www.sgh.com

Deterministic and Probabilistic Seismic

Soil Structure Interaction Analysis of the Mühleberg Nuclear Power Plant SUSAN

Building

David K. Nakaki, Simpson Gumpertz & Heger

Philip S. Hashimoto, Simpson Gumpertz & Heger

James J. Johnson, James J. Johnson & Associates

Yahya Bayraktarli, BKW FMB Energie AG

Olivier Zuchuat, BKW FMB Energie AG

Soil Structure Interaction Knowledge and Effect on the

Seismic Assessment of NPP Structures and Components

October 6-8, 2010 Ottawa, ON, Canada

Overview of the Presentation

• Introduction

• Summary of the deterministic and probabilistic seismic

response analysis methodology

• Application to Mühleberg SUSAN Building

2

Introduction

• Seismic probabilistic safety assessment (PSA) of

Mühleberg Nuclear Power Plant (KKM) is currently being

updated.

• New seismic response analyses were performed using

current methods to determine median structure

responses for seismic fragility evaluation of structures,

systems, and components.

• Deterministic and probabilistic seismic response

analyses was performed for the KKM SUSAN Building

3

Methodology

• Establish Free Field Ground Motion

• Develop Median Earthquake Strain Compatible Site Soil

Properties

• Develop Fixed Base Structure Model

– Determine natural frequencies and mode shapes

• Determine SSI Parameters

– Foundation impedances

– Scattering matrices

• Perform SSI Response Analysis

4

Seismic SSI Response Analysis

• Deterministic SSI Response Analysis

– Single median-centered response analysis using CLASSI

– Results used to understand the soil-structure system dynamic

behavior.

• Probabilistic SSI Response Analysis

– Perform statistical sampling and Latin Hypercube Simulation

(LHS) experimental design

– Execute Seismic Methodology Analysis Chain with Statistics

(SMACS) methodology documented in NUREG/CR-2015.

– N = 30 simulations using LHS approach

– Perform SSI analyses for N = 30 simulations

– Compute median (50%) and 84% in-structure response spectra

(ISRS)

5

KKM Free Field Ground Motion

• Time histories match the site 10-4 mean 5% damped

Uniform Hazard Spectra (UHS)

• Control motion is defined at the soil surface

6

1.0E-04 Mean Horizontal

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.1 1 10 100

Frequency (Hz)

Sp

ec

tra

l A

cc

ele

rati

on

(g

)

(-)14 m Surface (-)7 m

1.0E-04 Mean Vertical

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100

Frequency (Hz)

Sp

ec

tra

l A

cc

ele

rati

on

(g

)

(-)14 m Surface (-)7 m

Time Histories for Deterministic Analysis

• Two horizontal components and one vertical component

developed in general compliance with requirements of

ASCE 43-05

7

Time Histories for Probabilistic Analysis

• Thirty time history sets generated such that the median

spectral acceleration of the ensemble matched the

1.0E-04 UHS

• Ensemble was conditioned such that the spectral

acceleration coefficient of variation (COV) was

approximately 0.2 over the frequency range of interest (2

to 20 Hz).

• Additional variability included for horizontal and vertical

peak variability in accordance with recommendations of

EPRI TR-103959

8

Ensemble of Thirty Time Histories

0.0

0.5

1.0

1.5

2.0

2.5

1 10 100

Spe

ctra

l Acc

ele

rati

on

(g)

Frequency (Hz)

H1

9

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1 10 100

Spec

tral

Acc

eler

atio

n (

g)

Frequency (Hz)

V

0.0

0.5

1.0

1.5

2.0

2.5

1 10 100

Spe

ctra

l Acc

ele

rati

on

(g)

Frequency (Hz)

H2

Median-Centered Soil Properties

• General site conditions consist of soil overburden on

rock substrate

• Low strain soil properties based on existing available site

data.

• Site response analysis was performed to establish

earthquake strain compatible soil properties for the

layered site.

– Shear wave velocity

– Soil damping

– Poisson’s ratio

– Density

10

Median-Centered Shear Wave Velocity Profile

11

0

50

100

150

200

250

300

350

400

450

500

0 1000 2000 3000 4000 5000 6000 7000D

ep

th (f

t)Shear Wave Velocity (ft/sec)

Low Strain Median Centered Strain Compatible

SUSAN Building Configuration

• Squat, rectangular, embedded reinforced concrete

structure

• Nominal grade elevation: 0 m

• Foundation plan dimensions: 19 m (EW) x 27.5 m (NS)

• Top of foundation located at Elevation (-)11 m

• Nominal floor elevations at

Elevations (-)7.3 m, (-)4 m, 0 m, 3.5 m, and 7.5 m.

