Recent Advances in Seismic Soil-Structure Interaction Analysis of NPPs

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1 Recent Advances in Seismic Soil-Structure Interaction Analysis of NPPs Mansour Tabatabaie, Ph.D., P.E. SC Solutions NEA/CSNI-IAGE / IAEA ISSC SSI Workshop Ottawa, Canada October 6-8, 2010

2 SSI ANALYSIS PROCEDURE Seismic soil-structure interaction (SSI) analysis of nuclear power plants (NPPs) in the United States is often performed in the frequency domain using SASSI. This enables the analyst to properly: a) Address the effects of wave propagation in an unbounded soil media b) Incorporate strain-compatible soil shear moduli and damping properties c) Specify input motion in the free field using the deconvolution method and/or spatially variable incoherent ground motions

3 SSI ANALYSIS PROCEDURE The original code was published in 1981 and consisted of 6 program modules. Over the past 30 years, the program SASSI has evolved. A current version of the code incorporates many enhancements that have culminated in 28 program modules that perform a variety of tasks.

4 LAYOUT OF ORIGINAL SASSI CODE

5 1 AXSYM FBASE 5,10 8 PARTIAL LAYOUT OF MTR /SASSI PROGRAM 7 RIMP 5 HOUSE 4 ANALYS MATRIX 6 POINT STRESS MOTION SITE 2 5 SOLVE 8 COMBN8 8 CNTRL RANDOM CONVER MOTOR 9 LOADS 10 14,15 8n

6 LARGE-SCALE SSI MODEL Seismic response of NPPs in the United States is often required for frequencies up to 33 Hz. In addition, NPPs founded on hard rock in the Eastern United States are now required to be analyzed to frequencies up to 50 Hz. For a typical nuclear island about 100m x 100m in plan dimensions, embedded 10m in engineered backfill (Vs = 250 m/s) and founded on hard rock, 3-D detailed FE SSI analysis using SASSI requires: > Max soil element size ~ 250 / 5 / 50 = 1 m > No. of interface soil nodes ~ 100 x x 100 x 10 = 14,000 > No. of virtual soil nodes ~ 100 x 100 x 10 14,000 = 98,600 There could another 60,000 nodes in the structure model to provide adequate mesh refinement to extract response spectra.

7 CONVENTIONAL SASSI MODELING & ANALYSIS CONSTRAINTS Seismic SSI analysis of NPPs using SASSI has had two main constraints in the past: a) Because of large storage and processing requirements, SASSI has been constrained to coarse soil and structure FE models, which has made it difficult to address the high frequency passing requirements for SSI analysis. b) Because SASSI uses frequency domain procedure, it is limited to equivalent linear systems, which makes it difficult to address local nonlinear effects in the structure such as base sliding and/or uplift, component isolation, etc.

8 HOW TO ADDRESS PROBLEM SIZE?

9 LARGE CORE SOLUTION (LCS) MODEL The LCS model takes advantage of modern computer technologies, which now makes it possible to efficiently analyze large-scale, deeplyembedded nuclear island models in SASSI. Advantages of LCS: a) Total SSI system can be analyzed in one step. b) Provides highly efficient and accurate solution. c) Eliminates large file storage requirements. d) Structure model can be a duplicate copy of corresponding FE model used for design without need for renumbering the nodes and/or elements. This facilitates model development, translation, calibration and maintenance for SSI analysis.

10 APPLICATION OF LCS MODEL TO LARGE-SCALE NUCLEAR ISLAND MODEL Nuclear Island Plan View of EPR TM Nuclear island

11 Depth Below Ground Surface (m) Depth Below Ground Surface (m) Depth Below Ground Surface (m) Soil Structure Interaction (SSI) Knowledge and Effect on the GENERIC SOIL PROFILES & PROPERTIES Density (kn/m 3 ) Vs (m/s) Vp (m/s) Extension of generic soil Extension of generic soil Extension of generic soil u 2u 3u 4u 5u 5a 1n5a 1n2u 2n3u 3r3u 2sn4u u 2u 3u 4u 5u 5a 1n5a 1n2u 2n3u 3r3u 2sn4u u 2u 3u 4u 5u 5a 1n5a 1n2u 2n3u 3r3u 2sn4u

12 Z-Acceleration (g's) Y-Acceleration (g's) X-Acceleration (g's) Soil Structure Interaction (SSI) Knowledge and Effect on the ACCELERATION TIME HISTORIES OF REFERENCE EUR-SOFT MOTIONS Time (sec) Time (sec) Time (sec)

13 Spectral Acceleration (g's) Soil Structure Interaction (SSI) Knowledge and Effect on the ACCELERATION RESPONSE SPECTRA OF REFERENCE EUR-SOFT MOTIONS X-Dir. Y-Dir. Z-Dir Damping = Frequency (Hz)

14 STCICK VS DETAILED FE SASSI MODEL EPR TM NUCLEAR ISLAND

15 SASSI FOUNDATION MODEL OF EMBEDDED EPR TM NUCLEAR ISLAND El m Sidewalls Not Connected to Soil NI Basemat AB SB 1 SB 2/3 SB 4 RB FB 2 NAB El m Sidewalls Not Connected to Soil Sidewall Nos. Tendon Gallery

