Abstract: Spent fuel racks are steel structures designed to store the spent fuel assemblies removed from the nuclear power reactor. They rest in free-standing conditions submerged in the depths of the spent fuel pool. During a strong-motion earthquake, racks undergo large displacements subjected to inertial forces. An accurate estimation of their response is essential to achieve a safe pool layout and a reliable structural design. A transient analysis with direct integration of the equation of motion throughout the whole earthquake duration becomes therefore unavoidable. The computational cost associated to this analysis leads to the use of simplified finite element models giving rise to a certain dose of uncertainty. This paper carries out a parametric analysis of the key modelling properties for a two-rack system. This technique examines the behavior of the main transient outputs as a modelling parameter is systematically varied. Numerical results provide a source of insight into the general behavior of the rack system and an effective tool to propose an efficient and reliable modeling and meshing. The trade-off between outputs and computational cost and is also discussed.

1. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa.
ENSA (Grupo SEPI)
ESREL 2017
Portoroz, Slovenia
Alberto GONZALEZ MERINO
Parametric analysis of modelling properties
governing the seismic response of
free-standing spent fuel racks
HORIZON 2020
Marie Skłodowska-Curie Actions
Training in Reducing Uncertainty
in Structural Safety

2. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa.
Outline
• Spent Fuel Rack
o Introduction
o Challenges of their seismic analysis
• Current analysis methodology
• Sources of uncertainty
• Parametric analysis of modelling properties (OFAT)
• Sensitivity analysis of modelling properties
o Scatter plots
o Sobol order indices
o PCE metamodelling
• Conclusion

3. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa.
Steel structures designed to store nuclear spent fuel assemblies removed
from the nuclear power reactor.
• Slightly spaced by only a few centimeters,
• free-standing conditions,
• submerged in water.
Spent Fuel Racks
Spent Fuel Pool
6x4 racks
Fuel storage
rack unit
~4m
~12m
Nuclear Fuel
assemblies

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Highly nonlinear behavior
o Contacts are changing-status singularities affecting the stiffness matrix
o Friction hysteresis and damping bring energy-dissipative effects.
Transient Dynamic response
o Input time-history acceleration loading and time-depending variables,
o Inertial and damping effects,
o Direct integration of the equation of motion (superposition principle),
o Numerical integration through iterative algorithms: Newmark and
alpha method.
Fluid-Structure Interaction
o Water coupling between pool & racks, racks & racks → ‘in-phase’
motion,
o Dynamic fluid and fuel assemblies inside the storage cells.
Challenges of the rack seismic analysis

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RACK SYSTEM
STRUCTURAL MODEL
SEISMIC MODEL
Soler, A.I., & Singh, K.O.
(1982)
FLUID MODEL
Loads and displacements to
• Calculate local stresses
• Check instabilities
Current analysis methodology
SHELL63
MASS21

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7. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa.
Sources of uncertainty
Modelling features
Hydrodynamic mass approach
Numerical integration algorithms
FE meshing
Dynamic frictional contactsStochastic input data
Spent Fuel Pool
6x4 racks
Fuel storage
rack unit
~4m
~12m
Nuclear Fuel
assemblies

8. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa.
Parametric analysis
One-factor-at-a-time (OFAT)
A. Data Input
••Seism time-history
••Rack mass &
submerged weight
••Fuel mass &
submerged weight
••Eigen-frequency X
••Eigen-frequency Z
••Hydrodynamic mass
matrix
B. Modelling properties
••FE mesh
discretization
••Rack-to-Pool
friction coefficient
••Rack-to-Pool
contact stiffness
••Fuel-to-cell contact
stiffness
••Fuel-cell gap
••Fuel flexural rigidity
C. Analysis parameters
••Integration
parameter (INTPARA)
••Convergence criteria
(CNVTOL)
••Equilibrium
iterations (NEQIT)
••Stiffness proportional
damping (ALPHAD)
••Mass proportional
damping (BETAD)
••Time marching
(DELTIM)

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• Mesh discretisation
B: Parametric analysis of modelling properties
0.0E+00
2.0E+04
4.0E+04
6.0E+04
8.0E+04
1.0E+05
1.2E+05
1.4E+05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0 10 20 30 40 50
Max vertical force on support (N)
Relative sliding displacement R1-Pool (m)
Max. Sliding disp.
Min. Sliding disp.
Max. Vertical force

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• Rack-to-pool friction coefficient
B: Parametric analysis of modelling properties
0.0E+00
2.0E+04
4.0E+04
6.0E+04
8.0E+04
1.0E+05
1.2E+05
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.2 0.3 0.4 0.5 0.6 0.7 0.8
Max vertical force on support (N)
Relative sliding displacement R1-Pool (m)
Max. Sliding disp.
Min. Sliding disp.
Max. Vertical force

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• Rack-to-pool contact stiffness
B: Parametric analysis of modelling properties
0.0E+00
3.0E+04
6.0E+04
9.0E+04
1.2E+05
1.5E+05
1.8E+05
2.1E+05
2.4E+05
-0.12
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
1.E+06 1.E+07 1.E+08 1.E+09 1.E+10 1.E+11 1.E+12
Max. Vertical force on support (N)
Relative sliding displacement R1-Pool (m)
Max. Sliding disp.
Min. Sliding disp.
Max. Vertical force

12. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa.
• Fuel-to-cell contact stiffness
B: Parametric analysis of modelling properties
-3.0E+04
0.0E+00
3.0E+04
6.0E+04
9.0E+04
1.2E+05
1.5E+05
1.8E+05
2.1E+05
2.4E+05
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10
Max. Vertical force on support (N)
Relative sliding displacement R1-Pool (m)
Max. Sliding disp.
Min. Sliding disp.
Max. Vertical force

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• Fuel-cell inner gap
B: Parametric analysis of modelling properties
0.0E+00
2.5E+04
5.0E+04
7.5E+04
1.0E+05
1.3E+05
1.5E+05
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
2 4 6 8 10 12 14
Max vertical force on support (N)
Relative sliding displacement R1-Pool (m)
Max. Sliding disp.
Min. Sliding disp.
Max. Vertical force

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• Fuel beam flexural rigidity
B: Parametric analysis of modelling properties
0.0E+00
3.0E+04
6.0E+04
9.0E+04
1.2E+05
1.5E+05
1.8E+05
2.1E+05
2.4E+05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
2.E+00 2.E+01 2.E+02 2.E+03 2.E+04 2.E+05 2.E+06
Max. Vertical force on support (N)
Relative sliding displacement R1-Pool (m)
Max. Sliding disp.
Min. Sliding disp.
Max. Vertical force

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Sensitivity analysis : Monte Carlo

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Sensitivity analysis: Distribution of variables
Type Name Distribution Min Max
1 Data input Acceleration time-history Uniform 90% 100%
2 Data input Rack mass and submerged weight Uniform 90% 100%
3 Data input Fuel mass and submerged weight Uniform 90% 100%
4 Data input Eigen-frequencies in X Uniform 5Hz 17.6Hz
5 Data input Eigen-frequencies in Z Uniform 80Hz 88.8Hz
6 Data input Hydrodynamic mass Uniform 90% 100%
7 Model properties Rack-to-Pool friction coefficient Normal 0.20 0.80
8 Model properties Rack-to-Pool contact stiffness Uniform 1E6 1E12
9 Model properties Fuel-to-Cell contact stiffness Uniform 1E4 1E10
10 Model properties Fuel-cell gap Uniform 2mm 14mm
11 Model properties Fuel beam flexural rigidity Uniform 2E0 2E6
12 Analysis parameter Integration parameter (INTPARA) Uniform 0 0,05
13 Analysis parameter Convergence parameter (CNVTOL) Uniform 1E-7 1E-2
14 Analysis parameter Number of equilibrium iterations (NEQIT) Uniform 2 22
15 Analysis parameter Rayleigh stiffness proportional damping
(ALPHAD)
Uniform 0% 10%
16 Analysis parameter Rayleigh mass proportional damping
(BETAD)
Uniform 0% 10%
17 Analysis parameter Maximum allowed time step (DELTIM) Uniform 3E-3 1.5E-4

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Sensitivity analysis: Scatter plots
modelling properties Vs sliding displacement
Displ.base.R1_Max_
Fbeaminertia
Displ.base.R1_Max_
Fgap
Displ.base.R1_Max_
FC
Displ.base.R1_Max_
Rcontastiff
Displ.base.R1_Max_
Fcontastiff
Displ.base.R1_Max_

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Fz.feet.R1_Max_
Fbeaminertia
Fz.feet.R1_Max_
Fgap
Fz.feet.R1_Max_
FC
Fz.feet.R1_Max_
Rcontastiff
Fz.feet.R1_Max_
Fcontastiff
Fz.feet.R1_Max_
HydroMass
Sensitivity analysis: Scatter plots
modelling properties Vs vertical force on support

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Sensitivity analysis: Sobol index and PCE
modelling properties Vs sliding displacement

20. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa.
Sensitivity analysis: Sobol index and PCE
modelling properties Vs vertical force on support

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Conclusions
Minor variations in the modelling parameters lead to a wide
deviations in final results due to the iterative process of the transient
analysis.
• a 10 levels mesh discretization provides stable results within a limited
computation time so it is considered cost effective,
• sliding displacements are strongly influenced by the friction coefficient,
especially in the range of 0.2 to 0.6,
• assuming stiff rack-to-poll contacts lead to a safe structural design since
the peaks of vertical force on supports are maximized,
• a resonance effect can happen in the fuel rattling and the rack rocking in
function of fuel-to-cell contact stiffness,
• an influence of fuel gaps in the sliding displacements is only visible for
gaps larger than 8 mm,
• flexural rigidity has slight influence in the general behavior of the rack
unit.

22. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa.
ENSA (Grupo SEPI)
Thanks for your attention!
HORIZON 2020
Marie Skłodowska-Curie
Actions
Training in Reducing
Uncertainty
in Structural Safety
Equipos Nucleares, S.A.

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This project has received funding from the European Union’s
Horizon 2020 research and innovation programme under the
Marie Skłodowska-Curie grant agreement No. 642453.
trussitn.eu/alberto-gonzalez-merino/

24. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa.
Impact of the research
• better understanding of the rack seismic behaviour,
• reduction of the current safety margins (nuclear authorities),
• reduction of the nominal gap between units (designers),
• increase the storage capacity of the existing fuel storage pools
(NPP operator),
• increase in the operation span of nuclear power plants without
fuel reprocessing or dry cask storage (electric company),
Also applicable to the dynamic analysis of any other
submerged sliding structure. (Engineering)