Seismic Evaluation of Auxiliary Buildings and Effects of 3D Locational Dynamic Response in SPRA

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Seismic Evaluation of Auxiliary Buildings and Effects of 3D Locational Dynamic Response in SPRA PSA 2017, Pittsburgh September 25 th, 2017 Brian

1 Seismic Evaluation of Auxiliary Buildings and Effects of 3D Locational Dynamic Response in SPRA PSA 2017, Pittsburgh September 25 th, 2017 Brian Cohn Jieun Hur, Eric Althoff, Halil Sezen, and Richard Denning and Tunc Aldemir Nuclear Engineering & Civil, Environmental and Geodetic Engineering

2 Outline Project Framework Objectives General Information o Auxiliary Building o Nonstructural Components in Auxiliary Building o Target Components o How to Estimate Failure Probabilities? Dynamic Characteristics of 3D Models Building Asymmetry Flexibility of Building Floor of 3D models Time History Analysis Conclusions & Future Work 2

3 Project Framework Advanced Mechanistic 3D Spatial Modeling and Analysis Methods to Accurately Represent Nuclear Facility External Event Scenarios 3

4 Objectives Generate reliable simplified structural models for efficient SPRA Determine uncertainties throughout the structural modeling and seismic analysis Investigate the effects of building asymmetry and the floor flexibility on the seismic response Evaluate the variation of seismic response of a building which can affect on the performance of nonstructural components under seismic shakings Integrate risk assessment of severe accident scenarios based on the results of the individual case studies 4

5 Auxiliary Building : General Descriptions Auxiliary Building Nonstructural Components 5

6 Auxiliary Building Connecticut Yankee NPP Plan Sheet 6

Nonstructural Components : in different locations How vulnerable nonstructural components (NSCs) in buildings under seismic shakings o How much their locations in a building can affect their dynamic

7 Nonstructural Components : in different locations How vulnerable nonstructural components (NSCs) in buildings under seismic shakings o How much their locations in a building can affect their dynamic behavior and operational failure? o Are the failure probabilities of identical NSCs in a floor of a building same? 3D Ground Motions o How correlated are the failure probabilities of more than two NSCs in a building? o What is the best way to probabilistically estimate the performance of NSCs? 7

8 Auxiliary Building : General Descriptions 3D Asymmetric Building Rf FL 2 nd FL k3 m3 m2 NSC2 Asymmetric Stiffness (Location of Walls) Asymmetric Mass distribution (Location of Loadings) 1 st FL Basement k2 m1 NSC1 k1 2D Models 3D Symmetric Building Symmetric Stiffness (Location of Walls) Symmetric Mass distribution (Location of Loadings) Rf FL 2 nd FL 1 st FL Basement m3 k3 m2 k2 m1 k1 NSC2 NSC1 8

9 Probability of failure (P f ) Resistance/capacity model (R) Strength/demand model (S) Probability density function f() Cumulative distribution function F() P f = P R S < 0 r = f R,S r, s, dddd Nonstructural Components : Estimation of Failure probability Assuming that resistance and demand models are statistically independent, P f = f s s f R r dsdr r = 1 F s r f R r dr = G S r f R r dr where G X represents the complementary cumulative distribution function of X. 9

10 Nonstructural Components : Joint Failure probability of two components The joint probability of failure of two components with correlated resistance models (R) and correlated strength/demand (S) models they can be found as P f = P R 1 S 1 < 0 R 2 S 2 < 0 = f R1,R 2,S 1,S 2 r 1, r 2, s 1, s 2 ds 1 ds 2 dr 1 dr 2 r 2 r 1 Assuming that resistance and demand models are statistically independent, P f = f S1,S 2 s 1, s 2 f R1,R 2 r 1, r 2 ds 1 ds 2 dr 1 dr 2 r 2 r 1 = 1 + F S1,S 2 r 1, r 2 F S1 r 1 F S2 r 2 f R1,R 2 r 1, r 2 dr 1 dr 2 = G S1 r 1 + G S2 r 2 G S1,S 2 r 1, r 2 f R1,R 2 r 1, r 2 dr 1 dr 2 where G X represents the complementary cumulative distribution function of X. 10

