser, såsom förenklade analytiskametoder, modeller baserade på massa-fjäder system, akustiska element, Arbitrary Lagrangian-Eulerian (ALE) och coupled Eulerian-Lagrangian (CEL).

I rapporten presenteras två numeriska beräkningsexempel, avsedda attbelysa skillnader mellan de olika FSI metoderna. I den första studien,studeras sloshing av en vätskefylld tank där olika numeriska metoder jämförsmot experimentellt uppmätta vågrörelser hos den fria vattenytan. Dessutomjämförs de hydrodynamiska trycken på tankens väggar mellan de olikanumeriska metoderna. Resultaten visar att de flesta analysmetoder ger mycket goda resultat avseende våghöjden jämfört med de experimentellaresultaten. Det bör dock nämnas att tanken belastades av en enkel harmoniskrörelse med en frekvens som inte gav upphov till några resonansvågor ivattnet. Även när det gäller det hydrodynamiska trycket erhölls en godöverensstämmelse mellan de olika analysmetoderna, dock fanns ingaexperimentellt uppmätta tryck att jämföra mot. Det noterades också att den huvudsakliga variationen i tryckfördelning uppstod nära den fria vattenytan, vilket indikerar att den huvudsakligen beror på det konvektiva trycket, d.v.s. orsakat av ytvågor. Detta illustrerar att finita element program som förenklatbeskriver FSI analyser genom att endast inkludera den impulsiva massan inte bör användas för denna typ av analys. I det andra beräkningsexemplet,jämförs de numeriska metoderna vid olika typer av seismiska tidssignaler,d.v.s. en stor jordbävning bestående av huvudsakligen lågfrekvent innehållvilket är typiskt för en jordbävning på USA:s västkust, samt en mindre jordbävning med relativt hög grad av högfrekvent innehåll vilket motsvarar en svensk jordbävning. En viktig iakttagelse var att den relativa ökningen avinducerade spänningar i strukturen, med respektive utan hänsyn till vattnet,var betydligt större för den svenska jordbävningen än för motsvarande amerikanska. En möjlig orsak till detta kan vara att den svenskajordbävningen inte är tillräckligt stor för att excitera den relativt styva strukturen utan vatten, men att den orsakar signifikanta dynamiska effekter ivattnet som ger upphov till högre spänningar i betongen. Detta belyserdärmed vikten av att inkludera vatten i seismiska analyser.