1. www.inl.gov
Seismic Group Lead
Nuclear Science and Technology
Idaho National Laboratory
Justin Coleman, P.E.
May 20th, 2015
Advanced Seismic Probabilistic Risk
Assessment using Nonlinear Soil-Structure
Interaction Analysis
STIMS: INL/CON-15-35086

2. What is the Need for Nonlinear SSI?
KK 2007 Fukushima 2011 North Anna 2011
Design Value (g) 0.20 0.26 (Original)
0.45 (Update)
0.18
Recorded Value (g) 0.32 0.56 0.26
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All Exceeded Design Ground Motion
• The estimated design ground motion has recently been exceeded at Nuclear Power Plants
• NLSSI needed to capture nonlinear behavior during larger earthquakes
• Gapping and Sliding
• Material Nonlinearity

3. Linear versus Nonlinear Analysis
• Larger magnitude seismic events
dominate risk calculations
• Linear elastic seismic analysis tools
are poor at predicting structural
performance during larger
earthquakes
• Nonlinear tools are needed to
evaluate risk in large magnitude
earthquake events, including beyond
design basis shaking
Linear Seismic
Analysis
Generally provides
conservative facility
design for low
amplitude events
Cannot model time-
based phenomena
which correlates
failures
Soil and structure
do not separate
Cannot quantify
margin to failure
Non-Linear
Seismic
Analysis
Better reflects
physics of NPPs
during larger
earthquakes, other
severe accidents
Can model time-
based phenomena
which correlates
failures
Soil and structure
can separate
Can quantify
margin to failure
3

4. 4

5. 5
Project Specific Goals
• Goal: Develop advanced methods and tools that reduce
uncertainties and provide a best estimate understanding of seismic
risk
• Use advanced tools to investigate if in-structure response scales linearly
with ground motion
• Compare System Seismic Core Damage Frequency (SCDF) using
Traditional and Advanced SPRA
• Significant difference is Advanced SPRA credits gapping and sliding
• Determine if inclusion of gapping and sliding in NLSSI analysis changes
SCDF
• Develop method for using NLSSI (gapping and sliding) in SPRA
calculations
• NLSSI run times should be reasonable
• Need to limit number of NLSSI runs as much as possible

6. Brief Summary of Scope
• Perform Prob. Response Analysis of NPP Structure
– Linear SSI (CLASSI, frequency domain)
– Nonlinear SSI (LS-DYNA, time domain)
• Linear SSI Results Processing
– Develop fragilities per EPRI TR-103959
– SCDF for a plant system (Emergency Cooling Pump)
• Nonlinear SSI Results Processing
– Develop responses at multiple ground motion scale factors (3?)
– Response distribution at each ground motion level
– Capacity distributions independent of ground motion level
– Conditional failure probabilities by convolution per GM level
System conditional failure probability by Boolean math
– SCDF: convolve system conditional failure probability with hazard

7. NPP Structure & Plant System Components
Mode Freq.(Hz) Description
1, 2 5.27 1st horizontal mode for containment
3, 4 8.46 1st horizontal mode for internals
5, 6 12.37 2nd horizontal mode for internals
7 15.64 1st vertical mode for containment
8, 9 16.24 2nd horizontal mode for containment
10 27.83 1st vertical mode for internals
13, 14 32.89 3rd horizontal mode for internals
• Pump M-11
• Dist. Panel E-23
• Block Wall 2B-G2-1
• Battery E-58
• Medium V. Switchgear E-1
Structure Frequencies
System Components

8. Soil Properties
• Linear
– Elastic half space
– Basalt properties
– Representative median and β values assigned
• Nonlinear
– Nonlinearity limited to uplift and sliding
– Friction coefficient μ, median = 0.70, β = 0.25
Property Median Lognormal Std. Deviation
Unit Weight 159 lb/ft3 -
Poisson’s Ratio 0.35 -
Shear Wave Velocity 3,720 ft/sec 0.27
Shear Modulus 68,320 k/ft2 0.55
Damping 2% 0.4

9. Hazard and Ground Motion
• Hazard
– Reference Mean 1.0E-04 PGA is equal to 0.4g
– Objective is for NLSSI response to stay “linear” at Reference PGA
• GM
– Matched to horizontal and vertical UHS.

10. Linear SSI Fragility Results
Component Floor Am βc HCLPF
Pump 670-M-11 EL 61’ 2.70g 0.45 0.95g
Battery 670-E-59 EL 22’ 1.14g 0.28 0.59g
Dist. Panel 670-E-23
EL 61’ 1.60g 0.59 0.40g
Block Wall 2B-G2-1
EL 61’ 0.60g 0.28 0.31g
Switchgear 670-E-1
EL 22’ 1.90g 0.47 0.64g

11. Linear SSI SCDF Results
• With wall 3.5E-05
• No Wall 4.6E-06

12. 12
NLSSI Approach
• Commercial finite-element code (LS-DYNA)
• Several nonlinear hysteretic material models for soil, concrete, steel
• Explicit code
• No iterations, therefore faster in impact and contact problems
• Always stable below a maximum time step
• Maximum time step controlled by the stiffest and shortest element
• Mainly used in non-structural/geotechnical engineering applications

13. 13
NLSSI analysis: Procedure
665 ft 665 ft
214 ft
• Linear soil
• Rigid basemat
• Rayleigh damping for soil and
structure
• Element size ≈ 8 ft
(corresponds to max freq of
40Hz)
• Tried 2 domain sizes
• Verified by comparing surface
response at the edge of the
domain to free-field response
from a 1D SRA

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NLSSI analysis: Procedure
Outcrop input
CTOT = r×V × A
For a uniform soil halfspace,
outcrop input acceleration at any depth = free-field acceleration at the surface
• Boundary nodes at each
elevation are constrained to
move together
• No transmitting boundaries
used

15. 15
NLSSI analysis: Sample results
CLASSI input vs LS-DYNA surface
free-field accelerations

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NLSSI analysis
• Run times (with 4 cores) for acceleration suite 1 (45 sec)
• 12 hours
• Analysis cases for LM:
• Basemat tied to the soil (no sliding or gapping)
• Separation allowed (sliding and gapping possible) and a coefficient of
friction of 0.8 is used
• Separation allowed (sliding and gapping possible) and a coefficient of
friction of 0.5 is used

17. 17
NLSSI analysis: Sample results
CLASSI vs LS-DYNA basemat
accelerations

18. 18
Conclusions
• Linear and NLSSI responses match well in the free field and on the
basemat for 0.4g
• Some differences are unavoidable
• No significant sliding is noticed for 0.4 g ground motion and coefficient of
friction at 0.8
• Sliding expected for larger ground motions
• Current problem is more complex than imagined for time-domain analysis
• Long computation time in time domain due to stiff beam elements
• Difference in beam formulations
• Idealization of the superstructure
• Traditional approach: as few elements as possible (suitable for frequency-
domain approach)
• Time-domain approach: larger time step; avoid, stiff, short elements

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Conclusions
• When applying appropriate methodologies NLSSI can be used to capture
realistic structural response (gapping and sliding) during larger ground
motions
• Next project steps
• Run 90+ sets of time histories for the NLSSI analysis
• Quantify in-structure response of these runs at locations of interest
• Calculate SCDF of NLSSI and compare with Linear SSI

20. The National Nuclear Laboratory
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