ML19011A347
| ML19011A347 | |
| Person / Time | |
|---|---|
| Site: | NuScale |
| Issue date: | 01/11/2019 |
| From: | Rad Z NuScale |
| To: | Document Control Desk, Office of New Reactors |
| Shared Package | |
| ML19011A346 | List: |
| References | |
| RAIO-0119-64104 | |
| Download: ML19011A347 (148) | |
Text
RAIO-0119-64104 January 11, 2019 Docket No.52-048 U.S. Nuclear Regulatory Commission ATTN: Document Control Desk One White Flint North 11555 Rockville Pike Rockville, MD 20852-2738
SUBJECT:
NuScale Power, LLC Supplemental Response to NRC Request for Additional Information No. 133 (eRAI No. 8936) on the NuScale Design Certification Application
REFERENCES:
- 1. U.S. Nuclear Regulatory Commission, "Request for Additional Information No. 133 (eRAI No. 8936)," dated August 05, 2017
- 2. NuScale Power, LLC Response to NRC "Request for Additional Information No. 133 (eRAI No.8936)," dated January 31, 2018 The purpose of this letter is to provide the NuScale Power, LLC (NuScale) supplemental response to the referenced NRC Request for Additional Information (RAI).
The Enclosures to this letter contain NuScale's supplemental response to the following RAI Question from NRC eRAI No. 8936:
03.07.02-7 is the proprietary version of the NuScale Supplemental Response to NRC RAI No.
133 (eRAI No. 8936). NuScale requests that the proprietary version be withheld from public disclosure in accordance with the requirements of 10 CFR § 2.390. The enclosed affidavit (Enclosure 3) supports this request. Enclosure 2 is the nonproprietary version of the NuScale response.
This letter and the enclosed responses make no new regulatory commitments and no revisions to any existing regulatory commitments.
If you have any questions on this response, please contact Marty Bryan at 541-452-7172 or at mbryan@nuscalepower.com.
Sincerely, Zackary W. Rad Director, Regulatory Affairs NuScale Power, LLC Distribution: Gregory Cranston, NRC, OWFN-8H12 Samuel Lee, NRC, OWFN-8H12 Marieliz Vera, NRC, OWFN-8H12 NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvalis, Oregon 97330, Office: 541.360.0500, Fax: 541.207.3928 www.nuscalepower.com
RAIO-0119-64104 : NuScale Supplemental Response to NRC Request for Additional Information eRAI No. 8936, proprietary : NuScale Supplemental Response to NRC Request for Additional Information eRAI No. 8936, nonproprietary : Affidavit of Zackary W. Rad, AF-0119-64104 NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvalis, Oregon 97330, Office: 541.360.0500, Fax: 541.207.3928 www.nuscalepower.com
NuScale Supplemental Response to NRC Request for Additional Information eRAI No. 8936, proprietary NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvalis, Oregon 97330, Office: 541.360.0500, Fax: 541.207.3928 www.nuscalepower.com
NuScale Supplemental Response to NRC Request for Additional Information eRAI No. 8936, nonproprietary NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvalis, Oregon 97330, Office: 541.360.0500, Fax: 541.207.3928 www.nuscalepower.com
Response to Request for Additional Information eRAI No.: 8936 Date of RAI Issue: 08/05/2017 NRC Question No.: 03.07.02-7 10 CFR 50 Appendix S requires that the safety functions of structures, systems, and components (SSCs) must be assured during and after the vibratory ground motion associated with the Safe Shutdown Earthquake (SSE) through design, testing, or qualification methods.
In FSAR Section 3.7.5, the applicant provided a brief description of the computer programs used in the analysis and design of the site-independent seismic Category I and Category II structures. However, it did not provide sufficient information regarding the verification &
validation (V&V) of these programs. The applicant is requested to provide in the DCA information summarizing the V&V of the computer programs used to determine design-basis seismic demands for NuScale seismic Category I and II structures. The demonstration should test those characteristics of the software that mimic the physical conditions, material properties, and physical processes that represent the NuScale design in numerical analysis. The V&V should cover the full range of parameters used in NuScale design-basis seismic demand calculations including the discretization and aspect ratio of finite elements, Poissons ratio, frequencies of analysis, and other parameters pertinent to seismic system analyses.
NuScale Response:
1.0 Introduction This response summarizes the verification and validation (V&V) of the SASSI2010 program (Reference 6) used for the soil-structure-interaction (SSI) analysis of the NuScale Reactor Building (RXB) and Control Building (CRB). This report addresses the staff expectations regarding the applicants response to request for additional information (RAI) 8936, Question 03.07.02-7, listed in Table 1-1.
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The NRC staff stated in its feedback on the RAI response that the applicant is expected to provide information regarding the V&V of SASSI2010 to the extent it is applied to the NuScale seismic analysis. Specifically, the applicant should demonstrate the parameters used in NuScale design-basis, seismic demand calculations are within the range of applicability of the SASSI2010 computer program.
The NRC also stated that validation of certain parameters identified may have been captured in separate RAI questions and, in such cases, the applicant may provide appropriate references to these RAIs to take credit. Also, if certain aspects of SASSI2010 V&V for NuScale-specific application are encompassed by vendor-provided, generic SASSI2010 V&V documentation, the applicant may provide appropriate references to this documentation to take credit.
The V&V problems summarized in this report consist of a combination of the following:
- NuScale-specific examples.
- Vendor-provided examples.
- Examples created for comparison.
The responses to the expectations by the NRC staff are also provided in Section 2.0.
Each V&V problem and its results are provided in Sections 6.1 through 6.17.
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Table 1-1. RAI 8936 Question 03.07.02-7 eRAI# RAI Question# RAI Question 8936 03.07.02-7 In FSAR Section 3.7.5, the applicant provided a brief description of the computer programs used in the analysis and design of the site-independent seismic Category I and Category II structures. However, it did not provide sufficient information regarding the verification & validation (V&V) of these programs. The applicant is requested to provide in the DCA information summarizing the V&V of the computer programs used to determine design-basis seismic demands for NuScale seismic Category I and II structures. The demonstration should test those characteristics of the software that mimic the physical conditions, material properties, and physical processes that represent the NuScale design in numerical analysis. The V&V should cover the full range of parameters used in NuScale design-basis seismic demand calculations including the discretization and aspect ratio of finite elements, Poissons ratio, frequencies of analysis, and other parameters pertinent to seismic system analyses.
1.1 Tested Application Range A list of the NRC-identified parameters and additional tested application ranges is provided in Table 1-2.
Descriptions of the SASSI2010 validation problems being summarized in this response are provided in Table 1-3, cross-referenced with the applicable parameter and tested application range being validated.
For brevity, the V&V problems for the following SASSI2010 capabilities have been omitted from this response because they are not included in the range of the NuScale application:
- 2-D analysis capability
- 3-D thin plate/shell element
- 2-D four-node plane strain element
- 3-D inter-pile element NuScale Nonproprietary
Table 1-2. Summary Table of NRC-Identified Parameters and Tested Application Range Item Identified Parameter and Tested Application Range SASSI2010 No. Limitation NRC-Identified Parameters 1 Mesh sensitivity - evaluation of solutions for different mesh sizes of finite elements -
2 Aspect ratio - evaluation of solutions for maximum finite element aspect ratio used -
3 Poisson's ratio - evaluation of solutions for maximum Poisson's ratio used 0.48 4 Frequencies of analysis - demonstration that the frequencies of analysis used are -
adequate 5 Impedance functions - validation of impedance (or transfer) functions against the -
benchmark solutions for frequencies up to 50 Hz for embedded structures 6 Extended subtraction method (ESM) - adequacy of ESM as compared to the direct -
method (DM) 7 Non-vertically propagating shear waves - evaluation of solutions for non-vertically -
propagating shear waves and determination of whether this is an important effect to be included in the NuScale seismic analysis 8 Number of soil layers - confirmation that the number of soil layers used in the 100 NuScale analysis is within the maximum soil layers validated for SASSI2010 9 Number of interaction nodes - confirmation that the number of interaction nodes 20,000 used in the NuScale analysis is within the maximum interaction nodes validated for SASSI2010 10 Interpolated transfer functions - validation of the interpolation methodology used in -
SASSI2010 Other Parameters 11 Validation of kinematic (wave scattering) SSI solution -
12a Validation of element dynamic properties and stress calculation 3-D eight node -
12b solid element 3-D beam element 3-D spring element 3-D thick shell element 12c 12d 13 Validation of symmetric and anti-symmetric boundary conditions to analyze a half- -
model 14 Validation of response due to incoherent ground motion -
15a Validation of post-processing for generation of Transfer Function Maximum -
15b Accelerations Acceleration Time Histories Acceleration Response Spectra 15c 15d NuScale Nonproprietary
Table 1-3. Cross-Reference of SASSI Validation Problems with Tested Application Range Problem Section No. Problem No.
Tested Application Range (refer to Table 1-2) 1 2 3 4 5 6 7 8 9 10 11 12a 12b 12c 12d 13 14 15a 15b 15c 15d Description NuScale Specific SASSI2010 V&V Problems 6.1 - SAP2000 vs SASSI X X X X X X X Comparison of RXB Fixed-Base Results 6.2 - SAP2000 vs SASSI X X X X X X X Comparison of CRB Fixed-Base Results 6.3 - Effect of Aspect Ratios on X X X X X Seismic Responses 6.4 - RXB - Comparison of ESM X X X X X X X X X X X X X vs DM Results 6.5 - RXB Subjected to Non- X X X X X X X X Vertically Propagating Seismic Waves 6.6 - RXB Spring Sensitivity X X X X X X X X X X X Study 6.16 - RXB Refined Mesh Study X 6.17 - CRB Refined Mesh Study X Vendor Supplied SASSI2010 V&V Problems 6.7 1 RXB with Surface X X X X X X X Foundation 6.8 2 Scattering Response of X X X X X X X X Embedded Rigid Cylinders 6.9 3 Lotung SSI Experiment X X X X X Additional SASSI2010 V&V Problems 6.10 7 Two solid elements form a X X Case1 column of 1'x1' in cross section and 4' in height supported on the surface of a rigid half-space.
6.11 7 Five beam elements used X X X X Case 2a to form a cantilever supported on the surface of a rigid half-space, forced vibration loading.
7 Same as Case 2(a), X X X X Case 2b seismic loading 6.12 7 Two spring elements form X X X Case 7 two single-degree-of-freedom (SDOF) systems supported on the surface of a rigid half-space.
6.13 9 Response of Circular X X X X Foundation to Spatially Random Ground Motion 6.14 10 Free-field Response due X X X to Inclined SH-, SV- and PV-Waves 6.15 11 Dynamic Response of a X X X X X Square Foundation to Obliquely Incident Seismic Waves NuScale Nonproprietary
2.0 Responses to NRC Identified Parameters Responses to each of the NRC-identified parameters listed in Table 1-2 are provided in this section.
2.1 Mesh Sensitivity - Evaluation of Solutions for Different Mesh Sizes of Finite Elements Studies have been performed to evaluate the sensitivity of results to different mesh refinements.
The results from the studies have been summarized in Section 6.3, Aspect Ratio Study, Section 6.16, RXB Refined Mesh Study, and Section 6.17, CRB Refined Mesh Study.
2.2 Aspect Ratio - Evaluation of Solutions for Maximum Finite Element Aspect Ratio Used A study has been performed to evaluate the validity of results with the maximum aspect ratio used. Results from the study are summarized in Section 6.3, Aspect Ratio Study.
2.3 Poissons Ratio - Evaluation of Solutions for Maximum Poissons Ratio Used The soil profiles used for NuScale are a collection of soil profiles used for other plants representing soft, medium, hard, and very hard sites.
The SASSI2010 Users Manual (Reference 6) recommends a maximum Poissons ratio of 0.48.
To satisfy this recommendation, the following adjustment to the Poissons ratio is made when necessary:
For a saturated soil case, if the compression wave velocity, Vp, calculated from the shear wave velocity, Vs, and Poissons ratio, , is less than 5,000 fps, it is adjusted to 5,000 fps. However, if the resulting Poissons ratio is greater than 0.48, v is reduced so that the Poissons ratio is 0.48.
2.4 Frequencies of Analysis - Demonstration that Frequencies of Analysis Used are Adequate For the certified seismic design response spectra (CSDRS) input, the peak ground acceleration is defined at 50 Hz. For the SASSI analysis for the CSDRS input, the cut-off frequency was established at 52 Hz. This is acceptable because it is higher than 50 Hz.
For the CSDRS-high frequency (CSDRS-HF) input, the peak ground acceleration is defined at 100 Hz. For the SASSI analysis for the CSDRS-HF input, the cut-off frequency was established NuScale Nonproprietary
at 72 Hz. Using a 72-Hz cutoff frequency is acceptable because it is above the frequency at which maximum acceleration occurs (25 Hz horizontal and 50 Hz vertical).
