Seismic Protection of Lead-Cooled Reactors

Transcription

1 Seismic Protection of Lead-Cooled Reactors Finite Element Modelling and Dynamic Analyses of Isolated NPPs Francisco Beltrán SILER Project Training Course Verona, May 2012

2 TABLE OF CONTENTS Documents for reference What is different from fixed-base modelling? General approach Modelling steps Typical results Concluding remarks

3 DOCUMENTS FOR REFERENCE Primer on Seismic Isolation, ASCE (2004) Overview document (58 pages) Excellent introduction: It covers: Basic concepts Current state of seismic isolation technology Highlights issues and concerns unique to the design of isolated structures Principles, isolation systems, examples, performance Design & Analysis of isolated structures Testing of isolators

4 DOCUMENTS FOR REFERENCE Seismic Analysis of Safety-Related Nuclear Structures, ASCE 4 (rev. 2) Revision to ASCE 4-98, to be released in 2012 Section on seismically isolated structures completely revised: Environmental and operating conditions Isolator performance Modelling and analysis requirements Only three types of seismic isolators are considered as viable alternatives for nuclear safety-related structures: Sliding bearings with restoring forces provided by gravity Low-damping elastomeric bearings Lead-rubber elastomeric bearings

5 DOCUMENTS FOR REFERENCE Design of Seismic Isolated Structures, Naeim & Kelly (Wiley, 1999) From theory to practice: very good textbook (300 pages) It covers: Theoretical basis Isolation systems components (US) Code provisions for seismic isolation Mechanical characteristics & modelling of isolators Buckling & stability of elastomeric isolators Design earthquake ground motions Design examples & computer applications

6 WHAT IS DIFFERENT FOR FEA MODELLING? Shift of fundamental frequencies of the structure In NPPs, typically go from 2-8 Hz to Hz Implications for modelling: Isolation system governs the response: accurate modelling of stiffness, damping and spatial distribution of isolators becomes essential. Non-linear behaviour at the isolators can be important. Importance should be assessed. (taken from ASCE Primer on Seismic Isolation) Beware of the mass proportional part of Rayleigh damping.

7 WHAT IS DIFFERENT FOR FEA MODELLING? but fixed-base frequencies are also important Isolation system usually does not isolate from vertical motion Vertical-horizontal coupling can occur: vertical ground motion can excite horizontal motion of the isolated structure (see Politopoulos & Moussallam, EESD, 2011). Interaction can be very significant (see Tokamak complex at ITER). Implications for modelling: Rules for modelling fixed-base structures should be respected for the isolated structure. Isolation does not justify a less detailed modelling above the isolation system, specially for structures not respecting the seismic design golden rules (regular distribution of mass and stiffness, direct and continuous load paths, etc.)

8 WHAT IS DIFFERENT FOR FEA MODELLING? Time-variability of isolator properties should be introduced Lack of experience on long-term behaviour Present target design life for a NPP is years Limited data on variation of properties when subject to sustained gravity loads over long periods of time (in excess of 10 years) Radiation induced change of properties Neoprene: if integrated dose exceeds 10 6 rad (gamma radiation) PTFE: if integrated dose exceeds 10 4 rad (gamma radiation) Implications for modelling: Three set of properties are commonly used for isolators: Best estimate Lower bound Upper bound

9 WHAT IS DIFFERENT FOR FEA MODELLING? Maximum displacements are an essential result Lateral displacements concentrate at the isolation system Govern the design of the utilities going into the isolated structure and the gap or moat around the structure Implications for modelling: Output is not just internal forces and moments + Floor Response Spectra (FRS) (taken from ASCE Primer on Seismic Isolation)

10 GENERAL APPROACH Pre-design Estimate preliminary characteristics of: - Isolation system - Superstructure Compute global response (simplified): - Maximum displacements - Story shears Assess performance Compare with target Adequate? Yes Compute global response (refined): - Verify performance - Time-history / Non-linear No Isolator properties from manufacturers, other projects Seismic input Modify characteristics - Isolation system / spatial distribution - Superstructure Final isolator distribution & properties (e.g. from specific qualification testing) Simplified analyses can be based on equivalent static computations Time-history analysis is usually unavoidable for final assessment

