ML21050A162

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Nie - Presentation_Uncertainties in ISRS
ML21050A162
Person / Time
Issue date: 10/22/2020
From: Vladimir Graizer, Jinsuo Nie, Dogan Seber, Jim Xu
NRC/RES/DE
To:
T. Weaver
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Text

Uncertainties in In-Structural

Response

Spectra Estimated by Using Multiple Acceleration Time Histories October 20-22, 2020 DOE/NRC Natural Phenomena Hazards Meeting Virtual Jinsuo Nie, Jim Xu, Vladimir Graizer, and Dogan Seber Division of Engineering Office of Regulatory Research Nuclear Regulatory Commission

DISCLAIMER NOTICE The findings and opinions expressed in this presentation are those of the authors, and do not necessarily reflect the view of the U.S. Nuclear Regulatory Commission.

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Topics of This Presentation

  • In-Structure Response Spectra (ISRS) as a Better Representation of Input Power Distribution
  • ISRS as Acceptance Criteria To Determine the Number of Input Time Histories
  • Uncertainties in Input Time Histories and Coefficient of Variation in ISRS
  • Effect of Phase Uncertainty on the Number of Input Time Histories
  • Major conclusion: four or five time histories in the current practices may not be sufficient, especially for soil-structure systems with very low frequencies.

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ISRS Is Better than Input RS to Represent Input Power Distribution 4

Comparison of Time History A consisting of mainly 15 frequencies and a broadband Time History B.

PSD - Power spectral density RS - Response spectrum SRP - Standard Review Plan TH - Time history

[J. Nie, J. Pires, and D.

Seber. Interfacing Seismic Hazard Analysis with Structural Engineering Requirements, 2018 DOE-NRC NPH Meeting]

ISRS for Multiple Oscillators 5

Assurance from RS Enveloping Frequency (Hz)

Spectral Acceleration (g) 11 Hz Except for ZPA, the majority of the ISRS is NOT assured by RS enveloping!

[J. Nie, J. Pires, and D. Seber (2019). Understanding the assumptions in input response spectra for seismic time history analyses. Transactions, the 25th Structural Mechanics in Reactor Technology, SMiRT25.]

ISRS for Oscillators of Frequencies from 0.1 Hz to 100 Hz

ISRS Ratio Showing Different Power Distribution 6

Assurance from RS Enveloping Frequency (Hz)

Spectral Acceleration (g) 11 Hz Except for ZPA, the majority of the ISRS is NOT assured by RS enveloping!

Contour Plot of ISRS Ratio (ISRS / Input RS)

ISRS ratio is used to minimize the effect of minor differences in the input RS.

ISRS as Acceptance Criteria To Determine the Number of Input Time Histories

  • For linear analyses, the current practices are at least 5 time histories (ASCE 4-16) or 4 (SRP 3.7.1).
  • Use a relatively large number of input acceleration time histories to estimate the true mean and Coefficient of Variation (CV) of the ISRS.
  • Use CVISRS to determine the number of input time histories required to achieve a stable mean ISRS which falls within +/-10% of the true mean for a given confidence level (CL).
  • Assumptions: (1) input acceleration time histories are statistically independent, (2) ISRS relative to their mean are statistically independent, and (3) they have identical distribution.

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  • The sample mean M and sample CV of the RS (i.e., MRS, MISRS, CVRS, and CVISRS) are estimated from 500 input time histories.
  • The CV of MRS and MISRS can be found as:
  • Using the sample CVISRS, Ns time histories to achieve a MISRS within

+/-10% of the true mean can be determined by:

  • The essential task becomes to estimate an accurate sample CVISRS.

ISRS as Acceptance Criteria 8

100 2

, CL=68%; 384 2

, CL=95%

=

=
for N time histories

Uncertainties in Input Time Histories

  • We separate the uncertainty in Fourier amplitude spectra and the uncertainty in Fourier phase spectra of the acceleration time histories.
  • Fourier phase spectra are commonly observed to be distributed uniformly in

[0, 2] and are considered irreducible.

  • Fourier amplitude spectrum and Fourier phase spectrum are generally uncorrelated.
  • The uncertainty in the Fourier amplitude spectra should increase CVRS (for non RS matched time histories) and CVISRS, and will need to be addressed in a future study.