Based on the model discretization and the soil shear wave velocity, the wave passing frequencies are provided in Table 2-1. For Soil Types 7, 8, and 9, the wave passing frequencies are higher than the soil column frequencies listed in Table 2-2; thus, the model is refined enough to provide accurate SSI analysis results.
The cutoff frequencies are also much higher than the soil column frequencies, thus, more than adequate to capture the major frequency components of responses.
Table 2-1. Wave Passing Frequencies.
Soil Type No. Soil Type Description CSDRS Compatible CSDRS-HF Compatible Input (Hz) Input (Hz) 11 Soft soil 12 -
8 Firm soil-soft rock 108 -
7 Rock 157 157 9 Hard rock - 254 Table 2-2. Shear Wave Frequencies of Soil Column above RXB Foundation Bottom Elevation.
Excitation Soil Type Soil Type CSDRS CSDRS-HF No. Description Compatible Soil Compatible Soil Frequency Frequency (Hz) (Hz)
CSDRS 11 Type 11 (soft soil) 2.27 -
8 Type 8 (rock) 10.03 -
7 Type 7 (hard rock) 14.50 -
CSDRS- 7 Type 7 (hard rock) - 14.55 HF 9 Type 9 (hard rock) - 23.43 Typical transfer functions of the RXB are shown in Figure 2-1 through Figure 2-3. The transfer functions are at the node in the northwest corner at the top of the RXB basemat. The transfer functions at the calculated frequencies are shown as circles. These figures show there are no spurious spikes and the number of calculated frequencies is adequate.
NuScale Nonproprietary
Figure 2-1. Cracked RXB Transfer Functions due to X Component CSDRS Input at Node 3996 on Top of Basemat for Soil Type 7.
NuScale Nonproprietary
Figure 2-2. Cracked RXB Transfer Functions due to CSDRS Y Input at Node 3996 on Top of Basemat for Soil Type 7.
NuScale Nonproprietary
Figure 2-3. Cracked RXB Transfer Functions due to CSDRS Z-Input at Node 3996 on Top of Basemat for Soil Type 7.
NuScale Nonproprietary
Typical transfer functions of the CRB are shown in Figure 2-4 through Figure 2-6. The transfer functions are at the node in the southeast corner at the CRB roof. The transfer functions at the calculated frequencies are shown as circles. These figures show there are no spurious spikes and the number of calculated frequencies is adequate.
Figure 2-4. Uncracked CRB Transfer Functions for CSDRS X-Input at Node 39860, Southeast Corner of Roof at El. 140'-0", for Soil Type 7.
NuScale Nonproprietary
Figure 2-5. Uncracked CRB Transfer Functions for CSDRS Y-Input at Node 39860, Southeast Corner of Roof at El. 140'-0", for Soil Type 7.
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Figure 2-6. Uncracked CRB Transfer Functions for CSDRS Z-Input at Node 39860, Southeast Corner of Roof at El. 140'-0", for Soil Type 7.
NuScale Nonproprietary
2.5 Impedance Functions - Validation of Impedance (or Transfer) Functions Against Benchmark Solutions for Frequencies up to 50 Hz for Embedded Structures.
Validation of the SASSI2010 program for impedance and scattering calculation is provided in Section 6.7, Reactor Building with Surface Foundation, and Section 6.8, Scattering Response of Embedded Rigid Cylinders.
2.6 Extended Subtraction Method - Adequacy of ESM as Compared to Direct Method The results of a study of the adequacy of the ESM method compared to the DM used for the SSI analysis of the RXB have been summarized in Section 6.4.
2.7 Non-Vertically Propagating Shear Waves - Evaluation of Solutions for Non-Vertically Propagating Shear Waves and Determination of Whether this Is an Important Effect to be Included in the NuScale Seismic Analyses The results of a study of the effects of non-vertically propagating waves on the NuScale analyses have been summarized in Section 6.5.
Validation of the SASSI2010 program for non-vertically propagating waves is summarized in Section 6.14, Free Field Response due to Inclined SH-, SV-, and P-Waves, and Section 6.15, Dynamic Response of a Square Foundation to Obliquely-Incident Seismic Waves.
2.8 Number of Soil Layers - Confirmation that the Number of Soil Layers Used in NuScale Analysis Is within the Maximum Soil Layers Validated for SASSI2010 The maximum number of soil layers is 100, as specified in the SASSI Users Manual (Reference
- 6) for input to the SITE module (Section 5.2.1, Input A.2, Page 5-5).
In the NuScale SSI analyses, there 57 soil layers above the uniform half-space, which is less than the limit of 100 specified by the SASSI2010 Users Manual.
2.9 Number of Interaction Nodes - Confirmation that the Number of Interaction Nodes Used in NuScale Analyses Is within the Maximum Interaction Nodes Validated for SASSI2010 The number of interaction nodes is limited by the RAM of the computer used. Another limitation is that the total number of nodes, including the interaction nodes, cannot exceed 99,999, because only five digits are permitted by the fixed-format input. Per the latest SASSI Users NuScale Nonproprietary
Manual (Reference 6), the free-format input can be used and the limitation of 99,999 lifted. For the NuScale SASSI SSI analyses, fixed-format input was used and the maximum number of nodes used is 99,071 for the triple building model, including the interaction nodes and nodes of the three NuScale buildings. The number of interaction nodes used for the triple building model is 14,456.
2.10 Interpolated Transfer Functions - Validation of the Interpolation Methodology Used in SASSI2010 The interpolation of the transfer function by SASSI has been validated by a few validation problems described in the V & V report, VV-17-22-031 (Reference 7) being summarized in this response. For example, the validation of transfer function interpolation is provided in Section 6.11 by comparing the SASSI2010 interpolated transfer functions with those calculated from the exact, closed-form formulas shown in Figure 6-64 and Figure 6-65.
2.11 Any Other Important Parameters used in NuScale Seismic Analysis Other important parameters used in the NuScale analysis and the sections describing their validation are listed in Table 1-2 and Table 1-3.
3.0 Assumptions There are no unverified assumptions used in this response. Assumptions used for each individual problem are identified in the reference for each problem.
4.0 Methodology The following methods are used to validate and verify the capabilities of the SASSI2010 program:
- Comparison with closed-form solutions, analytical results, or experimental test data published in the technical literature.
- Comparison with results generated by an independent computer program.
- Comparison with results from sensitivity studies to validate program limitations, such as maximum number of soil layers, maximum value of Poissons ratio, or maximum element aspect ratio.
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5.0 Acceptance Criteria The acceptance criteria used for the V & V are:
- NUMERICAL ACCURACY criterion based on the requirement that the difference in pertinent response values is less than 5%.
- GOOD AGREEMENT criterion base on numerical matching against closed-form solutions, analytical results, or experimental test data.
- EXPECTED BEHAVIOR criterion based on basic knowledge and sound engineering judgment.
6.0 Summary of Verification and Validation Results This section presents a summary of the SASSI2010 V&V problems. The input is briefly described and typical outputs are presented for each problem.
6.1 NuScale-Specific SASSI2010 V&V - SAP2000 Versus SASSI Comparison of RXB Fixed Base Results The purpose of this problem is to verify the capability of SASSI2010 (Reference 6) to model the dynamic properties of the NuScale RXB in terms of modal frequencies and base reactions. The fixed-base responses of the RXB are compared between SASSI2010 and SAP2000 (Reference 8).
The fixed-base RXB SASSI2010 model is summarized in Table 6-1. The SAP2000 model is shown in Figure 6-1. The corresponding SASSI2010 model is shown in Figure 6-2.
((2(a),(c) Table 6-1. Reactor Building SASSI2010 Model Element Summary. Item Description Quantity Backfill Soil Solid Elements 9,236 Foundation Mat Solid Elements 2,839 Beam Elements 6,453 Plate Elements 18,818 ((
}}2(a),(c)
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Figure 6-1. Reactor Building SAP2000 Model. Figure 6-2. Reactor Building SASSI2010 Model. NuScale Nonproprietary
6.1.1 Reactor Building Modal Frequency Comparison The modal frequencies are obtained by determining the frequencies of the peaks in a transfer function calculated by SASSI2010. For example, typical transfer functions at the RXB roof are shown in Figure 6-3 through Figure 6-5. The frequencies obtained from transfer functions are compared with those calculated by SAP2000 in Table 6-2. As can be seen by the comparison in Table 6-2, SASSI2010 provides accurate structural modal frequencies. Table 6-2. Comparison of Reactor Building Modal Frequencies. Modal SAP2000 SASSI Difference(%) Direction Mode No. Frequency Frequency (Hz) (Hz) at Transfer Function Peaks Y (N-S) 2 3.26 3.06 -6.1 Z (Vertical) 3 3.33 3.37 1.2 X (E-W) 16 5.50 5.33 -3.1 Figure 6-3. Fixed-Base RXB Y Response Transfer Function due to Y-Input at Center of Roof. NuScale Nonproprietary
Figure 6-4. Fixed-Base RXB Z Response Transfer Function due to Z-Input at Center of Roof. Figure 6-5. Fixed-Base RXB X Response Transfer Function due to X-Input at Northeast Top Corner of Roof (N30762). NuScale Nonproprietary
6.1.2 Case 12 - Reactor Building Reaction Comparison To compare base reactions, the models are subjected to unit gravity loads in the X, Y, and Z directions and the sum of the maximum forces in the base springs is calculated. In SASSI2010, a unit gravity load is simulated by applying an acceleration time history, which slowly increases and decays as shown in Figure 6-6. The comparison of the base reactions computed by the SASSI2010 and SAP2000 programs is provided in Table 6-3. The SASSI2010 reactions are within 0.88% of the reactions from SAP2000. Table 6-3. Comparison of RXB Static Total Reactions. Output Global FX Global FY Global FZ Case kips kips kips SAP2000 Model IGX 868,025 - - IGY - 871,940 - IGZ - - 859,077 SASSI Model IGX 875,641 - - IGY - 874,080 - IGZ - - 855,993
% Difference = (SASSI-SAP2000-1)x100 IGX 0.88% - -
IGY - 0.25% - IGZ - - -0.36% NuScale Nonproprietary
((
}}2(a),(c)
Figure 6-6. 1g Step Acceleration Input Time History. 6.1.3 Conclusion There is GOOD AGREEMENT between the results calculated by SASSI2010 and the independent program SAP2000. This validates the capability of SASSI2010 to accurately model the RXB. 6.2 NuScale-Specific SASSI2010 V&V - SAP2000 Versus SASSI Comparison of Control Building Fixed-Base Results The purpose of this problem is to verify the capability of SASSI2010 to model the dynamic properties of the NuScale CRB in terms of modal frequencies and base reactions. The fixed-base responses of the CRB are compared between SAP2000 and SASSI2010. The properties of the fixed-base CRB SASSI2010 model are summarized in Table 6-4. The SAP2000 model is shown in Figure 6-7. The corresponding SASSI2010 model is shown in Figure 6-8. ((
}}2(a),(c)
NuScale Nonproprietary
Table 6-4. Control Building SASSI2010 Model Element Summary. Item Description Quantity Backfill Soil Solid Elements 3,555 Foundation Mat Solid Elements 411 Beam Elements 1,393 Plate Elements 4,069 ((
}}2(a),(c)
Figure 6-7. CRB SAP2000 Model. NuScale Nonproprietary
Figure 6-8. CRB SASSI2010 Model. NuScale Nonproprietary
6.2.1 Control Building Modal Frequency Comparison The modal frequencies are obtained by determining the frequencies of the peaks in a transfer function calculated by SASSI2010. For example, typical transfer functions at the CRB roof are shown in Figure 6-9 through Figure 6-11. The frequencies obtained from SASSI2010 transfer functions are compared with those calculated by SAP2000 in Table 6-5. As can be seen by the comparison in the table, SASSI2010 provides accurate structural modal frequencies. Table 6-5. Comparison of Control Building Modal Frequencies. Modal Direction SAP2000 SASSI Diff.(%) Mode No. Frequency Frequency (Hz) (Hz) at Transfer Function Peaks. Z (Vert) 72 6.35 6.35 0.00 X (E-W) 106 11.37 11.50 1.14 Y (N-S) 114 14.81 14.38 -2.90 Figure 6-9. SASSI Fixed-Base Cracked CRB Z Transfer Function due to Z-Input at Roof Center (Node 39757). NuScale Nonproprietary
Figure 6-10. SASSI Fixed-Base Cracked CRB X Transfer Function due to X-Input at East Side of Roof (Node 39866). NuScale Nonproprietary
Figure 6-11. SASSI Fixed-Base Cracked CRB Y Transfer Function due to Y-Input at North Side of Roof (Node 39783). NuScale Nonproprietary
6.2.2 Control Building Reaction Comparison To compare base reactions, the models are subjected to unit gravity loads in the X, Y, and Z directions and the sum of the maximum forces in the base springs are calculated. In SASSI2010, a unit gravity load is simulated by applying an acceleration time history, which slowly increases and decays, as shown in Figure 6-12. The comparison of the base reactions computed by the SASSI2010 and SAP2000 programs is provided in Table 6-6. The SASSI2010 reactions are within 0.24% of the reactions from SAP2000. Table 6-6. Comparison of Control Building Static Total Reactions. Output Global FX Global FY Global FZ Case kips kips kips SAP2000 IGX 127,750 - - IGY - 127,750 - IGZ - - 127,750 SASSI IGX 127,962 0 0 IGY 0 127,978 0 IGZ 0 0 128,052
% Difference = (SASSI-SAP2000-1)x100 IGX 0.17% - -
IGY - 0.18% - IGZ - - 0.24% NuScale Nonproprietary
((
}}2(a),(c)
Figure 6-12. 1g Step Acceleration Input Time History. 6.2.3 Conclusion There is GOOD AGREEMENT between the results calculated by SASSI2010 and the independent program SAP2000. This validates the capability of SASSI2010 to accurately model the CRB. 6.3 NuScale-Specific SASSI2010 V&V - Effect of Aspect Ratios on Seismic Responses A study has been performed to determine if the seismic responses calculated by the SASSI2010 program are affected by the shell element aspect ratios. A 58-11 wide by 85-0 high portion of the RXB spent fuel pool wall was extracted and three identical structures using different element aspect ratios were analyzed. A cantilever wall model was created by attaching the wall to a rigid baseplate. The cantilever wall will be subjected to the NS (Y) horizontal seismic motion perpendicular to the plane of the cantilever wall. NuScale Nonproprietary
