seismic ssi incoherency effects for candu reactor building ... 2 - mo… · s s g g,0 z z z z...

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OECD NEA SSI WorkshopOECD NEA SSI Workshop

Ottawa, Canada, October 6Ottawa, Canada, October 6--8, 20108, 2010

Seismic SSI Incoherency Effects for Seismic SSI Incoherency Effects for

CANDU Reactor Building StructureCANDU Reactor Building Structure

Dan M. GhiocelDan M. Ghiocel Ghiocel Predictive Technologies Inc., USAGhiocel Predictive Technologies Inc., USA

http://www.ghiocelhttp://www.ghiocel--tech.comtech.com

George Stoyanov, Sudip AdhikariGeorge Stoyanov, Sudip Adhikari

Tarek AzizTarek Aziz AECL Ltd., CanadaAECL Ltd., Canada

http://aecl.comhttp://aecl.com

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Presentation Purpose:Presentation Purpose:

Discuss key aspects of incoherent SSI analysis of the CANDU

RB structure for two soil conditions, a stiff soil site with Vs=3,000

fps and a rock site with Vs=5,500 fps

- Evaluate wave passage effects.

- Compare SSI results of a RB Stick and a RB Shell model


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Presentation Content: Presentation Content:

1.Seismic Incoherent SSI Analysis Methodology

2.CANDU 6 Reactor Building Case Studies

3.Conclusions



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The complex frequency response is computed as follows:

• Coherent SSI response:Coherent SSI response:

••Incoherent SSI response:Incoherent SSI response:

1. Seismic Incoherent SSI Methodology1. Seismic Incoherent SSI Methodology

i c

s s g g g,0U ( ) H ( )*S ( )*H ( )*U ( )

c

s s g g,0U ( ) H ( )*H ( )*U ( )

Complex Fourier transform of relative Complex Fourier transform of relative

spatial variations of motion at interaction spatial variations of motion at interaction

nodes that is stochastic by nature nodes that is stochastic by nature

Structural transfer function given Structural transfer function given

input at interaction nodesinput at interaction nodes

Coherent ground transfer function at Coherent ground transfer function at

interface nodes given control motioninterface nodes given control motion

Incoherent ground transfer function Incoherent ground transfer function

given coherent ground motion and given coherent ground motion and

coherency model (random spatial variation coherency model (random spatial variation

in horizontal plane)in horizontal plane)

Complex Fourier transform Complex Fourier transform

of control motionof control motion

gS ( ) [ ( )][ ( )]{ }

Spectral factorization of coherency kernel Random phases (stochastic part)Spectral factorization of coherency kernel Random phases (stochastic part)


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Use simplified superposition rules for combining incoherency modes

or their random effects:

i) Linear superposition of motion incoherency modes at free-

field or input level (AS in EPRI studies) – single SSI analysis

ii) Quadratic superposition of incoherency mode SSI response

TF amplitude (SRSS in EPRI studies) – multiple SSI analysis

Four deterministic incoherent SSI approaches in ACS SASSI:

1)Linear/algebraic summation (AS) w/ phase adjustment (EPRI)

2)Linear/algebraic summation (AS) w/o phase adjustment *

3)SRSS of SSI Response TF Amplitude w/ zero-phase (EPRI)

4)SRSS of SSI Response TF Amplitude w/ non-zero phase *

* Note: Not considered in EPRI studies (EPRI TR# 1015111)

Deterministic Incoherent SSI ApproachesDeterministic Incoherent SSI Approaches

Seismic Motion Coherency Seismic Motion Coherency SpectrumSpectrum

• Assuming that motion is a Gaussian vector process, then it is fully defined

in frequency domain by

Thus, for two arbitrary points in horizontal plane, j and k, the coherency

spectrum or coherence is defined by

Uj,Uk

Uj,Uk 1/2

Uj,Uj Uk,Uk

S ( )( )

[S ( )S ( ]

• The “plane-wave” coherency function for SSI analysis is defined as a

complex function (Abrahamson, 1991-2007) including “spatial incoherency”

(amplitude) and “wave passage” (phase) effects

U Ui,Uk LUi,Uk( ) ( ) D,i D,k Dexp [i (X X ) / V ]

local variability

amplitude variability phase shift

1/2

Uj,Uk Uj,Uj Uk,Uk Uj,UkS ( ) [S ( )S ( )] ( )


spatial correlation

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2. CANDU 6 Reactor Building (RB) Case Studies2. CANDU 6 Reactor Building (RB) Case Studies

CANDU 6 RB StructureCANDU 6 RB Structure SSI Stick ModelSSI Stick Model SSI Shell ModelSSI Shell Model


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CANDU 6 Study for Incoherent SSI Response CANDU 6 Study for Incoherent SSI Response