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[J. Nie, J. Xu, V. Graizer, and D. Seber (2020). Estimating stable mean responses for linear structural systems by using limited number of acceleration time histories. 2020 ASME Pressure Vessels and Piping Division Conference, PVP2020, Virtual Meeting. For this figure and those in the rest of this presentation. (ML20287A295)]

Procedure to Calculate CVISRS

  • We analyzed 21 cases:
  • 20 target PSD functions from SRP Rev. 4, Section 3.7.1, Appendix B
  • One Phase Wave (i.e., a unit PSD function)
  • For each PSD function:
  • Prescribe the Fourier amplitude spectrum deterministically based on the PSD function;
  • Randomly generate 500 sets of Fourier phase spectra over [0, 2]; and
  • Invert these Fourier spectra to 500 acceleration time histories.
  • This procedure follows the RVT approach, and exactly produces the input response spectra as the average.
  • 151 single-degree-of-freedom oscillators (0.1 Hz -

100 Hz) with a damping ratio of 5% were used to generate the response time histories.

  • For each oscillator (conceptually a simple structure or a structural mode), the 500 response time histories were used to generate the ISRS and estimate the sample CVISRS.

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Example Case of Input RS and ISRS 11 500 Sample Input RS, Mean RS, and Mean +/- One Standard Deviation 500 Sample ISRS, Mean ISRS, Mean +/-

One Standard Deviation (top),

and CV (bottom)

COV - Coefficient of Variation

CVRS of Input Time Histories

  • Except for very low frequencies (below 0.2 Hz), the variations in the CVRS are generally very small among the 20 different PSD functions.
  • The spread in the CVRS from 0.6 Hz to 30 Hz appears to be constant
  • Regardless of frequencies
  • Independent of the vastly different PSD functions
  • The largest CVRS is about 30% and the smallest CVRS is 7%.
  • All CVRS curves are generally decreasing functions of frequency.

12 Thin grey curves: CVRS for the 20 target PSD functions Thick red curve: mean CVRS Green and blue curves: bounds of CVRS

Observations in CVISRS ZPA Effect: CVISRS maintains a higher level than CVRS beyond the zero-period acceleration (ZPA) frequency of the response:

  • Roughly reflects the CVRS at the oscillator frequency.
  • The ZPA on the ISRS is simply the RS of the input motion at the oscillator frequency.

13 Oscillator: 0.49 Hz Oscillator: 19.74 Hz COV - Coefficient of Variation

Example Cases of 151 CVISRS

  • Each of the 21 PSD functions represents an input motion with uncertain phase spectra.
  • For each input motion, the 151 CVISRS are plotted together to assess how a complex structure of many modes would respond at various locations in the structure.
  • The effect of modal combination would most likely increase the CVISRS.

14 CVISRS for 151 Oscillators for SRP Target PSD Function for Central and Eastern U.S., Mw 6-7, D: 0-10 km CVISRS for 151 Oscillators for SRP Target PSD Function for Western U.S., Mw 7+, D10 km CVISRS for 151 Oscillators for the Unit PSD Function COV - Coefficient of Variation

Effect of Phase Uncertainty on NS

  • The maximum CVISRS is around 0.4 for most of the 20 cases, except for the four low-magnitude cases (Mw 5-6) that have a maximum CVISRS above 0.53.
  • For stiffer structural systems (for example, with a fundamental frequency of 5 Hz), the maximum CVISRS is about 30%, the same as that of the input motion.
  • A higher structural mode would basically carry the CVRS of the input motion at lower frequencies to CVISRS.

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  • We proposed an approach to explicitly use CVISRS to determine the minimum number of input acceleration time histories to estimate stable mean responses for linear structural systems.
  • This study considered only the uncertainty in the phase spectrum but not: (1) the uncertainty in Fourier amplitude spectrum and (2) the effect of modal combination.
  • The CVRS of the input motion are generally a monotonically decreasing function of frequency and it does not vary much for significantly different PSD functions (for RVT type time histories).
  • The maximum CVISRS across all frequencies is around 40%.
  • NS = 16 for CL = 68%, NS = 61 for CL = 68% for low fundamental frequencies.
  • For stiffer systems (for example, 5 Hz), the maximum CVISRS is about 30%
  • NS = 9 for a CL of 68%, NS = 35 for a CL of 95%.
  • This study indicates that the four or five time histories in the current practice may not be sufficient, especially for soil-structure systems with very low frequencies.

Conclusions 16

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