Results in terms of modal frequencies, in-structure response spectra (ISRS), forces, and moments were calculated and compared to the results calculated using the independent, validated SAP2000 program (Reference 8). 6.3.1 Mathematical Model The cantilever wall has a thickness of 6-0. The width and height are 707" and 1020", respectively. The following three models with different aspect ratios were analyzed by both SASSI2010 and SAP2000. Model 1 The shell model in Figure 6-13 in an isometric standard view shows the boundary restraints at the bottom of the rigid base. The two nodes selected for displacement calculation are also shown in Figure 6-14. This model is designated as Model 1. The cantilever wall is monolithically connected to the rigid base, as in a cantilever beam. Model 2 For the aspect ratio study, each shell element is subdivided into four (2x2), as shown in Figure 6-15. The seven elements at Z=645" are subdivided into two elements (2x1). The two nodes selected for displacement calculation are also shown in Figure 6-16. This refined model is designated as Model 2. Model 3 The model is further subdivided as shown in Figure 6-17 by dividing each element in Model 2 into two elements in the X direction (2x1). The two nodes selected for displacement calculation are shown in Figure 6-18. This model is designated as Model 3. The three models are summarized in Table 6-7. Table 6-7. Summary of the Three Models. Model No. of Nodes No. of Shell Elements Maximum Aspect Ratio Model 1 (7x16) 248 210 8.4 Model 2 (14x29) 870 798 4.2 Model 3 (28x29) 1882 1596 2.1 There are three material properties used for the models. The elements modeled with the three different materials can be seen in Figure 6-13 through Figure 6-18 as three different colors. Material 1, shown in red, is used for the upper part of the wall (Z=132" to 1020"). Material 2, NuScale Nonproprietary
shown in brown, is used for the bottom part of the wall (Z=0" to 132"). Material 3, shown in blue, is used for the rigid base plate. ((
}}2(a),(c)
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Figure 6-13. Isometric Cantilever Wall Model 1 (7 elements x 16 elements). NuScale Nonproprietary
Figure 6-14. Selected Elements for Moment and Shear Force, Model 1. NuScale Nonproprietary
Figure 6-15. Isometric Cantilever Wall Model 2 (14 elements x 29 elements). NuScale Nonproprietary
Figure 6-16. Selected Elements for Moment and Shear Force, Model 2. NuScale Nonproprietary
Figure 6-17. Isometric Cantilever Wall Model 3 (28 elements x 29 elements). NuScale Nonproprietary
Figure 6-18. Selected Elements for Moment and Shear Force, Model 3. NuScale Nonproprietary
6.3.2 Structural Frequency Comparison between the Different Models The modal frequencies calculated by SASSI2010 are the frequencies at the peaks of the transfer functions. The transfer functions calculated by the three models of different meshes are shown in Figure 6-19. Comparison of the first four frequencies in Table 6-9 shows the dominant structural frequencies are not affected by mesh size or aspect ratio. Table 6-9. Comparison of Modal Frequencies between the Three Models. Wall Lateral Model 1 Frequency Model 2 Frequency Model 3 Frequency Mode No. Aspect ratio (Hz) Aspect ratio (Hz) Aspect ratio (Hz) 8.4 4.2 2.1 SAP2000 SASSI2010 SAP2000 SASSI2010 SAP2000 SASSI2010 1st 1.15 1.16 1.16 1.16 1.16 1.16 2nd 6.83 6.91 6.91 6.92 6.88 6.92 3rd 18.26 18.74 18.74 18.82 18.54 18.82 4rd 34.47 35.75 35.75 35.80 34.86 35.80 Figure 6-19. Transfer Functions of the Three Models. 6.3.3 Ground Excitation The model of the fixed-base cantilever wall is subjected to an out-of-plane seismic ground motion in the Y direction shown in Figure 6-20. NuScale Nonproprietary
Figure 6-20. Input Ground Accelerations. 6.3.4 Out-of-Plane Moment and Shear Force Comparison between Different Models Comparison of the average out-of-plane shear forces and moments at the centroids of the transition elements shown in Figure 6-14, Figure 6-16, and Figure 6-18 calculated by SAP2000 and SASSI2010 due to the seismic acceleration time history applied in the out-of-plane (Y) direction are presented in Table 6-10. M22 is the bending moment about the X-axis and V23 is the out-of-plane shear in the Y-direction on a horizontal section of the wall. The values presented in the table are obtained by averaging the centroidal values of the transition elements over the width of the wall. Comparison of average out-of-plane shear forces and moments in Table 6-10 shows the largest difference between the models is 3.5%. The largest difference between SASSI2010 and SAP2000 is 5.9%. Thus, the mesh used in Model 1, which has the highest aspect ratio used in the NuScale building models, is acceptable. Table 6-10. Comparison of Out-of-Plane Moment, M22, and Out-of-Plane Shear, V23, between Different Models. Component Program Model 1 Model 2 Model 3 % Difference % Difference Aspect Aspect Aspect between between ratio 8.4 ratio 4.2 ratio 2.1 Model 2 and Model 3 and Model 1 Model 1 M22 SAP2000 1,950,006 1,948,408 1,948,346 -0.1% -0.1% (out-of-plane SASSI2010 1,974,857 1,965,229 1,966,579 -0.5% -0.4% moment % Difference 1.3% 0.9% 0.9% --- --- about X) between (lb-in-in) SASSI2010 and SAP2000 V23 SAP2000 3,994 4,057 4,058 1.6% 1.6% (out-of-plane SASSI2010 4,231 4,094 4,081 -3.2% -3.5% shear in Y % Difference 5.9% 0.9% 0.6% --- --- direction) between (lb-in) SASSI2010 and SAP2000 NuScale Nonproprietary
6.3.5 Y- ISRS Comparison between the Different Models The ISRS will be calculated in the Y (NS) direction at two selected locations shown in Figure 6-13 through Figure 6-18. The node numbers of the two locations in the three models are provided in Table 6-11. Table 6-11. Node Numbers of the Two Selected Locations. Model Node Numbers Location 1 Location 2 Model 1 (Aspect ratio 8.4) 241 244 Model 2 (Aspect ratio 4.2) 856 862 Model 3 (Aspect ratio 2.1) 1654 1666 The Y-ISRS of the three models as calculated by SAP2000 at Location 1 and 2 are shown in Figure 6-21 and Figure 6-22, respectively. The Y-ISRS of the three models as calculated by SASSI2010 at Location 1 and 2 are shown in Figure 6-23 and Figure 6-24, respectively. Comparisons of the ISRS plots at the two nodes show that the ISRS are not affected by the mesh size or aspect ratio of the transition elements. Thus, the mesh sizes (high aspect ratio) used in the base case, or Model 1, are acceptable. Comparisons of the Y-ISRS between SAP2000 and SASSI2010 at Location 1 and Location 2 of Model 1 are shown in Figure 6-25 and Figure 6-26, respectively. These figures show that SASSI2010 is able to duplicate the ISRS calculated by an independent, validated program. NuScale Nonproprietary
Figure 6-21. Y-ISRS at Location 1 by SAP2000. Figure 6-22. Y-ISRS at Location 2 by SAP2000. NuScale Nonproprietary
Figure 6-23. Y-ISRS at Location 1 by SASSI2010. Figure 6-24. Y-ISRS at Location 2 by SASSI2010. NuScale Nonproprietary
Figure 6-25. Y-ISRS at Node 241 by SAP2000 and SASSI2010. NuScale Nonproprietary
Figure 6-26. Y-ISRS at Node 244 by SAP2000 and SASSI2010. 6.3.6 Conclusion There is GOOD AGREEMENT between the results calculated by SASSI2010 and the independent program SAP2000. There is also GOOD AGREEMENT between the different SASSI2010 refinement models. This validates the refinement used in the RXB model. It also validates the aspect ratio of 8:1 used in the RXB model. 6.4 NuScale-Specific SASSI2010 V&V - RXB - Comparison of ESM versus DM Results The ESM was implemented into SASSI2010 as an approximate and faster method of forming the impedance matrix, as opposed to the exact DM. The SSI analysis of the NuScale RXB was performed with SASS2010 using the ESM. A full model of the RXB was used with interaction nodes defined at seven planes (north, south, east, west, bottom, mid, and top planes). The full RXB model is shown in Figure 6-27. NuScale Nonproprietary
To verify that using the ESM with seven planes, or 7P, of interaction nodes is sufficient, a study was performed in which results obtained using the ESM were compared with results obtained by the DM, in which all of the excavated soil nodes are specified as interaction nodes. Analyzing the full RXB model with the DM would mean specifying all of the excavated soil nodes as interaction nodes, which would exceed the SASSI2010 limit of 20,000 interaction nodes. Therefore, a half model of the RXB was created for the ESM versus DM comparison, as shown in Figure 6-28. The interaction nodes specified for the ESM and DM are shown in Figure 6-29. The number of interaction nodes in each model is provided in Table 6-12. Section 6.4.1 and Section 6.4.2 contain comparisons of transfer functions and ISRS, respectively. Table 6-12. Number of Interaction Nodes in RXB Models. Model Number of Interaction Nodes RXB Full Model (ESM-7P) 7,950 RXM Half Model (ESM-7P) 4,080 RXM Half Model (DM) 14,880 Figure 6-27. RXB SASSI Full Model. NuScale Nonproprietary
Figure 6-28. SASSI Half RXB Model without Hidden Lines. NuScale Nonproprietary
Figure 6-29. Interaction Nodes for RXB Half Model - DM (top) and 7P (bottom). NuScale Nonproprietary
6.4.1 Comparison of Transfer Functions X, Y, and Z response transfer functions at node 30350 (center of roof) are shown in Figure 6-30. Figure 6-30. Cracked RXB Transfer Functions at Node 30350, Center of Roof for Soil Type 7. NuScale Nonproprietary
6.4.2 Comparison of ISRS The X, Y, and Z combined ISRS at node 30350 (center of roof) are shown in Figure 6-31, Figure 6-32, and Figure 6-33, respectively. Figure 6-31. Cracked RXB East-West (X) ISRS at Node 30350, Roof Slab between Grid Lines RX-4 and RX-5 due to Five CSDRS Inputs for Soil Type 7. NuScale Nonproprietary
Figure 6-32. Cracked RXB North-South (Y) ISRS at Node 30350, Roof Slab between Grid Lines RX-4 and RX-5 due to Five CSDRS Inputs for Soil Type 7. NuScale Nonproprietary
Figure 6-33. Cracked RXB Vertical (Z) ISRS at Node 30350, Roof Slab between Grid Lines RX-4 and RX-5 due to Five CSDRS Inputs for Soil Type 7. 6.4.3 Conclusions As presented in Section 6.4.1, the transfer functions show REASONABLE AGREEMENT between the 7P ESM and DM. As presented in Section 6.4.2, the ISRS calculated by 7P ESM show REASONABLE AGREEMENT with those calculated by the DM. Because the DM cannot be performed for the analysis of the large, complex RXB full model to calculate SSI seismic responses for design purposes, the ESM using the 7P interaction nodes is a practical compromise to calculate a reasonably accurate SSI response for design purposes. 6.5 NuScale-Specific SASSI2010 V&V - RXB Subjected to Non-vertically Propagating Seismic Waves Results from a study addressing the uncertainties associated with the SSI analysis of the NuScale RXB subjected to non-vertically propagating (inclined) shear waves are summarized in this section. NuScale Nonproprietary
The study consists of two parts. Section 6.5.1 provides analysis results of the free-field being subjected to non-vertically propagating waves. Section 6.5.2 documents the analysis of the RXB subjected to non-vertically propagating waves. 6.5.1 Response of Free-Field to Non-Vertically Propagating Waves This section presents the response of the free-field to non-vertically propagating waves. The free-field motion is used in the SSI formulation, which provides the input motion for the RXB excitation. The evaluation of free-field motion is an important part of the evaluation of the inclined wave effect on SSI responses. To determine the response of the free-field to vertically or non-vertically propagating waves, a SASSI2010 model consisting of only the free-field soil without any structure was analyzed. The coordinate system and variables used to define wave propagation throughout this document are shown in Figure 6-34. For this study, angles of incidence of wave propagation, , equal to 0°, 17°, and 30° are used. The angle of incidence is measured from the vertical axis and in the X-Z plane, as shown in Figure 6-34. Because Soil Type 7 is nearly a uniform soil profile with a shear wave velocity, Vs, of 5,000 ft/sec, =17° corresponds to an apparent wave velocity of approximately Vs/sin(17°) = 17,100 ft/sec (5.2 km/sec) and =30° corresponds to an apparent wave velocity of approximately Vs/sin(30°) = 10,000 ft/sec (3.0 km/sec). Figure 6-34. Definition of Angle of Incidence, (from Reference 6). NuScale Nonproprietary
Comparisons of X-response acceleration response spectra (ARS) at the surface due to SV- and P-waves are presented in Section 6.5.1.1. The study also generated comparisons of Z-response ARS due to SV- and P-waves; however, the results are not presented here, for brevity. 6.5.1.1 Free-Field X-Response ARS at Surface due to SV- and P-Waves Figure 6-35 shows the X-response ARS at the surface due to SV-waves for =0°, 17°, and 30°. These curves are identical, because the control point is at the ground surface and the same time history is used as the horizontal component for the three cases. The CSDRS at the rock outcrop (dashed line) is shown for reference only. The three ARS at the surface due to SV-waves for =0°, 17°, and 30° are identical. NuScale Nonproprietary
Figure 6-35. Soil Type 7 - Free-Field Uncoupled East-West (X) ARS at Surface, Capitola Input. NuScale Nonproprietary
Figure 6-36 shows the X-response ARS at the ground surface due to SV- and P-waves for =17° and =30°. The combined response obtained by square root of the sum of the squares (SRSS) combination of the two curves (X due to inclined SV-wave and X due to inclined P-wave) is also shown. Because the control point is at the ground surface, the X/SV curves for =0° and =17° are identical. Figure 6-37 shows a comparison of the combined X-response ARS at the ground surface for =0°, 17°, and 30°. The =0° curve represents the CSDRS motion at this depth. The =17° and =30° curves include the horizontal response due to P-waves; thus, exceed the motion associated with the CSDRS with vertical wave represented by the angle of zero degrees that was chosen as the design basis. Figure 6-36. Soil Type 7 - Free-Field East-West (X) ARS at Surface, Capitola Input for (a)
=17° and (b) =30°.
