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1 Seismic SSI Incoherency Effects for CANDU Reactor Building Structure Dan M. Ghiocel Ghiocel Predictive Technologies Inc., USA George Stoyanov, Sudip Adhikari Tarek Aziz AECL Ltd., Canada OECD NEA SSI Workshop Ottawa, Canada, October 6-8,

2 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 2

3 Presentation Content: 1.Seismic Incoherent SSI Analysis Methodology 2.CANDU 6 Reactor Building Case Studies 3.Conclusions 3

4 1. Seismic Incoherent SSI Methodology The complex frequency response is computed as follows: Coherent SSI response: Complex Fourier transform c s s g g,0 of control motion Incoherent ground transfer function given coherent ground motion and coherency model (random spatial variation in horizontal plane) i c s s g g g,0 U ( ) H ( )*H ( )*U ( ) Incoherent SSI response: Structural transfer function given input at interaction nodes Coherent ground transfer function at interface nodes given control motion U ( ) H ( )*S ( )*H ( )*U ( ) S g( ) [ ( )][ ( )]{ } Spectral factorization of coherency kernel Complex Fourier transform of relative spatial variations of motion at interaction nodes that is stochastic by nature Random phases (stochastic part) 4

5 Deterministic Incoherent SSI Approaches Use simplified superposition rules for combining incoherency modes or their random effects: i) Linear superposition of motion incoherency modes at freefield 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# ) 5

6 Seismic Motion Coherency Spectrum Assuming that motion is a Gaussian vector process, then it is fully defined in frequency domain by local variability S ( ) [S ( )S ( )] ( ) Thus, for two arbitrary points in horizontal plane, j and k, the coherency spectrum or coherence is defined by 1/2 Uj,Uk Uj,Uj Uk,Uk Uj,Uk S ( ) Uj,Uk Uj,Uk ( ) 1/2 [S Uj,Uj( )S Uk,Uk ( ] The plane-wave coherency function for SSI analysis is defined as a complex function (Abrahamson, ) including spatial incoherency (amplitude) and wave passage (phase) effects U Ui,Uk ( ) LUi,Uk ( ) D,i D,k D amplitude variability exp [i (X X ) / V ] spatial correlation phase shift 6

7 2. CANDU 6 Reactor Building (RB) Case Studies CANDU 6 RB Structure SSI Stick Model SSI Shell Model 7

8 CANDU 6 Study for Incoherent SSI Response On Two Different Soil Conditions 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 8

9 2007 Abrahamson Coherence for Rock and Soil Sites HORIZONTAL HARD-ROCKROCK SOIL VERTICAL (EPRI TR # , December 2007) 9

10 ACCELERATION (g) Seismic Site-Specific Specific Inputs Defined by 5% Damping UHRS UHSRS for Rock Site (max. in Hz range) UHSRS for Soil Site (max. at 10 Hz) 5% Damped Spectra Comparison FREQUENCY (HZ) 10

11 Top of Internal Structure (IS) ISRS. X-Direction Rock Site Z-Direction 11

12 Top of Internal Structure (IS) ISRS. X-Direction Soil Site Z-Direction 12

13 Top of IS Acceleration in X-Dir for Soil Site SHELL STICK 13

14 Top of IS Acceleration in Z-Dir for Soil Site SHELL STICK STICK 14

15 Top of CS Acceleration in Z-Dir for Soil Site SHELL STICK 15

16 Coherent & Incoherent (Including Wave Passage) ATF at Base Center for X and Z Dir for Rock Site X-Direction Z-Direction 16

17 Coherent & Incoherent (Including Wave Passage) ATF at Base Center for X and Z Dir for Soil Site X-Direction Z-Direction 17

18 Coherent & Incoherent ISRS at Top of CS in X-Dir Coherent Incoherent ROCK Coherent SOIL Incoherent 18

19 Coherent & Incoherent ISRS at Top of CS in Z-Dir Coherent Incoherent Coherent Incoherent 19

20 Coherent & Incoherent ISRS at Top of CS for X-Direction Rock Site Z-Direction 20

21 Coherent & Incoherent ISRS at Top of CS for X-Direction Soil Site Z-Direction 21

22 Coherent & Incoherent ISRS at Base Center for X-Direction Rock Site Z-Direction 22

23 Coherent & Incoherent ISRS at Base Center for Soil Site X-Direction Z-Direction ANIMATIONS

24 3. 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. 24

25 Thank you! 25