16 EXCAVATED SOIL MODEL OF EMBEDDED EPR TM NUCLEAR ISLAND

17 SSI ANALYSIS CASES Case No. Soil Case Reference EUR Outcrop Motion Analysis Case 1 1u Soft 1u-s 2 Soft 2u-s 2u 3 Medium 2u-m 4 3u Medium 3u-m 5 Medium 4u-m 4u 6 Hard 4u-h 7 5u Hard 5u-h 8 5a Hard 5a-h 9 1n2u Soft 1n2u-s 10 2n3u Medium 2n3u-m 11 2sn4u Medium 2sn4u-m 12 3r3u Medium 3r3u-m 13 1n5a Hard 1n5a-h

18 MAXIMUM ACCELERATION CONTOURS IN X-DIR. EPR TM NUCLEAR ISLAND

19 MAXIMUM ACCELERATION CONTOURS IN Z-DIR. EPR TM NUCLEAR ISLAND

20 COMPARISON OF MAXIMUM ACCELERATIONS (SOIL ANALYSIS CASE 2SN4U-M) Location Elev. (m) X Y Z Stick Model Center of NI Basemat Reactor Building IS Reactor Building IS Safeguard Building Safeguard Building 2/ Safeguard Building Fuel Building Reactor Containment Bldg Reactor Shield Bldg Location Elev. (m) X Y Z Detailed FE Model Center of NI Basemat Reactor Building IS Reactor Building IS Safeguard Building Safeguard Building 2/ Safeguard Building Fuel Building Reactor Containment Bldg Reactor Shield Bldg

21 Y-Spectral Acceleration (g's) X-Spectral Acceleration (g's) Z-Spectral Acceleration (g's) Soil Structure Interaction (SSI) Knowledge and Effect on the COMPARISON OF ACCELERATION RESPONSE SPECTRA (SOIL ANALYSIS CASE 2SN4U-M) Stick Model Detailed Model Reference Outcrop Motion Stick Model Detailed Model Reference Outcrop Motion Damping = 5% 2.0 Damping = 5% Frequency (Hz) Frequency (Hz) Stick Model Detailed Model Reference Outcrop Motion Damping = 5% Top of Reactor Containment Bldg., Eelv m Frequency (Hz)

22 Elevation (m) Elevation (m) Elevation (m) Elevation (m) Soil Structure Interaction (SSI) Knowledge and Effect on the COMPARISON OF INTERSTORY SHEAR FORCES & OVERTURNING MOMENTS (SOIL ANALYSIS CASE 2SN4U-M) Shear, Vx Moment about Y-axis, My Shear, Vy Moment about X-axis, Mx ,000 1,500 Vx (MN) ,000 20,000 30,000 40,000 My (MN-m) ,000 1,500 Vy (MN) ,000 20,000 30,000 40,000 Mx (MN-m) Detailed Model Stick Model Detailed Model Stick Model Detailed Model Stick Model Detailed Model Stick Model

23 CONCLUSIONS a) Stick models are capable of determining global seismic responses, but they can lead to excessively conservative results in the vertical direction due to the limited number of modes that can be modeled b) Detailed FE models capture local responses, thus eliminating the need for modeling single DOF oscillators. c) Effects of the basemat flexibilities can be considered in the detailed FE models. d) Meshing can be made sufficiently small in detailed FE models to capture the response due to high frequency input motions.

24 HOW TO ADDRESS LOCAL NONLINEARITIES? a) Base sliding and/or uplift b) Side soil debonding c) Component isolation d) Other local nonlinearities

25 DISTRIBUTED PARAMETER FOUNDATION (DPF) MODEL The DPF model is a hybrid frequency/time domain procedure that allows the structure to be partitioned from the total SSI system and analyzed in the time domain while the foundation media is modeled using the frequency-domain procedures. DPF method involves four basic steps: a) Calculating dynamic impedance at each foundation interaction node from soil reaction forces and interaction displacements in the frequency domain using SASSI. b) Developing equivalent simple-damped oscillators with constant parameters (spring, mass and dashpot) representing the dynamic impedance functions obtained in a. c) calculating foundation scattering motions at the same interaction nodes from SASSI. d) implementing the results as boundary conditions in the time-domain dynamic response analysis of the structure.

26 DPF MODEL IN SASSI

27 FLOW DIAGRAM OF LINEAR SSI ALIGNMENT SASSI Linear Seismic SSI Model Target Linear Solution Dynamic Impedance Functions Linearize: KMC Model Scattering Motion Check Alignment Linear Seismic SSI Model Time-Domain Linear Solution

28 X-Acceleration (g's) X-Acceleration (g's) Soil Structure Interaction (SSI) Knowledge and Effect on the FLOW DIAGRAM OF DPF MODEL IN SASSI m Primary Containment 6.0 SASSI, One-Step NODE ADINA, KMC 13.5 m (Embedment) Reactor Building Foundation Damping = 5% Diameter = 40 m Frequency (Hz) Node Z Y SASSI, One-Step ADINA, KMC NODE X 1.5 Node Node Node Damping = 5% Node 25 Foundation Base slab Node Frequency (Hz) Typical In-Structure Response

29 NEAR FIELD INELASTIC SPRINGS FOR MODELING BASEMAT SLIDING AND/OR UPLIFT AND SIDEWALL/SOIL DEBONDING U = U e + U p P P P P u = + P y U = U e + U p U e U p

30 FLOW DIAGRAM OF NONLINEAR SSI ALIGNMENT Linearized KMC Model Scattered Motion Nonlinear Near- Field Springs Aligned Linear Seismic Model Time-Domain Nonlinear Seismic Model

31 THANK YOU FOR YOUR ATTENTION QUESTIONS?