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Figure 6-37. Soil Type 7 - Comparison of Combined Free-Field East-West (X) ARS at Surface, Capitola Input. 6.5.2 SSI Analysis of RXB with Non-Vertically Propagating Waves This section documents the SSI analysis of the NuScale RXB embedded in Soil Type 7 subjected to non-vertically propagating waves. The ISRS due to the Capitola input propagating at various angles of incidence are presented. Based on the results of Section 6.5.1, the uncombined ISRS are compared. Results are presented for the following three cases, shown schematically in Figure 6-38:
- Case 1: Control point at surface, =0°.
- Case 2: Control point at surface, =17°.
- Case 3: Control point at surface, =30°.
For this summary report, the ISRS comparison will be presented at the center of the RXB roof. The averaged-enveloped-widened ISRS at the given node from the soil cases, and the cracked and uncracked models is included as a heavy, black, dashed line in Figure 6-39 through Figure 6-41. Each averaged-enveloped-widened ISRS is the average of the combined ISRS due to five vertically propagating CSDRS-compatible time histories. The floor ISRS from the FSAR at the node elevation is included as a solid orange line. NuScale Nonproprietary
Figure 6-38. RXB Analysis Cases (not to scale). This section presents comparisons of the direct ISRS at Node 30350 (El. 181, roof center). The =0° curve represents the response to the design basis case. The =0°, =17°, and =30° curves do not include the coupling terms. The CSDRS at rock outcrop (thin dashes) is shown for reference only. In Figure 6-39, the floor ISRS curve envelops the =17° and =30° curves. NuScale Nonproprietary
Figure 6-39. RXB - East-West (X) ISRS, Node 30350, El. 181, Roof Center, Capitola Input. NuScale Nonproprietary
In Figure 6-40, the floor ISRS curve envelops the =17° and =30° curves, except for peaks at 3.3 Hz, 7 Hz, 8.5 Hz, and 10 Hz. When the average ISRS of the five time histories is used, the exceedances are expected to be smaller. Figure 6-40. RXB - North-South (Y) ISRS, Node 30350, El. 181, Roof Center, Capitola Input. NuScale Nonproprietary
In Figure 6-41, the floor ISRS curve envelops the =17° and =30° curves, except for peaks at 3.5 Hz and from 30 to 100 Hz. When the average ISRS of the five time histories is used, the exceedances are expected to be smaller. Figure 6-41. RXB - Vertical (Z) ISRS, Node 30350, El. 181, Roof Center, Capitola Input. NuScale Nonproprietary
6.5.3 Conclusion The results from the SSI analyses with non-vertically propagating waves show EXPECTED BEHAVIOR. 6.6 NuScale-Specific SASSI2010 V&V - RXB Spring Sensitivity Study The results from a study addressing the adequacy of the spring stiffness used to model the rigid connection between the basemat and backfill soil to free-field in the SSI analysis of the RXB are summarized in this section. In the model used to generate the Final Safety Analysis Report (FSAR) results, the stiffness of the rigid springs was 1010 lb/in. For this study, the stiffness of the rigid springs will be increased to 1011 lb/in. Results in terms of transfer functions, ISRS, and forces and moments are compared to see if increasing the spring stiffness has any effect on the results. The RXB SASSI2010 model with the backfill soil is shown in Figure 6-42. The rigid spring elements that connect the sides and bottom surface of the basemat and backfill soil to the free-field are shown in Figure 6-43. The total number of rigid spring elements is 4,470. Figure 6-42. RXB SASSI Model Including Backfill Soil. NuScale Nonproprietary
Figure 6-43. SASSI Model 4,470 Rigid Spring Elements Connecting Backfill Soil to Free-field. 6.6.1 Comparison of Transfer Functions Comparisons of transfer functions (TFs) in the northwest corner at the top of the basemat are shown in Figure 6-44 through Figure 6-46. There are no discernible differences in the TFs between spring K = 1010 lb/in and spring K = 1011 lb/in. NuScale Nonproprietary
Figure 6-44. Cracked RXB X Acceleration Transfer Function Amplitude Comparison at Node 3996, Northwest Corner on Top of Basemat, for Soil Type 7. NuScale Nonproprietary
Figure 6-45. Cracked RXB Y Acceleration Transfer Function Amplitude Comparison at Node 3996, Northwest Corner on Top of Basemat, for Soil Type 7. NuScale Nonproprietary
Figure 6-46. Cracked RXB Z Acceleration Transfer Function Amplitude Comparison at Node 3996, Northwest Corner on Top of Basemat, for Soil Type 7. NuScale Nonproprietary
6.6.2 Comparison of ISRS Comparisons of ISRS in the northwest corner at the top of the basemat are shown in Figure 6-47 through Figure 6-49. There are no discernible differences in the ISRS generated with spring K = 1010 lb/in. and spring K = 1011 lb/in. Figure 6-47. RXB - East-West (X) ISRS, Node 3996, Northwest Corner on Top of Basemat, Capitola Input. NuScale Nonproprietary
Figure 6-48. RXB - North-South (Y) ISRS, Node 3996, Northwest Corner on Top of Basemat, Capitola Input. NuScale Nonproprietary
Figure 6-49. RXB - Vertical (Z) ISRS, Node 3996, Northwest Corner on Top of Basemat, Capitola Input. 6.6.3 Comparison of Spring Forces The maximum forces in the 4,470 rigid spring elements shown in Figure 6-43 are compared in this section. The maximum forces in the rigid springs due to the three input directions have been combined using the SRSS method. Table 6-13 contains the sum of the maximum spring forces in the rigid spring elements for the cases with spring K=1010 lb/in and spring K=1011 lb/in and the percent difference, which equals l [(K=1011) - (K=1010)]/(K=1010)x100l. This table shows the largest percent difference between the two cases is 0.17% in the Y (NS) direction. The average of the percent difference of the maximum forces over the rigid spring elements is provided in Table 6-14. The average differences are about 0.3% in all directions. Table 6-13. Sum of Maximum Spring Forces in Rigid Spring Elements, Capitola Input. Direction Total of Maximum Spring Force (kips) Spring K= 1010 lbs-in. Spring K= 1011 lbs-in. Difference X (EW) 1,071,556 1,071,494 0.01% Y (NS) 1,406,865 1,404,451 0.17% Z (VT) 1,670,423 1,669,582 0.05% NuScale Nonproprietary
Table 6-14. Average Difference of Forces over Rigid Spring Elements, Capitola Input. Direction Difference X (EW) 0.29% Y (NS) 0.29% Z (VT) 0.27% 6.6.4 Conclusions Comparisons of transfer functions in Section 6.6.1 and comparisons of ISRS in Section 6.6.2 show GOOD AGREEMENT and show increasing the rigid spring stiffness has no discernible effect on the transfer functions and ISRS. Comparisons of maximum spring forces in Section 6.6.3 show GOOD AGREEMENT and, at most, the total spring forces changed by 0.17%, as shown in Table 6-13. Based on the results presented in this study, it is concluded that the stiffness of 1010 lb/in. is sufficient to model the soil springs connecting the RXB basemat and backfill to the free-field. 6.7 Vendor Example 1 - Reactor Building with Surface Foundation This problem is supplied by the SASSI2010 vendor in Reference 6. The problem consists of a pressurized water reactor supported on a uniform, damped half-space, as shown in Figure 6-50. It is subject to vertically propagating shear waves. The analysis consists of two parts:
- Foundation impedance analysis - the impedance coefficients of the rigid, massless basemat are calculated and compared with published results.
- Interaction analysis - SSI analysis is performed.
