ww

w.in

l.gov

Application of Nonlinear SSI Analysis in Seismic PRA

Chandu BolisettiResearch Scientist

Seismic Research Group, INL

DOE NPH Conference18th and 19th October, 2016

Outline

• Introduction

• Demonstrative application of NLSSI in SPRA

– Numerical modeling

– Sample results

– Risk analysis

• Sensitivity of risk to the slope of hazard curve

• Concluding remarks

• Nonlinear response is closer to reality especially beyond design basis

• Nonlinear effects– Nonlinear SSI and structural

response– Seismic isolation

• Design calculations should be conservative and risk calculations should be best estimate

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 0.5 1 1.5 2 2.5 3 3.5

Peak

spe

ctra

l acc

eler

atio

n (g

)

Multiplication factor of DBE

Projected Location 1 Response at Site A LinearProjected Location 1 Response at Site B NLSSI

Spears and Coleman (2014)

Introduction – Why nonlinear?

4

Introduction

Nonlinear site response

Nonlinear behavior of soil around the foundationGeometric nonlinearities:

gapping and sliding

Structural nonlinearitiesEquivalent-linear

State-of-the-art

Nonlinear SSI

Equivalent-linear

Equivalent-linear

Not considered

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

System Components

* Interaction concern for E-23. Study sensitivity to including and excluding from PRA model.

Application of NLSSI in SPRA

6

Steps for SPRA

• Perform seismic response analyses for idealized NPP structure

• Linear analyses using CLASSI (SGH)• 30 realizations calculated using Latin Hypercube sampling

subjected to 30 scaled GMs• Nonlinear analyses using LS-DYNA (INL)

• 30 realizations calculated using Latin Hypercube sampling subjected to 30 scaled GMs at 4 intensities

• Perform fragility calculations (SGH)• Calculate component capacity distributions• Calculate component conditional probabilities of failure

• Risk assessment for plant system (INL)

7

NLSSI model

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)

• Verified against CLASSI and SASSI

8

Foundation-soil interface modeling

Demand distributions: Free-field - X

Demand distributions: 61’ elevation - Y

Component fragility calculations

Component Dir Freq(Hz)

SAm(g) βc

Pump X 20 7.46 0.16

Battery Y 8.3 3.10 0.10

Distribution Panel X 7.5 6.24 0.42

Block Wall Y 0.89 0.73 0.17

Switchgear Y 5 - 10 4.80 0.42

Component capacity distributions

• Calculate demand and capacity distributions for each component

• Calculate P(demand>capacity) for each component at each intensity level

• Fit lognormal curves through these probabilities for each component to calculate fragilities

12

Conditional probabilities of failurePump Battery

Switch gearDistribution

panel

Blockwall

13

Correction of fitted fragilities

Tentative correction: failure probabilities for linear and nonlinear analyses are assumed to be equal for bins where linear response is expected (all bins below 0.4g)

14

Risk calculations – hazard curves

Hazard_1: Original curve

Hazard_2: Slope halved in log scale and curve anchored at (0.4g, 1E-04)

15

Risk calculations – hazard_1, corrected fragilities (with blockwall)

Linear NonlinearLSE

NonlinearMLE

Risk 3.48E-05 3.32E-05 3.2E-05

Reduction (%) 5 8

16

Risk calculations – hazard_1, corrected fragilities (without blockwall)

Linear NonlinearLSE

NonlinearMLE

Risk 4.62E-06 4.03E-06 3.81E-06

Reduction (%) 13 17

17

Risk calculations – hazard_2, corrected fragilities (without blockwall)

Linear NonlinearLSE

NonlinearMLE

Risk 9.98E-06 6.93E-06 6.85E-06

Reduction (%) 31 31

Concluding remarks

• Time-domain and frequency-domain responses match well when the time-domain response is linear

• Gapping and sliding can decrease the median demands• Gapping and sliding generally decreased the median

demands at low frequencies

• Gapping and sliding can also increase the median demands at higher frequencies

• Further investigation into the effects of gapping and sliding is required

• NLSSI can considerably reduce the system risk, based on the slope of the hazard curve

Acknowledgments

• Department of Energy

• Mohamed Talaat and Phil Hashimoto, SGH

• Bob Kennedy, Advisory Panel, Seismic Research Group,

INL

• Bob Spears and Justin Coleman, Seismic Research

Group, INL

Seismic Research Groupearthquake.inl.gov