• Very robust structural system

• Includes an interface structure on the east side which

provides access to the Reactor Building.

12

SUSAN Building Fixed Base Model

• SAP2000 Fixed Base Model – Beam and plate elements

– Median material properties

– 200 modes extracted

• Significant Fixed Base Modes – 9.40 Hz Fundamental EW (Y) mode

– 10.83 Hz Fundamental NS (X) mode

– 15.33 Hz Torsional mode

– 17.90 Hz Interface Structure Vertical

(Z) mode

– 19.82 Hz Fundamental Vertical (Z)

mode

• Output – Nodal geometry

– Mass matrix

– Natural frequencies and mode shapes

13

Development of SSI Parameters

• Hybrid method employed to calculate the embedded

foundation impedances and scattering matrices.

• The embedded foundation is modeled in SASSI2000

with the median soil properties.

• The unconstrained (flexible) impedances from the

SASSI2000 model are generated.

• The embedded region is idealized as rigid relative to the

surrounding soil.

• Scattering and impedance functions of the rigid

embedded foundation are generated by imposing rigid

body constraints within the embedded region.

14

SUSAN Building Impedance and Scattering

• Excavated soil volume

displaced by the embedded

portion of the structure is

modeled in SASSI2000

• Quarter symmetry model

15

Deterministic Median In-Structure Response Spectra

X (NS) Direction, centers of floors Y (EW) Direction, centers of floors

16

Probabilistic SSI Response Analysis

• Consider variability of soil/foundation behavior, structure

dynamic properties, and input motion

• Statistical sampling and Latin Hypercube Simulation

experiment design

• SMACS analysis

– SSI response analysis of the N = 30 simulations

– Compute ISRS and probability distributions

17

Statistical Sampling and Latin Hypercube Simulation

• Model variability of the soil/foundation behavior by

modifying soil stiffness (shear modulus) and damping

through scale factors in the simulations

• Model variability in the structure dynamic properties by

shifts in fixed-base frequencies (stiffness) and modal

damping

18

Latin Hypercube Simulation Design

• Input

– Lognormal distribution of input parameters

– Soil shear modulus COV = 0.40

– Soil damping COV = 0.40

– Structure frequency COV = 0.15

– Structure damping COV = 0.35

• Analysis Techniques

– Latin Hypercube Simulation with 30 simulations

• Output

– Set of input scale factors for the earthquake simulations

– Scale factors are applied to parameters above

– Scale factors have median values of 1.0 and COV’s above

19

SMACS Analysis

• Perform response simulations using the ensemble of 30

earthquake acceleration time histories with the 30

combinations of soil stiffness and damping and structure

frequency and damping.

• Output in-structure response spectra and calculate

probability distributions

20

SUSAN Building In-Structure Response Spectra

21

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0.1 1 10 100Sp

ect

ral A

cce

lera

tio

n, g

Frequency, Hz

SUSAN Building Probabilistic, Elevation 0 m, Center of Floor, Z-Direction

Median84%

Probabilistic Median In-Structure Response Spectra

X (NS) Direction, centers of floors Y (EW) Direction, centers of floors

22

Probabilistic Median and 84%In-Structure Response

Spectra

X (NS) Direction, Elevation 0 m Y (EW) Direction, Elevation 0 m

23

Comparison of Median Deterministic and Probabilistic

In-Structure Response Spectra

Y (EW) Direction, Elevation 0 m Z (Vertical) Direction, Elevation 0 m

24

Advantages of the SMACS Approach

• Development of the fixed base structure model and

calculation of the modal properties represents most of

the engineering effort. Greater effort can be dedicated to

developing detailed models.

• Calculation of the impedance and scattering functions of

the embedded foundation represents significant

computation time, but is only done once using the hybrid

approach.

• By using SMACS to perform the SSI response analysis,

the thirty LHS SSI simulations were completed in

minutes.

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Summary and Conclusions

• Deterministic and probabilistic SSI analysis were

performed for the KKM SUSAN Building

• The deterministic SSI analysis were used to benchmark

the probabilistic analysis.

• Deterministic and probabilistic methods produced

consistent results.

• Sharp spectral acceleration peaks in the deterministic

analysis are reduced by the probabilistic analysis.

• High variability was obtained at resonant frequencies of

the structure/soil system in the probabilistic analysis.

26