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Figure 6-50. Lumped-Mass Stick Models of the Containment and Internal Structures. NuScale Nonproprietary
6.7.1 Foundation Impedance Analysis Results Figure 6-51 shows results from the foundation impedance analysis compared with published results. ((
}}2(a),(c)
Figure 6-51. Horizontal Stiffness Coefficients, Vs=2,000 ft/sec. NuScale Nonproprietary
To obtain results up to a higher frequency, the soil shear wave velocity was increased to 5,000 ft/sec and the impedance was recalculated. Figure 6-52 shows the results up to 50 Hz. ((
}}2(a),(c)
Figure 6-52. Horizontal Stiffness Coefficients, Vs=5,000 ft/sec. 6.7.2 SSI Analysis Results Figure 6-53 shows the 2%-damped ARS of the horizontal motion at the top of the internal structure. Results are compared with the computer program FASS. NuScale Nonproprietary
Figure 6-53. Absolute Acceleration Response at Top of Internal Structure. 6.7.3 Conclusion There is GOOD AGREEMENT between the impedance calculated by SASSI2010 and published results. There is GOOD AGREEMENT between the SASSI2010 results and the results calculated by an independent program. This validates the capability of SASSI2010 to perform the SSI analysis of a containment structure. 6.8 Vendor Example 2 - Scattering Response of Embedded Rigid Cylinders This problem is supplied by the SASSI2010 vendor in Reference 6. In this problem, the scattering responses of embedded rigid cylinders subjected to vertically propagating SV-waves and horizontally propagating SH-waves is computed. Results of the analyses are compared with solutions published by Day (Reference 10). This problem also validates the ESM by comparing results using the ESM with results using the DM. NuScale Nonproprietary
Figure 6-54 shows the soil profiles considered in the analyses. Figure 6-55 shows the configuration of the model for H = 0.5, where H is the ratio of the cylinder embedment depth to the cylinder radius. Results are also generated for cases of H = 1.0 and H = 2.0. The cylinder was modeled as a half-model with the XZ plane as the plane of symmetry. One layer of the nodal points is shown in Figure 6-56. Figure 6-54. Soil Profiles Used for SASSI2010 Example 2. NuScale Nonproprietary
Figure 6-55. Geometry of Cylinder Foundation Cross Section for H=0.5. Figure 6-56. Excavated Soil Model at Elevation -32.5 ft for H=0.5. NuScale Nonproprietary
Results for Case 1, H = 0.5, are shown in Figure 6-57 and Figure 6-58. The ESM and DM results show good agreement with Days solution up to a0 = 8 (f=39 Hz). Figure 6-57. Response of Foundation due to Vertically Propagating SV-Wave, Case 1, H=0.5 (a) Translational Response. NuScale Nonproprietary
Figure 6-58. Response of Foundation due to Vertically Propagating SV-Wave, Case 1, H=0.5 (b) Rocking Response. 6.8.1 Conclusion There is GOOD AGREEMENT between the results calculated by SASSI2010 and the published results by Day (Reference 10). This validates the capability of SASSI2010 to calculate the scattering of an embedded structure and the capability of SASSI2010 to analyze half-models. NuScale Nonproprietary
6.9 Vendor Example 3 - Lotung SSI Experiment This problem is supplied by the SASSI2010 vendor in Reference 6. In this problem, a SASSI2010 model of a one-quarter scale containment structure is created and analyzed. Results are compared with actual recorded data. The SASSI model is shown in Figure 6-59. Figure 6-59. Configuration of SASSI Finite Element Model. NuScale Nonproprietary
Figure 6-60 shows a comparison of the ARS calculated at the top of the containment with recorded data. Figure 6-60. Comparison of Responses at the Top of the Containment. 6.9.1 Conclusion There is GOOD AGREEMENT between the results calculated by SASSI2010 and experimental data. This validates the capability of SASSI2010 to perform the SSI analysis of a containment structure. 6.10 Additional SASSI2010 V&V Problem 7 Case 1 - Validation of Solid Element This example verifies the stress calculation of the solid (brick) element. Two brick elements with an associated mesh of 12 nodes were used to form a column supported on the surface of a rigid half-space. The column model has the following properties: area of 1 ft², elastic modulus (E) of NuScale Nonproprietary
4.32x106 ksf, Poisson's ratio () of 0.3, and damping ratio () of 5%. The masses were lumped at the four nodes on top of the column, each having a value of 293 k-sec2/ft. The finite element model is shown in Figure 6-61. A fixed-base condition is simulated by assigning a shear wave velocity of 10,000 ft/sec to the free-field soil. 6.10.1 Excitation An axial load of 1.0x106 kips is applied at the top of the column as shown in Figure 6-61. The normalized excitation time history is shown in Figure 6-62. 6.10.2 Results The comparison between the SASSI2010 values and the corresponding reference values, as provided in Table 6-15, shows that SASSI2010 calculates accurate results. The reference value is obtained by hand calculation: Szz = 1.0x106 kips / 1 ft2 = 1.0x106 ksf Table 6-15. Case 1 Comparison between SASSI2010 and Reference Values. Case Item Compared SASSI Reference Case 1a Element 1 Stress Szz (ksf) 1.03x106 1.0x106 Element 2 Stress Szz (ksf) 1.03x106 1.0x106 NuScale Nonproprietary
Figure 6-61. Column Modeled by Rectangular Brick Elements. NuScale Nonproprietary
((
}}2(a),(c)
Figure 6-62. Normalized Input Time History. 6.10.3 Conclusion There is GOOD AGREEMENT between the SASSI2010 results and the closed-form solution. This validates the capability of SASSI2010 solid element to produce accurate results. 6.11 Additional SASSI2010 V&V Problem 7 Case 2 - Validation of 3-D Beam Element This problem verifies the dynamic behavior and force and moment calculation of the beam element subjected to the following two loading cases:
- Case 2a: harmonic lateral force.
- Case 2b: harmonic ground motion.
Five beam elements of this type with six nodal points were used to form a cantilever beam with a length of 5 ft supported on the surface of a rigid half-space, as shown in Figure 6-63. A fixed-base condition is simulated by assigning a shear wave velocity of 10,000 ft/sec to the free-field soil. NuScale Nonproprietary
6.11.1 Excitation The cantilever beam is subjected to a harmonic lateral force excitation at the top of the cantilever, as shown in Figure 6-63(a) and a harmonic ground excitation, as shown in Figure 6-63(b). The normalized excitation time history is the same as that shown in Figure 6-62. 6.11.2 Reference Values Let Hx () denote the transfer function for the response displacement (x) due to the harmonic loads given by Clough and Penzien (Reference 5) as follows: in which k is the stiffness of the column, is the circular frequency of excitation, is the damping ratio, and n is the fundamental frequency of the column given by in which m is the mass and k (=3EI/L3) is the flexural stiffness of the cantilever beam having a value equal to 1.04x106 k/ft, n is the fundamental circular frequency computed from Equation (A1-2) giving a value equal to 29.8 rps, (i.e., fn = 4.74 cps). E is the elastic modulus equal to 4.32x106 ksf, I is the bending moment of inertia equal to 10 ft4, L is the beam length equal to 5 ft, and is the damping ratio of 0.05. The analytical solution for the response at the top of the beam (Node 6) due to the harmonic ground acceleration (g) input, published by Clough and Penzien (Reference 5), is given by 6.11.3 Results The comparison between the SASSI2010 values and the corresponding reference values, as provided in Table 6-16, shows that SASSI2010 calculates accurate results. NuScale Nonproprietary
The displacement transfer function for Case 2a and acceleration transfer function for Case 2b at the top (Node 6) of the cantilever are compared in Figure 6-64 and Figure 6-65, respectively, with those calculated using the theoretical formulas. The comparisons show that the SASSI2010-calculated and interpolated transfer functions are very close to the theoretical ones. Table 6-16. Case 2 Comparison between SASSI2010 and Reference Values. Case Item Compared SASSI Reference Case 2a Frequency (Hz) 4.59 4.74 Transfer Function Peak 1.03x10-5 0.962x10-5 Nodes 1 and 2 Shear (kips) 1.04x106 1x106 Node 1 Bending Moment (kip-ft) 5.20x106 5x106 Node 3 Bending Moment (kip-ft) 3.12x106 3x106 Case 2b Frequency (Hz) 4.59 4.74 Transfer Function Peak 10.2 10.05 Nodes 1 and 2 Shear (kips) 3.92x104 3.76x104 Node 1 Bending Moment (kip-ft) 1.96x105 1.88x105 Node 3 Bending Moment (kip-ft) 1.18x105 1.13x105 NuScale Nonproprietary
Figure 6-63. Case 2, Cantilever Beam Subjected to (a) Harmonic Lateral Force Excitation and (b) Horizontal Ground Excitation. NuScale Nonproprietary
((
}}2(a),(c)
Figure 6-64. Case 2a, Displacement Transfer function at Top of Cantilever. NuScale Nonproprietary
((
}}2(a),(c)
Figure 6-65. Case 2b, Acceleration Transfer Function at Top of Cantilever. NuScale Nonproprietary
6.11.4 Conclusion There is GOOD AGREEMENT between the SASSI2010 results and the closed-form solution. This validates the capability of SASSI2010 beam element to produce accurate results. 6.12 Additional SASSI2010 V&V Problem 7 Case 5 - Validation of 3-D Spring Element This problem verifies the dynamic behavior and force calculation of the 3-D spring element. Two 3-D spring elements of this type were used to construct two SDOF systems supported on the surface of a rigid half-space, as shown schematically in Figure 6-66. Spring 1 has a lumped-mass (M1) equal to 1,170 k-sec²/ft at Node 2, a spring stiffness coefficient (K1) equal to 1.04x106 k/ft, and a damping ratio (1) of 5%. Spring 2 has a lumped-mass (M2) equal to 1,170 k-sec²/ft at Node 4, a spring stiffness coefficient (K2) equal to 2.08x106 k/ft, and a damping ratio (2) of 10%. A fixed base condition is simulated by assigning a shear wave velocity of 1.0x109 ft/sec to the free-field soil. 6.12.1 Excitation The harmonic vertical load applied to the springs is the same as shown in Figure 6-62 applied with a factor of 1.0x106. 6.12.2 Results The transfer function amplitudes of Spring 1 and Spring 2 are shown in Figure 6-67 and Figure 6-68, respectively. The frequencies of the SDOF systems are obtained from the frequencies of the peaks. The comparisons between the SASSI2010 values and the corresponding reference values, calculated using Equation (A1-2) from Table 6-17, show that SASSI2010 calculates accurate results. Table 6-17. Case 5 Comparison between SASSI2010 and Reference Values. Item Compared SASSI Reference Frequency No.1 (Hz) at Node 2 4.69 4.74 Frequency No.2 (Hz) at Node 4 6.64 6.72 Maximum Force in Spring 1 (kips) 1.03x106 1.0x106 Maximum Force in Spring 2 (kips) 1.02x106 1.0x106 NuScale Nonproprietary
Figure 6-66. Spring Elements Subjected to Vertical Force Excitation. Figure 6-67. Vertical Displacement Transfer Function Amplitude of Spring Element No.1 at Node 2. NuScale Nonproprietary
Figure 6-68. Vertical Displacement Transfer Function Amplitude of Spring Element No.2 at Node 4. 6.12.3 Conclusion There is GOOD AGREEMENT between the SASSI2010 results and the closed-form solution. This validates the capability of SASSI2010 spring element to produce accurate results. 6.13 Additional SASSI2010 V&V Problem 9 - Response of Circular Foundation to Spatially-Random Ground Motion This test problem verifies the capability of SASSI2010 to incorporate incoherence of ground motion. The test problem selected involves the calculation of the response of a rigid, massless, circular disk sitting on an elastic half-space subjected to spatially-random ground motion. This test problem has been previously solved analytically by Luco and Mita (Reference 1). The results obtained from the SASSI2010 analyses, in terms of the translational and rotational transfer functions, were compared with the corresponding results published by Luco and Mita to assess the analysis capabilities of SASSI2010 for this test problem. NuScale Nonproprietary
6.13.1 Analysis Model For the SASSI2010 analyses, the uniform elastic half-space was modeled with eight soil layers having a thickness (H) of 5 ft, followed by three layers having a thickness of 10 ft. The soil has the following properties: shear wave velocity of 2,000 fps, weight density of 0.130 k/ft³, Poisson's ratio, v, of 1/3, and damping ratio of 0.001%. ((
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Figure 6-69. SASSI2010 Model of Circular Disk. NuScale Nonproprietary
6.13.2 Excitation The disk will be subject to the following two ground motions:
- Horizontal ground motion excitation prescribed in the form of a vertically propagating SV-wave.
- Vertical ground motion excitation prescribed in the form of a vertically propagating P-wave.
6.13.3 Results and Comparisons The theoretical results are from Reference 1. For the case of horizontal input, the results obtained from the SASSI2010 analysis, in terms of the transfer function amplitude, are compared with the Reference 1 results in Figure 6-70. For the case of vertical input, the results obtained from the SASSI2010 analysis, in terms of the transfer function amplitude, are compared with the Reference 1 results in Figure 6-71. ((
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Figure 6-70. Comparison of Translational (X) and Torsional (ZZ) Response by SASSI2010 due to X Input with Results from Reference 1. NuScale Nonproprietary
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Figure 6-71. Comparison of Translational (Z) and Rocking (YY) Response by SASSI2010 due to Z Input with Results from Reference 1. 6.13.4 Case 9 Conclusion The results obtained from the SASSI2010 analysis show GOOD AGREEMENT with the corresponding solutions from Reference 1. Thus, the capability of SASSI2010 to incorporate incoherence of ground motion has been validated. 6.14 Additional SASSI2010 V&V Problem 10 - Free-Field Response due to Inclined SH-, SV-, and P-Waves This problem verifies the capability of SASSI2010 to model the response of the free-field to non-vertically propagating, that is, inclined seismic waves. The test problem selected involves calculation of the response of the free-field layer of soil over bedrock, as shown in Figure 6-72, subjected to seismic SH-, SV-, and P-waves. This test problem has been previously solved analytically by Wolf and Obernhuber (Reference 2 and Reference 3). NuScale Nonproprietary
The results obtained from the SASSI2010 analyses, in terms of the translational transfer functions, were compared with the corresponding results published by Wolf and Obernhuber for the following cases:
- Section 6.14.1: Case 10a, Response Due to SH-Waves Impinging on a Homogeneous Soil Layer.