11 GENERAL APPROACH This presentation focuses on final (refined) finite element analysis Detailed 3D model of superstructure and isolation system Usually includes a foundation soil representation for SSI Non-linear time history analysis It could be linear for low damping elastomeric bearings, if linear viscoelastic elements are used, with appropriate values of secant stiffness and equivalent damping. Bounding analyses to take into account range of property variations A number of analyses is required to characterize the response, corresponding to the range of isolator and soil properties variability

12 GENERAL APPROACH Factors to consider in FE modelling Accurate distribution of superstructure stiffness and mass Similar to fixed-base modelling. Accurate spatial distribution of isolators Results of potential uplift or differential horizontal movement at isolators depend on spatial distribution. Performance of isolators can also depend on vertical load. Effects of bi-directional loading on the performance of isolators Three-dimensional modelling is required. Translational and torsional displacements of the superstructure should be captured. Differential horizontal movement causes differences in vertical deformations. Accurate representation of isolator s response (it can be non-linear) Non-linear behaviour is very important for lead-rubber, high-damping rubber and friction pendulum (FPS) isolators.

13 GENERAL APPROACH Commercially available computer codes Special purpose codes SAP2000 (CSI) ETABS (CSI) General purpose codes ABAQUS (Simulia) ANSYS (Ansys) For safety-related structures: quality assurance is an issue Development under quality procedures Validation of installation in a particular machine

14 MODELLING STEPS Seismic input Three independent sets of threecomponent acceleration time-series Compatible with ground motion design response spectra

15 MODELLING STEPS Model of the superstructure Study of design drawings & CAD models (Note: images and drawings correspond to an old, obsolete, version of the Tokamak Complex building of ITER. Courtesy of F4E)

16 MODELLING STEPS Model of the superstructure Study of design drawings & CAD models Identify structural system Lateral force resisting system

17 MODELLING STEPS Model of the superstructure Study of design drawings & CAD models Identify structural system Lateral force resisting system

18 MODELLING STEPS Model of the superstructure Finite element modelling Usually based on 1D (beams, columns) and 2D (walls, slabs) finite elements A detailed FE model is usually based on: 4 6 nodes (column/shear wall elements) between floors 5 8 nodes (beam/slab elements) between gravity supporting lines Element size should allow to explicitly represent every single isolator. A very large FE model can result: Quality checks should be carried out and documented. Note: Given size of elements is based on a broad band ground motion spectrum, with main energy content between 2 and 12 Hz. Higher frequency excitation may require finer meshes.

19 MODELLING STEPS Model of the superstructure Model size: nodes elements 3500 MPCs Mass configuration: Self weight Dead load 25-50% of live load

20 MODELLING STEPS Model of the superstructure Finite elements Finite elements / Expanded to show actual cross sections

21 MODELLING STEPS Model of the superstructure Material constitutive models For nuclear applications, linear elastic models are used for structural materials: steelwork, reinforced concrete, pre-stressed concrete Energy dissipation is introduced by means of code-allowable damping ratios for each structural material. Density Material densities are adjusted to match the required mass configuration As an alternative, non-structural masses can be added

22 MODELLING STEPS Model of the superstructure Quality checks Overall geometry Wall/slab thickness Beam/column cross sections & orientation Material properties & assignment to finite elements Total mass / Position of CoG Boundary conditions Fixed base modes & Mode shapes Gravity load deformed shape Comparison with previous (simpler) models

23 MODELLING STEPS Model of the isolation system Geometry Input data: Lay-out of isolators Size of isolators Dimensions of plinths

24 MODELLING STEPS Model of the isolation system Geometry Low-damping isolators (900 x 900 mm, 6 layers of 20 mm elastomer)

25 MODELLING STEPS Model of the isolation system Idealization Isolators are represented using linear or non-linear springs

26 MODELLING STEPS Isolator behaviour Low damping elastomeric bearings (LD) Use equivalent linear springs + viscous damping (typically, 2-5%) Force Ke Displacement Vertical stiffness is much higher than horizontal Dynamic stiffness can be larger than static

27 MODELLING STEPS Isolator behaviour Lead-rubber bearings (LR) Damping is given by the hysteresis loop Initial horizontal stiffness corresponds to low load (e.g. wind) Vertical stiffness is commonly considered constant (linear) Coupling between horizontal responses (biaxial plasticity) is not usually available in general purpose computer programs.