11 Nonstructural Components : Joint Failure probability of two components Effect of Correlation ρ C = β 2 S1 β S1 β S2 2 + β R1 β 2 S2 2 + β R2 ρ S1S2 + β 2 S1 β R1 β R2 2 + β R1 β 2 S2 2 + β R2 ρ R111 ρ C : the correlation coefficient between failures of the NSC1 and NSC2 β SS and β SS : the logarithmic standard deviations of the structural responses (loads) for NSC1 and NSC2, respectively β RR and β RR the logarithmic standard deviations of the capacities for NSC1and NSC2, respectively ρ SSSS : the correlation coefficient between the structural response at the locations of NCS1 and NCS2 ρ RRRR : the correlation coefficient for the capacity of the two components 11

12 Building Asymmetry Case 0 Symmetric Case 1 Prototype Case 2 A bit more asymmetric Case 3 Case 4 Case 5 The most asymmetric 12

13 Case 0 Symmetric Symmetry Case 1 Prototype Case 2 Building Asymmetry Asymmetry Case 3 Case 4 Case 5 The most asymmetric * CM: Center of Mass * CR: Center of Rigidity * Same Mass and Rigidity for All Cases Since the locations of CM &CR change, the 3D dynamic response varies. 13

14 Building Asymmetry : Dynamic Characteristics Case 0 Symmetric Case 1 Prototype Case 5 The most asymmetric Dynamic characteristics (natural frequencies) of buildings changed, and the number of mode shapes increased. 14

3D Structural Models : Building Floor 3D models can capture various behaviors of floors Rigid Body Motion In-Plane Deformation Out-of-Plane Deformation Mode 1 Mode 2

15 3D Structural Models : Building Floor 3D models can capture various behaviors of floors Rigid Body Motion In-Plane Deformation Out-of-Plane Deformation Mode 1 Mode 2 Mode 3 Negative Deformation Rigid Slab Models Semi-rigid Slab Models No Deformation Positive Deformation Semi-rigid slabs can capture more local behaviors of floors 15

16 Time History Analysis : EQ- Ground Motion Histories Spectral Acceleration [g] E-4 Horizontal UHRS 1E-4 Vertical UHRS Horizontal and Vertical Target Uniform Hazard Response Spectra (UHRS) Frequency [Hz] Generated Ground Motion History with Three Components based on the UHRS Ground motion histories are applied for the Time History Analysis (THA) as external loadings 16

17 Time History Analysis Result : Floor Accelerations Absolute Accelerations of 2nd floor (unit: g) (a) Transverse Dir. (b) Longitudinal Dir. (c) Vertical Dir (d) Resultant 17

18 Time History Analysis Result : Floor Accelerations PGA (g) 1 st Floor 2 nd Floor 3 rd Floor Max. (g) MMM. PPP Max. (g) MMM. PPP Max. (g) MMM. PPP Transverse Dir Longitudinal Dir Vertical Dir * PGA: Peak Ground Acceleration Two horizontal acceleration responses are less amplified than the ground motion. Vertical floor acceleration should have higher amplification factors. Upper floors need higher amplification factors. 18

19 Time History Analysis : Floor Displacement Absolute Displacement of 2nd floor (unit: in) (a) Transverse Dir (b) Longitudinal Dir (c) Vertical Dir (d) Resultant 19

20 Time History Analysis : Maximum Floor Displacements ( unit: inch) 1 st Floor 2 nd Floor 3 rd Floor Transverse Dir Longitudinal Dir Vertical Dir Resultant Since the auxiliary building is a relatively rigid structure, the displacement response is small. Upper floors have the largest displacement in all directions. 20

21 2D vs. 3D : Time History Analysis (a) 3D - Asymmetric (b) 3D - Symmetric (c) 2D- Stick Model El Centro earthquake (1940): g (at 2.5 sec) and g (at 2.2 sec) 21

22 2D vs. 3D : Time History Analysis (a) () (b) Displacement Response at Roof Level: (a) Asymmetric Building, and (b) Symmetric Building 22