- Section 6.14.2: Case 10b, Response Due to SV- and P-Waves Impinging on a Homogeneous Soil Layer.
Figure 6-72. Description of the System and Coordinates and Soil Properties for Uniform Soil Case. NuScale Nonproprietary
6.14.1 Case 10a - Response Due to SH-Waves Impinging on a Homogeneous Soil Layer This section presents results due to incident SH-waves impinging on a homogeneous soil layer. SASSI results versus frequency are compared with the results from Reference 2 in Figure 6-73. Results are presented in terms of lYtl/lYbl, which is the horizontal amplification within (bedrock in-layer to surface outcrop). The SASSI results versus depth are compared with the results from Reference 2 in Figure 6-74 and Figure 6-75 for dimensionless frequency values of /4 and 3/2, respectively. The dimensionless frequency is defined as d/cLs, where d and cLs are the depth and shear wave velocity, respectively, of the soil layer. The SASSI results show excellent agreement with the results from Reference 2. NuScale Nonproprietary
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Figure 6-73. Comparison of Horizontal (Y) Response due to Incident SH-Waves versus Frequency with Results from Reference 2, Homogeneous Soil Layer. NuScale Nonproprietary
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Figure 6-74. Comparison of Horizontal (Y) Response due to Incident SH-Waves versus Depth with Results from Reference 2, Homogeneous Soil Layer, = /4. NuScale Nonproprietary
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Figure 6-75. Comparison of Horizontal (Y) Response due to Incident SH-Waves versus Depth with Results from Reference 2, Homogeneous Soil Layer, = 3/2. 6.14.2 Case 10b - Response Due to SV- and P-Waves Impinging on a Homogeneous Soil Layer This section presents results due to incident SV- and P-waves impinging on a homogeneous soil layer. SASSI results versus frequency for SV-waves are compared with the results from Reference 3 in Figure 6-76. Results are presented in terms of lXtl/lXbl, which is the horizontal amplification within (bedrock in-layer to surface outcrop). The SASSI results versus depth for SV-waves are compared with the results from Reference 3 in Figure 6-77 and Figure 6-78 for dimensionless frequency values of /2 and , respectively. NuScale Nonproprietary
The SASSI results versus depth for P-waves are compared with the results from Reference 3 in Figure 6-79 and Figure 6-80 for dimensionless frequency values of /2 and , respectively. Results for the SV-waves show excellent agreement, except in Figure 6-76 for the case of R = 60°, at a narrow frequency band around the dimensionless frequency of 4, where SASSI produces conservative results. Results for the P-waves show excellent agreement, except in Figure 6-80 for the case of R = 30° and depths of Z/d > 1. This is not significant for typical structures, because Z/d > 1 is in the bedrock. ((
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Figure 6-76. Comparison of Horizontal (X) Response due to Incident SV-Waves versus Frequency with Results from Reference 3, Homogeneous Soil Layer. NuScale Nonproprietary
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Figure 6-77. Comparison of Horizontal (X) Response due to Incident SV-Waves versus Depth with Results from Reference 3, Homogeneous Soil Layer, = /2. NuScale Nonproprietary
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Figure 6-78. Comparison of Horizontal (X) Response due to Incident SV-Waves versus Depth with Results from Reference 3, Homogeneous Soil Layer, = . NuScale Nonproprietary
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Figure 6-79. Comparison of Vertical (Z) Response due to Incident P-Waves versus Depth with Results from Reference 3, Homogeneous Soil Layer, = /2. NuScale Nonproprietary
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Figure 6-80. Comparison of Vertical (Z) Response due to Incident P-Waves versus Depth with Results from Reference 3, Homogeneous Soil Layer, = . 6.14.3 Conclusion There is GOOD AGREEMENT between the SASSI2010 results and the published results. This validates the capability of SASSI2010 to produce accurate results with non-vertically propagating seismic waves. NuScale Nonproprietary
6.15 Additional SASSI2010 V&V Problem 11 - Dynamic Response of a Square Foundation to Obliquely Incident Seismic Waves This problem verifies the capability of SASSI2010 to model the response of a structure to obliquely-incident seismic waves. The test problem selected involves the calculation of the response of a rigid, massless, square plate sitting on an elastic half-space, subjected to seismic SH-, SV-, and P-waves. This test problem has previously been solved analytically by Wong and Luco (Reference 4). The results obtained from the SASSI analyses, in terms of the translational and rotational transfer functions, were compared with the corresponding results published by Wong and Luco to assess the validity analysis capabilities of SASSI for this test problem. The rigid, massless, square plate is modeled with 64, 10x10 "thick shell" type elements with a thickness of 100 feet and is shown in Figure 6-81. This plate has a dimension of 80 feet on each side (a=40 feet) and is given a large value of elastic modulus equal to 1.0x1010 k/ft2. In the results presented in Reference 4 and in this validation problem, the horizontal angle of incidence with respect to the X axis, H, is equal to zero. In Reference 4, the vertical angle of incidence, v, is measured from the horizontal axis, while in SASSI2010, the vertical angle of incidence, , is measured from the vertical axis. This section presents the SASSI results and compares them to the theoretical results from Reference 4. The results are given at the center of the plate, in terms of dimensionless frequency ao= a/, where is the shear wave velocity. Figure 6-81. Rigid, Massless Plate on Elastic Half-Space. NuScale Nonproprietary
6.15.1 Case 11a - Response Due to SH-Waves This section presents results due to incident SH-waves. In Figure 6-82, the SASSI results for horizontal (Y) translation are compared with the results from Figure 3 of Reference 4. In Figure 6-83, the SASSI results for torsional (ZZ) response are compared with the results from Figure 4(a) of Reference 4. In the comparisons, the real values from Reference 4 are plotted as solid lines. The imaginary values from Reference 4 are plotted as dashed lines. The real values from SASSI are plotted as solid symbols. The imaginary values from SASSI are plotted as hollow symbols. Even though the SASSI results and the results from Reference 4 are obtained by different methods, the SASSI results show good agreement with the results from Reference 4. The comparison is also good for the extreme case of v = 0° (horizontally propagating wave). NuScale Nonproprietary
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Figure 6-82. Comparison of Horizontal (Y) Response due to Incident SH-Waves with Results from Reference 4. NuScale Nonproprietary
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Figure 6-83. Comparison of Torsional (ZZ) Response due to Incident SH-Waves with Results from Reference 4. NuScale Nonproprietary
6.15.2 Case 11b - Response Due to SV-Waves This section presents results due to incident SV-waves. In Figure 6-84, the SASSI results for horizontal (X) translation are compared with x. In Figure 6-85, the SASSI results for rocking (YY) response are compared with ax. In the comparisons, the real values from Reference 4 are plotted as solid lines. The imaginary values from Reference 4 are plotted as dashed lines. The real values from SASSI are plotted as solid symbols. The imaginary values from SASSI are plotted as hollow symbols. Even though the SASSI results and the results from Reference 4 are obtained by different methods, the SASSI results show good agreement with the results from Reference 4. NuScale Nonproprietary
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Figure 6-84. Comparison of Horizontal (X) Response due to Incident SV-Waves with Results from Reference 4. NuScale Nonproprietary
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Figure 6-85. Comparison of Rocking (YY) Response due to Incident SV-Waves with Results from Reference 4. NuScale Nonproprietary
6.15.3 Case 11c - Response Due to P-Waves This section presents results due to incident P-waves. In Figure 6-86, the SASSI results for vertical (Z) translation are compared with z. In Figure 6-87, the SASSI results for rocking (YY) response are compared with ax. In the comparisons, the real values from Reference 4 are plotted as solid lines. The imaginary values from Reference 4 are plotted as dashed lines. The real values from SASSI are plotted as solid symbols. The imaginary values from SASSI are plotted as hollow symbols. Even though the SASSI results and the results from Reference 4 are obtained by different methods, the SASSI results show good agreement with the results from Reference 4. NuScale Nonproprietary
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Figure 6-86. Comparison of Vertical (Z) Response due to Incident P-Waves with Results from Reference 4. NuScale Nonproprietary
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Figure 6-87. Comparison of Rocking (YY) Response due to Incident P-Waves with Results from Reference 4. NuScale Nonproprietary
6.15.4 Conclusion There is GOOD AGREEMENT between the SASSI2010 results and the published results. This validates the capability of SASSI2010 to produce accurate results with non-vertically propagating seismic waves. 6.16 NuScale Specific SASSI2010 V&V - RXB Refined Mesh Study 6.16.1 Description The purpose of this verification problem is to show that the element mesh size in the SAP2000 RXB model used to obtain static and dynamic responses documented in the FSAR produces acceptable results. The report further demonstrates that the mesh refinement of reinforced concrete beam and shell elements has negligible effects on the static and dynamic characteristics of the finite element model and solution results. Thus, further mesh refinement will not produce significant changes in the nodal displacements, maximum element forces or moments, dominant natural frequencies, modal mass participation ratios, or 4%-damped ISRS. To demonstrate the adequacy of the mesh size used in the FSAR model, the report presents a comparison of solution results for the FSAR model and the model with refined meshing. The report provides results for the maximum building displacements, maximum moments, maximum in-plane shear forces, dominant structural frequencies, mass participation ratios, and 4%- damped ISRS from the analysis of the two models. Figure 6-88 shows the original RXB meshing used in the FSAR model. The results documented in the FSAR are based on this meshing. Figure 6-89 shows the RXB model with a refined mesh obtained by further dividing the shell elements in half in each direction, followed by meshing of the frame elements, accordingly. Table 6-18 provides a comparison of the number of joints and elements between the FSAR and refined mesh models. Static loads will be applied to the two models in the form of unit gravity loads in the X (load case 1GX), Y (load case 1GY), and Z (load case 1GZ) directions to obtain static displacements, forces, and moments for comparison. Modal analyses of the two models will also be performed to obtain dynamic properties for comparison. Time history analyses are performed in the X, Y, and Z directions separately to obtain the ISRS at selected representative nodes in the RXB model. The CSDRS-compatible Capitola time histories are used as input ground motions for the time history analyses. NuScale Nonproprietary
Table 6-18. Comparison of SAP2000 Joints and Elements between the FSAR Model and the Refined Model. Item FSAR Model Refined Model Number of Joints 30,762 80,197 Number of Joint with Restraints 2,342 2,884 Number of Frame Elements 6,453 11,209 Number of Shell Elements 18,818 68,559 Number of Solid Elements 12,075 12,075 Number of Link-Support Elements 1,114 1,114 Figure 6-88. Overview of FSAR RXB Model with Original Mesh. NuScale Nonproprietary
Figure 6-89. Overview of RXB Model with Refined Mesh. 6.16.2 Results Comparisons of key static and dynamic responses are provided below. 6.16.2.1 Roof Vertical Displacement The middle node of the RXB roof (30410) is one of the most flexible points in the building. Table 6-19 shows the comparison of vertical displacement for the joint between the two models for load case 1GZ. As can be seen, the difference in the displacements is 0.1%. Figure 6-90 and Figure 6-91 show the roof vertical displacement contours for the FSAR and refined mesh model, respectively. Table 6-19. RXB Roof Vertical Displacements Due to 1GZ (FSAR and Refined Model). Joint Load Case Uz Displacement (in) %Difference FSAR Model Refined Model 30410 1GZ 1.380 1.382 0.1% NuScale Nonproprietary
Figure 6-90. 1GZ Uz Displacement Contours of Roof for FSAR Model. Figure 6-91. 1GZ Uz Displacement Contours of Roof for Refined Mesh Model. 6.16.2.2 Horizontal Displacements of Building Corner Joints The four corner joints at Z = 1824" are the most flexible points for lateral loads. Table 6-20 shows the X and Y displacement comparison for these corner nodes for the 1GX and 1GY load cases, respectively. The largest difference is 3.7%. NuScale Nonproprietary
Table 6-20. RXB Ux and Uy Displacements (FSAR and Refined Model). Joint Load Case Ux Displacement (in) %Difference FSAR Model Refined Model 29076 1GX -0.382 -0.392 2.6% 29098 1GX -0.381 -0.391 2.6% 29343 1GX -0.387 -0.397 2.6% 29365 1GX -0.390 -0.400 2.6% Joint Load Case Uy Displacement (in) %Difference FSAR Model Refined Model 29076 1GY -1.202 -1.246 3.7% 29098 1GY -1.200 -1.244 3.7% 29343 1GY -1.069 -1.096 2.5% 29365 1GY -1.069 -1.096 2.5% 6.16.2.3 Maximum Forces and Moments Figure 6-92 shows a comparison of the contour plot of the out-of-plane moment, M11, between the FSAR and refined mesh models of the north wall of the RXB. The contour plots are very similar. Figure 6-92. 1GY M11 Contours for North Outer Wall for the FSAR RXB Model (Top) and RXB Refined Mesh Model (Bottom). NuScale Nonproprietary
Table 6-21 shows a comparison of forces and moments between the FSAR model and refined mesh model. The following items are compared and the maximum percent difference is 11.9%:
- maximum RXB roof moments.