28 MODELLING STEPS Isolator behaviour Friction pendulum bearings (FP) Damping is given by the hysteresis loop No displacement until friction resistance is reached Vertical stiffness is commonly considered large or infinite Coupling between horizontal responses (biaxial plasticity) is not usually available in general purpose computer programs.

29 MODELLING STEPS Soil structure interaction Difficult problem by its own Details are out of the scope of this presentation Springs are usually introduced at the foundation basemat The springs represent the flexibility of the foundation soil Damping ratios associated to springs represent both material and radiation damping of foundation soil

30 MODELLING STEPS Damping Rayleigh damping Only source of damping when equivalent linear springs are introduced (low damping isolators) Adjust alpha and beta coefficients to have target damping ratios across the frequencies of interest

31 SEQUENCE OF ANALYSES Initial quality checks Static analyses - Gravity loads - Wind Look for suspicious or unexpected behaviour Check that wind displacements are small Correct modelling mistakes Eigenvalue analysis: - Natural frequencies - Mode shapes Look for suspicious or unexpected behaviour Identify main modes and check that deformed shape is smooth in these modes Correct modelling mistakes Non-linear time history analyses: - Several EQs - Range of soil/isolator properties - Response time histories Post-processing: - Displacements - Internal forces & moments - Floor response spectra Design values of structural response

32 SEQUENCE OF ANALYSES Number of required time-history analyses ASCE-4 (draft Rev. 2) In draft ASCE-4, only best estimate mechanical properties for isolators are introduced in the analyses Lower bound EQuake 1 (XYZ accelerog) Run 1 EQuake 2 (XYZ accelerog) Run 2 EQuake 3 (XYZ accelerog) Run 3 Draft ASCE-4 does not allow for variation of mechanical properties of isolators by more than 20% over the lifespan Best estimate prop. of soil Run 4 Run 5 Run 6 ASCE-4 looks for seismic demand at the 80% percentile level. Upper bound Run 7 Run 8 Run 9 Following this approach, peak maximum values of the response parameters of interest shall be used for design

33 SEQUENCE OF ANALYSES Number of required time-history analyses Eurocode 8 (EN :2004) Requires to consider the most unfavourable properties to be attained during lifetime. This consideration forces the introduction of variability of isolator properties in the analysis matrix (the most unfavourable properties are not known in advance). Mean values of properties can be used if extreme values do not differ 15% from the mean (only for low-importance class buildings). If the number of considered earthquakes exceeds a threshold (seven), average of computed responses can be used for design, instead of the peak maximum values.

34 TYPICAL RESULTS Isolation system Gravity load distribution

35 TYPICAL RESULTS Isolation system Seismic loading Horizontal load distribution / Maximum displacement

36 TYPICAL RESULTS Isolation system Seismic loading Vertical load distribution

37 TYPICAL RESULTS Isolation system Load combinations Safety factors

38 TYPICAL RESULTS Floor response spectra Horizontal East-West Upper basemat / Best estimate props Before peak broadening

39 TYPICAL RESULTS Floor response spectra Horizontal North-South Upper basemat / Best estimate props Before peak broadening

40 TYPICAL RESULTS Floor response spectra Vertical Upper basemat / Best estimate props Before peak broadening

41 TYPICAL RESULTS Floor response spectra Horizontal East-West Roof DGB / Best estimate props Before peak broadening

42 TYPICAL RESULTS Floor response spectra Horizontal North-South Roof DGB / Best estimate props Before peak broadening

43 TYPICAL RESULTS Floor response spectra Vertical Roof DGB / Best estimate props Before peak broadening

44 TYPICAL RESULTS Floor response spectra A second peak appears in the horizontal FRS Isolation is not as affective as expected due to coupling between horizontal and vertical motion in the superstructure

45 TYPICAL RESULTS Floor response spectra A second peak appears in the horizontal FRS In any case, horizontal FRS are below the ground design response spectra, except for some peaks at the upper elevations of the building. Vertical motion is not isolated Emphasis for design of floor mounted equipment goes to the vertical motion.

46 CONCLUDING REMARKS The biggest challenge for the analysis of isolated structures is incorporating the effects of non-linear isolator behaviour As for any non-linear problem, an approach going from simple computations to the final design complex analyses is recommended. 3D FE analyses of complex isolated structures can lead to unexpected results Those results should be investigated and confirmed by alternative analyses or independent verification.