23 2D vs. 3D : Time History Analysis (a) (a) (b) (b) Absolute Acceleration Response at Roof FL: (a) Asymmetric Building, and (b) Symmetric Building 23

24 Conclusions The seismic behavior of 2D structural models was compared to that of 3D models. 2D models were found not to be able to capture various mode shapes and maximum displacement and acceleration responses. Effects of building asymmetry was considered in seismic response assessment of building and nonstructural components. The more asymmetry in buildings, the higher dispersion of seismic responses due to the larger number of mode shapes. The flexibility of building floor was found critical for seismic response evaluation of nonstructural components restrained on floor. Floor flexibility affects all acceleration components. The amplification factor for the floor acceleration should be investigated for the simplified design and analysis. A larger number of simulations are needed to assess the degree of correlation among the failure probabilities of components located at different areas of a building. 24

25 Thank you! Questions? 25

26 3D Structural Models : Buildings with Flexible Floor Case 0 Symmetric Case 1 Prototype Case 5 The most asymmetric Mode Number Natural Frequency (Hz) Mass Participation Ratio Cumulative Mass Participation Ratio Case Case Case As expected, more asymmetric buildings have more varying mode shapes 26

Case 0 Symmetric Symmetry Case 1 Prototype Case 2 Dynamic Characteristics : Asymmetry + Flexibility of Floor Asymmetry Case 3 Case 4 Case 5 The most

27 Case 0 Symmetric Symmetry Case 1 Prototype Case 2 Dynamic Characteristics : Asymmetry + Flexibility of Floor Asymmetry Case 3 Case 4 Case 5 The most asymmetric As expected, more asymmetric buildings have more varying mode shapes Buildings with more flexible floors have smaller natural frequencies. 27

28 Time History Analysis Result : Absolute Floor Accelerations Mean (g) S.D. (g) C.O.V.(ratio) Median(g) 1 st FL 2 nd FL 3 rd FL Transverse Dir Longitudinal Dir Vertical Dir Resultant Transverse Dir Longitudinal Dir Vertical Dir Resultant Transverse Dir Longitudinal Dir Vertical Dir Resultant * S.D.: Standard Deviation * C.O.V.: Coefficient of Variation Vertical acceleration contributes the resultant acceleration most Upper floor has higher dispersion 28

29 Time History Analysis : Floor Displacements Mean S.D. Median C.O.V.(ratio) (inch) (inch) (inch) Transverse Dir Longitudinal Dir st FL Vertical Dir Resultant Transverse Dir Longitudinal Dir nd FL Vertical Dir Resultant Transverse Dir Longitudinal Dir rd FL Vertical Dir Resultant * S.D.: Standard Deviation * C.O.V.: Coefficient of Variation Transverse displacement contributes to the resultant displacement most. As expected, the dispersion of vertical displacement is the largest. 29

30 Time History Analysis Result : Floor Accelerations Absolute Accelerations of 1st floor (unit: g) (a) Transverse Dir. (b) Longitudinal Dir. (c) Vertical Dir (d) Resultant 30

31 Time History Analysis Result : Floor Accelerations Absolute Accelerations of 2nd floor (unit: g) (a) Transverse Dir. (b) Longitudinal Dir. (c) Vertical Dir (d) Resultant 31

32 Time History Analysis Result : Floor Accelerations (a) X-Dir. Absolute Accelerations of 3 rd floor (unit: g) (b) Y-Dir. (c) Z-Dir (d) Resultant 32

33 Time History Analysis Result : Floor Displacement Absolute Displacement of 1st floor (unit: in) (a) Transverse Dir (b) Longitudinal Dir (c) Vertical Dir (d) Resultant 33

34 Time History Analysis : Floor Displacement Absolute Displacement of 2nd floor (unit: in) (a) Transverse Dir (b) Longitudinal Dir (c) Vertical Dir (d) Resultant 34

35 Time History Analysis : Floor Displacement Absolute Displacement of 3 rd floor (unit: ft) (a) Transverse Dir (b) Longitudinal Dir (c) Vertical Dir (d) Resultant 35

Earthquake Loads According to IBC IBC Safety Concept

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