- maximum RXB roof in-plane shears.
- maximum moments in RXB slab at El. 75'-0".
- maximum in-plane shears in RXB slab at El. 75'-0".
- maximum moments in RXB slab at El. 100'-0".
- maximum in-plane shears in RXB slab at El. 100'-0".
- maximum moments in RXB north outer wall.
- maximum moments in RXB north pool wall.
- maximum in-plane shears in RXB north outer wall.
- maximum in-plane shears in RXB north pool wall.
Table 6-21. RXB Forces and Moment Comparison (FSAR and Refined Model). Location Item Load FSAR Refined % Case Model Mesh Model Difference Roof Moment about NS, M11 (lb-in-in) 1GZ 262,704 255,686 -2.67% Moment about EW, M22 (lb-in-in) 1GZ 39,563 40,756 3.02% In-Plane Shear, F12 (lb-in) 1GX 4,131 4,143 0.29% In-Plane Shear, F12 (lb-in) 1GY 26,007 26,751 2.86% Slab at El. Moment about NS, M11 (lb-in-in) 1GZ 27,593 27,363 -0.83% 75'-0 Moment about EW, M22 (lb-in-in) 1GZ 17,062 16,102 -5.63% In-Plane Shear, F12 (lb-in) 1GX 11,982 10,977 -8.39% In-Plane Shear, F12 (lb-in) 1GY 27,693 28,621 3.35% Slab at El. Moment about NS, M11 (lb-in-in) 1GZ 29,859 30,329 1.57% 100'-0 Moment about EW, M22 (lb-in-in) 1GZ 15,174 15,472 1.96% In-Plane Shear, F12 (lb-in) 1GX 9,188 8,094 -11.91% In-Plane Shear, F12 (lb-in) 1GY 32,937 31,748 -3.61% North Moment about Z, M11 (lb-in-in) 1GY 135,309 138,200 2.14% Outer Wall Moment about X, M22 (lb-in-in) 1GY 386,806 399,033 3.16% In-Plane Shear, F12 (lb-in) 1GX 38,526 37,934 -1.54% North Pool Moment about Z, M11 (lb-in-in) 1GY 466,952 479,578 2.70% Wall Moment about X, M22 (lb-in-in) 1GY 439,729 428,031 -2.66% In-Plane Shear, F12 (lb-in) 1GX 35,468 36,519 2.96% 6.16.2.4 Modal Properties Table 6-22 shows a close comparison of the dominant frequencies obtained using modal analysis with the FSAR and refined mesh RXB models. The first 12 modes that had the largest mass participation ratios in the X, Y, and Z directions were compared between the two models. NuScale Nonproprietary
Table 6-22. RXB Frequencies and Participating Mass Ratios (FSAR and Refined Model). FSAR Model Refined Mesh Model Frequency Modal Participation Mass Ratios Frequency Modal Participation Mass Ratios Hz UX UY UZ Hz UX UY UZ 1.93 0.000 0.010 0.000 1.89 0.000 0.010 0.000 2.87 0.000 0.520 0.000 2.83 0.000 0.530 0.000 3.23 0.000 0.000 0.021 3.23 0.000 0.000 0.021 4.50 0.000 0.013 0.000 4.49 0.000 0.012 0.000 4.66 0.130 0.000 0.000 4.65 0.140 0.000 0.000 4.78 0.028 0.000 0.000 4.77 0.043 0.000 0.000 4.90 0.008 0.000 0.000 5.10 0.007 0.000 0.000 5.17 0.000 0.046 0.000 5.10 0.000 0.044 0.000 5.25 0.180 0.000 0.000 5.23 0.210 0.000 0.000 5.44 0.140 0.000 0.000 5.42 0.110 0.000 0.000 5.70 0.000 0.005 0.000 5.69 0.000 0.006 0.000 5.70 0.000 0.000 0.014 5.69 0.000 0.000 0.012 6.16.2.5 ISRS for Capitola Time History The selected locations for ISRS using the Capitola time history are presented in Table 6-23, and the locations are shown in Figure 6-88 and Figure 6-93. For the joint at the corner of the RXB, ISRS in the X and Y directions are presented. For the joint on the slab, ISRS in all three directions are presented. The ISRS plots are shown in Figure 6-94 through Figure 6-98. Table 6-23. Locations Selected for Capitola ISRS Comparison Location Node X (East) Y (North) Z (Vert) Figure No. Description No. No. (in.) (in.) (in.) Corner Joints of the Building 1 29343 4092 -873 1824 Figure 6-94 (X) Southeast Corner at Roof Figure 6-95 (Y) Level, See Figure 6-88. Joints on the Slabs 2 23313 1666 -705 1020 Figure 6-96 (X) Joint on Slab at El. 100'-0 Figure 6-97 (Y) See Figure 6-93. Figure 6-98 (Z) NuScale Nonproprietary
Figure 6-93. El. 100'-0" ISRS Joint Location. Figure 6-94. Cracked X-ISRS due to Capitola Input at Node 29343 at Southeast Corner at Roof Level. NuScale Nonproprietary
Figure 6-95. Cracked Y-ISRS due to Capitola Input at Node 29343 at Southeast Corner at Roof Level. NuScale Nonproprietary
Figure 6-96. Cracked X-ISRS due to Capitola Input at Node 23313 at Joint on Slab at El. 100'-0". NuScale Nonproprietary
Figure 6-97. Cracked Y-ISRS due to Capitola Input at Node 23313 at Joint on Slab at El. 100'-0". NuScale Nonproprietary
Figure 6-98. Cracked Z-ISRS due to Capitola Input at Node 23313 at Joint on Slab at El. 100'-0". 6.16.3 Conclusions NuScale Nonproprietary
A comparison of static and dynamic results between the FSAR model and the refined mesh model, as presented in the foregoing sections, shows that there is GOOD AGREEMENT in the pertinent structural responses of the two models. Given this, the discretization and the mesh size used in the FSAR finite element model for the RXB is optimal and provides EXPECTED BEHAVIOR of static and dynamic analyses. Further mesh refinement will not produce significant changes in the nodal displacements, maximum element forces or moments, dominant natural frequencies, or the modal mass participation ratios. Furthermore, the ISRS from the refined model show GOOD AGREEMENT with ISRS from the FSAR model. The SAP2000 versus SASSI2010 comparison (Section 6.1) shows that SASSI2010 is able to reproduce the finite element results of an independent program. The refined mesh study shows the meshing of the RXB finite element model is adequate to capture the dynamic behavior of the RXB. 6.17 NuScale Specific SASSI2010 V&V - CRB Refined Mesh Study 6.17.1 Description The purpose of this verification problem is to show the element mesh size in the SAP2000 CRB model used to obtain static and dynamic responses documented in the FSAR produces acceptable results. The report further demonstrates the mesh refinement of reinforced concrete beam and shell elements has negligible effect on the static and dynamic characteristics of the finite element model and solution results. Thus, further mesh refinement will not produce significant changes in the nodal displacements, maximum element forces or moments, dominant natural frequencies, modal mass participation ratios, or 4%-damped ISRS. To demonstrate the adequacy of the mesh size used in the FSAR model, the report presents a comparison of solution results for the FSAR model and the model with refined meshing. The report provides results for the maximum building displacements, maximum moments, maximum in-plane shear forces, dominant structural frequencies, mass participation ratios, and 4%- damped ISRS from the analysis of the two models. Figure 6-99 shows the original CRB meshing used in the FSAR model. The results documented in the FSAR are based on this meshing. Figure 6-100 shows the CRB model with a refined mesh obtained by further dividing the shell elements in half in each direction, followed by meshing of the frame elements, accordingly. Table 6-24 provides a comparison of the number of joints and elements between the FSAR and refined mesh models. NuScale Nonproprietary
Static loads were applied to the two models in the form of unit gravity loads in the X (load case 1GX), Y (load case 1GY), and Z (load case 1GZ) directions to obtain static displacements, forces, and moments for comparison. Modal analyses of the two models were also performed to obtain dynamic properties for comparison. Time history analyses are performed in the X, Y, and Z directions separately to obtain the ISRS at selected, representative nodes in the CRB model. The CSDRS-compatible Capitola time histories are used as input ground motions for the time history analyses. Table 6-24. Comparison of SAP2000 Joints and Elements between the CRB FSAR Model and the Refined CRB Model. Item FSAR Model Refined Model Number of Joints 8,872 19,217 Number of Joint with Restraints 864 1,064 Number of Frame Elements 1,393 1,682 Number of Shell Elements 4,069 14,362 Number of Solid Elements 3,966 3,966 Number of Link-Support Elements 457 657 Figure 6-99. Overview of FSAR CRB Model with Original Mesh. NuScale Nonproprietary
Figure 6-100. Overview of CRB Model with Refined Mesh. 6.17.2 Results Comparisons of key static and dynamic responses are provided below. 6.17.2.1 Floor Vertical Displacement Table 6-25 shows the comparison of vertical displacement between the two models at Joint 39241, located at the center of the floor slab at El. 120-0 for load case 1GZ. As can be seen, the difference in the displacements is 1.6%. Figure 6-101 and Figure 6-102 show the slab vertical displacement contours for the FSAR and refined mesh model, respectively. Table 6-25. CRB Vertical Displacement in Slab at El. 120-0 Due to 1GZ (FSAR and Refined Model). Joint Load Case Uz Displacement (in) %Difference FSAR Model Refined Model 39241 1GZ 0.189 0.192 1.6% NuScale Nonproprietary
Figure 6-101. 1GZ Uz Displacement Contours of Slab at El. 120-0 for FSAR Model. NuScale Nonproprietary
Figure 6-102. 1GZ Uz Displacement Contours of Slab at El. 120-0 for Refined Mesh Model. 6.17.2.2 Horizontal Displacements of Building Corner Joints The four corner joints at Z = 1260" are the most flexible points for lateral loads. Table 6-26 shows the X and Y displacement comparison for these corner nodes for the 1GX and 1GY load cases, respectively. The largest difference is 5.4%. Table 6-26. CRB Ux and Uy Displacements (FSAR and Refined Model). Joint Load Case Ux Displacement (in) %Difference FSAR Model Refined Model 39082 1GX -0.222 -0.232 4.5% 39105 1GX -0.258 -0.268 3.9% 39477 1GX -0.232 -0.242 4.3% 39500 1GX -0.264 -0.274 3.8% Joint Load Case Uy Displacement (in) %Difference FSAR Model Refined Model 39082 1GY -0.215 -0.225 4.7% 39105 1GY -0.211 -0.222 5.2% 39477 1GY -0.203 -0.214 5.4% 39500 1GY -0.202 -0.212 5.0% 6.17.2.3 Maximum Forces and Moments NuScale Nonproprietary
Table 6-27 shows the comparison of averaged absolute maximum moments in the CRB slab at El. 120'-0" at Locations A (for M11) and B (for M22) for load case 1GZ. Figure 6-103 and Figure 6-104 show contours for M11 and M22 moments, respectively, for the FSAR model and refined mesh model. Table 6-27. CRB Averaged Absolute Maximum Moments in Slab at El. 120'-0" Due to 1GZ (FSAR and Refined Model). CRB Model FSAR Model Refined Mesh Model % Difference Moment About Global Y 38,323 37,665 -1.7% Axis (Elm. 3346) (Elm. 5678, 5679, 5680, (M11) 5681) Lb-in-in Moment About Global X 54,217 53,661 -1.0% Axis (Elm. 3452) (Elm. 6098, 6099, 6100, (M22) 6101) Lb-in-in Figure 6-103. 1GZ M11 Contours for Slab at El. 120'-0" for the FSAR CRB Model (Left) and CRB Refined Mesh Model (Right). NuScale Nonproprietary
Figure 6-104. 1GZ M22 Contours for Slab at El. 120'-0" for the FSAR CRB Model (Left) and CRB Refined Mesh Model (Right). 6.17.2.4 Modal Properties Table 6-28 shows a comparison of the dominant frequencies obtained using modal analysis with the FSAR and refined-mesh CRB models. The first 12 modes that have the largest mass participation ratios in the X, Y, and Z directions are compared between the two models. NuScale Nonproprietary
Table 6-28. CRB Frequencies and Participating Mass Ratios (FSAR and Refined Model). FSAR Model Refined Mesh Model Frequency Modal Participation Mass Ratios Frequency Modal Participation Mass Ratios Hz UX UY UZ Hz UX UY UZ 4.77 0.200 0.013 0.000 4.76 0.210 0.013 0.000 5.01 0.006 0.210 0.000 5.00 0.007 0.220 0.000 5.94 0.120 0.000 0.001 5.91 0.130 0.000 0.001 6.03 0.000 0.071 0.000 6.02 0.000 0.081 0.000 6.17 0.004 0.037 0.009 6.16 0.004 0.034 0.008 6.35 0.004 0.004 0.078 6.35 0.004 0.004 0.079 6.88 0.078 0.002 0.002 6.85 0.083 0.001 0.003 6.95 0.007 0.037 0.000 6.94 0.005 0.041 0.000 7.16 0.000 0.024 0.000 7.16 0.000 0.024 0.000 7.39 0.066 0.002 0.001 7.38 0.062 0.004 0.001 7.48 0.001 0.079 0.014 7.47 0.001 0.079 0.013 7.68 0.009 0.007 0.086 7.67 0.009 0.007 0.089 6.17.2.5 ISRS for Capitola Time History The selected locations for ISRS using the Capitola time history are presented in Table 6-29. For the joint at the corner of the CRB, ISRS in the X and Y directions are presented. For the joint on the slab, ISRS in three directions are presented. These corresponding plots are shown in Figure 6-106 through Figure 6-110. Table 6-29. Locations Selected for Capitola ISRS Comparison Location Node X Y Z Figure No. Description No. No. (East) (North) (Vert) (in) (in) (in) Corner Joints of the Building 1 39082 4500 -700 1260 Figure 6-106 (X) Southwest Corner at Roof Figure 6-107 (Y) Level.See Figure 6-105(a). Joints on the Slabs 2 38328 4868 178 1020 Figure 6-108 (X) Joint on Slab at El. 100'-0. Figure 6-109 (Y) See Figure 6-105(b). Figure 6-110 (Z) NuScale Nonproprietary