On Two Different Soil ConditionsOn Two Different Soil Conditions

Rock Site:Rock Site:

- Structure: Stick Model and Shell Model (HF Model)

- Soil Deposit: Uniform soil layering with Vs of about 5,500fps

- Control Motion: UHRS (max. in 20-40Hz range) with 0.32 ZPGA

- Incoherency: 2007 Abrahamson Coherence Function for Soil

- Wave Passage in X-Direction: Va = 10,000 fps

Stiff Soil Site:Stiff Soil Site:

- Structure: Stick Model and Shell Model (HF Model)

- Soil Deposit: Uniform soil layering with Vs of about 3,000fps

- Control Motion: UHRS Input (spectral peak in 10 Hz) with 0.41g

- Incoherency: 2007 Abrahamson Coherence Function for Soil Sites

- Wave Passage in X-Direction: Va = 7,000 fps

(EPRI TR # 1015110, December 2007)(EPRI TR # 1015110, December 2007)

2007 Abrahamson Coherence for Rock and Soil Sites2007 Abrahamson Coherence for Rock and Soil Sites

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HARDHARD--ROCKROCK SOILSOIL

HORIZONTALHORIZONTAL

VERTICALVERTICAL



10

0.01

0.10

1.00

10.00

0.1 1.0 10.0 100.0

AC

CE

LE

RA

TIO

N (g

)

FREQUENCY (HZ)

5% Damped Spectra Comparison

Seismic SiteSeismic Site--Specific Inputs Defined by Specific Inputs Defined by

5% Damping UHRS 5% Damping UHRS

UHSRS for Soil SiteUHSRS for Soil Site (max. at 10 Hz)(max. at 10 Hz)

UHSRS for Rock SiteUHSRS for Rock Site (max. in 20(max. in 20--40 Hz range)40 Hz range)


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Top of Internal Structure (IS) ISRS.Top of Internal Structure (IS) ISRS.

Rock SiteRock Site

XX--DirectionDirection ZZ--DirectionDirection


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Top of Internal Structure (IS) ISRS.Top of Internal Structure (IS) ISRS.

Soil SiteSoil Site



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Top of IS Acceleration in XTop of IS Acceleration in X--Dir for Soil SiteDir for Soil Site

SHELLSHELL

STICKSTICK


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Top of IS Acceleration in ZTop of IS Acceleration in Z--Dir for Soil SiteDir for Soil Site

SHELLSHELL

STICKSTICK

STICKSTICK


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SHELLSHELL

STICKSTICK

Top of CS Acceleration in ZTop of CS Acceleration in Z--Dir for Soil SiteDir for Soil Site


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Coherent & Incoherent (Including Wave Passage) Coherent & Incoherent (Including Wave Passage)

ATF at Base Center for X and Z Dir for Rock SiteATF at Base Center for X and Z Dir for Rock Site



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Coherent & Incoherent (Including Wave Passage) Coherent & Incoherent (Including Wave Passage)

ATF at Base Center for X and Z Dir for Soil SiteATF at Base Center for X and Z Dir for Soil Site



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Coherent & Incoherent ISRS at Top of CS in XCoherent & Incoherent ISRS at Top of CS in X--DirDir

ROCKROCK

SOILSOIL

CoherentCoherent IncoherentIncoherent



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Coherent & Incoherent ISRS at Top of CS in ZCoherent & Incoherent ISRS at Top of CS in Z--DirDir




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Coherent & Incoherent ISRS at Top of CS for Coherent & Incoherent ISRS at Top of CS for

Rock SiteRock Site



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Coherent & Incoherent ISRS at Top of CS for Coherent & Incoherent ISRS at Top of CS for

Soil SiteSoil Site



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Coherent & Incoherent ISRS at Base Center for Coherent & Incoherent ISRS at Base Center for

Rock SiteRock Site



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Coherent & Incoherent ISRS at Base Center for Coherent & Incoherent ISRS at Base Center for

Soil SiteSoil Site


ANIMATIONS 1ANIMATIONS 1--1010


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3. Conclusions3. Conclusions

1)The incoherency effects are significant for the two case studies, the stiff soil

site case and the rock site case.

2)The effects of wave passage appear to be insignificant for the two cases

studies.

3)The effect of structural modeling the CS by shell elements rather than by a

simple stick changes quite visibly the ISRS at the top of IS, especially in Z-

direction.

4)The CS-IS dynamic coupling is affected by the structural modeling of the

CS, although the IS stick is the same in both models.

The CS-IS dynamic coupling effects appear to be larger for the Shell

model, and for incoherent motions.

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Thank you!Thank you!


seismic ssi incoherency effects for candu reactor building ... 2 - mo… · s s g g,0 z z z z...

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