Figure 6-105. Locations of CRB ISRS. NuScale Nonproprietary
Figure 6-106. Cracked X-ISRS due to Capitola Input at Node 39082 at Southwest Corner at Roof Level. NuScale Nonproprietary
Figure 6-107. Cracked Y-ISRS due to Capitola Input at Node 39082 at Southwest Corner at Roof Level. NuScale Nonproprietary
Figure 6-108. Cracked X-ISRS due to Capitola Input at Node 38328 at El. 100'-0" Slab. NuScale Nonproprietary
Figure 6-109. Cracked Y-ISRS due to Capitola Input at Node 38328 at El. 100'-0" Slab. Figure 6-110. Cracked Z-ISRS due to Capitola Input at Node 38328 at El. 100'-0" Slab. NuScale Nonproprietary
6.17.3 Conclusions A comparison of static and dynamic results between the FSAR model and the refined mesh model, as presented in the foregoing sections, shows that there is GOOD AGREEMENT in the pertinent structural responses of the two models. Given this, the discretization and the mesh size used in the FSAR finite element model for the CRB is optimum and provides EXPECTED BEHAVIOR of static and dynamic analyses. Further mesh refinement will not produce significant changes in the nodal displacements, maximum element forces or moments, dominant natural frequencies, or the modal mass participation ratios. Furthermore, the ISRS from the refined model shows GOOD AGREEMENT with ISRS from the FSAR model. The SAP2000 versus SASSI2010 comparison (Section 6.2) shows that SASSI2010 is able to reproduce the finite element results of an independent program. The refined mesh study (Section 6.17) shows that the meshing of the CRB finite element model is adequate to capture the dynamic behavior of the CRB. 7.0 Computer Software The SASSI2010 (Reference 6), SAP2000 (Reference 8), and SHAKE (Reference 9) computer programs were used. 8.0 Conclusions This report summarizes the verification and validation of the computer program SASSI2010 and addresses the expectations by the NRC staff that the applicant should demonstrate that the parameters used in NuScale design-basis, seismic demand calculations are within the range of applicability of the SASSI2010 computer program. Parameters tested include the following (numbered in accordance with Table 1-2):
- 1. Mesh sensitivity - evaluation of solutions for different mesh sizes of finite elements.
- 2. Aspect ratio - evaluation of solutions for maximum finite element aspect ratio used.
- 3. Poissons ratio - evaluation of solutions for maximum Poissons ratio used.
- 4. Frequencies of analysis - demonstration that the frequencies of analysis used are adequate.
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- 5. Impedance functions - validation of impedance (or transfer) functions against the benchmark solutions for frequencies up to 50 Hz for embedded structures.
- 6. Extended subtraction method (ESM) - adequacy of ESM as compared to the direct method (DM).
- 7. Non-vertically propagating shear waves - evaluation of solutions for non-vertically propagating shear waves and determination of whether this is an important effect to be included in the NuScale seismic analysis.
- 8. Number of soil layers - confirmation that the number of soil layers used in NuScale analysis is within the maximum soil layers validated for SASSI2010.
- 9. Number of interaction nodes - confirmation that the number of interaction nodes used in NuScale analysis is within the maximum interaction nodes validated for SASSI2010.
10.Interpolated transfer functions - validation of the interpolation methodology used in SASSI2010. 11.Any other important parameters used in NuScale seismic analysis. A list of the NRC-identified parameters and additional tested application ranges is provided in Table 1-2. Descriptions of the SASSI2010 validation problems being summarized in this report are provided in Table 1-3, cross-referenced with the applicable parameter or tested application range being validated. The responses to the expectations by the NRC staff are also provided in Section 2.0. Selected SASSI2010 validation problems for various parameters used in the SSI analysis are summarized in Section 6.0. The results of the validation problems presented in Section 6.0 meet the acceptance criteria listed in Section 5.0. Thus, the SASSI2010 program has been validated for 3-D seismic SSI analysis. NuScale Nonproprietary
9.0 References Publications, Calculations, and Reports:
- 1. Luco, J.E. and A. Mita, Response of Circular Foundation to Spatially Random Ground Motion, Journal of Engineering Mechanics, ASCE, Vol. 113, No. 1, January 1987.
- 2. Wolf, J.P. and P. Obernhuber, Free-field Response from Inclined SH-waves and Love-Waves, Earthquake Engineering and Structural Dynamics, Vol, 10, 823-845, 1982.
- 3. Wolf, J.P. and P. Obernhuber, Free-field Response from Inclined SV- and P-waves and Rayleigh-Waves, Earthquake Engineering and Structural Dynamics, Vol, 10, 847-869, 1982.
- 4. Wong, H.L. and J.E. Luco, Dynamic Response of Rectangular Foundations to Obliquely Incident Seismic Waves, Earthquake Engineering and Structural Dynamics, Vol. 6, 3-16, 1978.
- 5. Clough, R.W., and J. Penzien, Dynamics of Structures, Second Edition, McGraw-Hill, Inc.,
1993. Software:
- 6. SASSI2010 Version 1.0 Users Manual, Berkeley California, May 2012.
- 7. SASSI2010 Software Validation and Verification, VV-17-22-031, Revision 0, ARES Corporation, Walnut Creek, California, February 2017.
- 8. SAP2000 Advanced Version 20.0.0, Computer and Structures, Inc., Walnut Creek, California.
- 9. SHAKE2000 Version 9.98.0, A Computer Program for the 1-D Analysis of Geotechnical Earthquake Engineering Problems, Users Manual, Gustavo A. Ordonez, April 2013.
Other Documents:
- 10. Day, S.M., "Finite Element Analysis of Seismic Scattering Problem," Ph.D. dissertation, University of California, San Diego, 1977.
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RAIO-0119-64104 : Affidavit of Zackary W. Rad, AF-0119-64104 NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvalis, Oregon 97330, Office: 541.360.0500, Fax: 541.207.3928 www.nuscalepower.com
NuScale Power, LLC AFFIDAVIT of Zackary W. Rad I, Zackary W. Rad, state as follows:
- 1. I am the Director, Regulatory Affairs of NuScale Power, LLC (NuScale), and as such, I have been specifically delegated the function of reviewing the information described in this Affidavit that NuScale seeks to have withheld from public disclosure, and am authorized to apply for its withholding on behalf of NuScale.
- 2. I am knowledgeable of the criteria and procedures used by NuScale in designating information as a trade secret, privileged, or as confidential commercial or financial information. This request to withhold information from public disclosure is driven by one or more of the following:
- a. The information requested to be withheld reveals distinguishing aspects of a process (or component, structure, tool, method, etc.) whose use by NuScale competitors, without a license from NuScale, would constitute a competitive economic disadvantage to NuScale.
- b. The information requested to be withheld consists of supporting data, including test data, relative to a process (or component, structure, tool, method, etc.), and the application of the data secures a competitive economic advantage, as described more fully in paragraph 3 of this Affidavit.
- c. Use by a competitor of the information requested to be withheld would reduce the competitor's expenditure of resources, or improve its competitive position, in the design, manufacture, shipment, installation, assurance of quality, or licensing of a similar product.
- d. The information requested to be withheld reveals cost or price information, production capabilities, budget levels, or commercial strategies of NuScale.
- e. The information requested to be withheld consists of patentable ideas.
- 3. Public disclosure of the information sought to be withheld is likely to cause substantial harm to NuScale's competitive position and foreclose or reduce the availability of profit-making opportunities. The accompanying Request for Additional Information response reveals distinguishing aspects about the method by which NuScale develops its vused in its seismic design and analysis.
NuScale has performed significant research and evaluation to develop a basis for this method and has invested significant resources, including the expenditure of a considerable sum of money. The precise financial value of the information is difficult to quantify, but it is a key element of the design basis for a NuScale plant and, therefore, has substantial value to NuScale. If the information were disclosed to the public, NuScale's competitors would have access to the information without purchasing the right to use it or having been required to undertake a similar expenditure of resources. Such disclosure would constitute a misappropriation of NuScale's intellectual property, and would deprive NuScale of the opportunity to exercise its competitive advantage to seek an adequate return on its investment. AF-0119-64104
- 4. The information sought to be withheld is in the enclosed response to NRC Request for Additional Information No. 133, eRAI 8936. The enclosure contains the designation "Proprietary" at the top of each page containing proprietary information. The information considered by NuScale to be proprietary is identified within double braces, "(( }}" in the document.
- 5. The basis for proposing that the information be withheld is that NuScale treats the information as a trade secret, privileged, or as confidential commercial or financial information. NuScale relies upon the exemption from disclosure set forth in the Freedom of Information Act ("FOIA"), 5 USC § 552(b)(4), as well as exemptions applicable to the NRC under 10 CFR §§ 2.390(a)(4) and 9.17(a)(4).
- 6. Pursuant to the provisions set forth in 10 CFR § 2.390(b)(4), the following is provided for consideration by the Commission in determining whether the information sought to be withheld from public disclosure should be withheld:
- a. The information sought to be withheld is owned and has been held in confidence by NuScale.
- b. The information is of a sort customarily held in confidence by NuScale and, to the best of my knowledge and belief, consistently has been held in confidence by NuScale.
The procedure for approval of external release of such information typically requires review by the staff manager, project manager, chief technology officer or other equivalent authority, or the manager of the cognizant marketing function (or his delegate), for technical content, competitive effect, and determination of the accuracy of the proprietary designation. Disclosures outside NuScale are limited to regulatory bodies, customers and potential customers and their agents, suppliers, licensees, and others with a legitimate need for the information, and then only in accordance with appropriate regulatory provisions or contractual agreements to maintain confidentiality.
- c. The information is being transmitted to and received by the NRC in confidence.
- d. No public disclosure of the information has been made, and it is not available in public sources. All disclosures to third parties, including any required transmittals to NRC, have been made, or must be made, pursuant to regulatory provisions or contractual agreements that provide for maintenance of the information in confidence.
- e. Public disclosure of the information is likely to cause substantial harm to the competitive position of NuScale, taking into account the value of the information to NuScale, the amount of effort and money expended by NuScale in developing the information, and the difficulty others would have in acquiring or duplicating the information. The information sought to be withheld is part of NuScale's technology that provides NuScale with a competitive advantage over other firms in the industry.
NuScale has invested significant human and financial capital in developing this technology and NuScale believes it would be difficult for others to duplicate the technology without access to the information sought to be withheld. I declare under penalty of perjury that the foregoing is true and correct. Executed on January 11, 2019. Zackary W. Rad AF-0119-64104}}