Comparison of Natural and Artificial Time Histories for Non-Linear Seismic Analyses of Structures

Transcription

1 OECD-NEA Workshop «Seismic Input Motions, Incorporating Recent Geological Studies» Tsukuba, Japan November Engineering consideration Comparison of Natural and Artificial Time Histories for Non-Linear Seismic Analyses of Structures E. Viallet - G. Heinfling - S. Goubet - C. Duval EDF / SEPTEN - FRANCE

2 Content Context and objectives Part 1 - Comparison of natural and artificial time histories Description of main tools and input data Natural and artificial accelerogram selection Results and analyses Part 2 - Considerations on the number of accelerograms to be used for NL calculations and a way to account for variability First case : Impact non-linearity A way to account for variability Application on 2 types of non-linearities Results and analyses Conclusion

3 Content Context and objectives Part 1 - Comparison of natural and artificial time histories Description of main tools and input data Natural and artificial accelerogram selection Results and analyses Part 2 - Considerations on the number of accelerograms to be used for NL calculations and a way to account for variability First case : Impact non-linearity A way to account for variability Application on 2 types of non-linearities Results and analyses Conclusion

4 Context and objectives Context French Basic Safety Rule RFS V.2.g (seismic design of structures) currently under revision Transient dynamic computations may be used to evaluate specific non-linear parameters Seismic input load must be carefully assessed Natural or artificial accelerograms Number of different calculation to get proper trends How to deal with variability Objectives of the paper Give some elements on : Potential effectiveness of artificial accelerogram to reproduce damage led by natural ones Number of accelerograms to be used and how to account for variability of results for engineering purpose

5 Content Context and objectives Part 1 - Comparison of natural and artificial time histories Description of main tools and input data Natural and artificial accelerogram selection Results and analyses Part 2 - Considerations on the number of accelerograms to be used for NL calculations and a way to account for variability First case : Impact non-linearity A way to account for variability Application on 2 types of non-linearities Results and analyses Conclusion

6 Part 1 Main tools Main tools Strong Motion Data Base and attenuation relationships (M,D) European Strong Motion Data Base Attenuation law : Ground Response Spectrum (M,D) Attenuation laws : Ground Motion Parameters (M,D) Natural accelerogram selection Artificial accelerogram generation Simplified (NL) RC structures Simplified NL reinforced concrete structure Dynamic response : Non linear displacement

7 SMDB regression laws European SMDB (Imperial college of London & al : 965 natural records) & Attenuation relationships For Ground Response Spectrum (RFS ) log10 GRS = am + br - log 10 R + c SOIL (+/- σ) For Ground Motion Parameters (CEA-EDF previous study) log10 GMP = αm + γ log 10 R + δ (+/- σ) A (maximal acceleration or peak ground acceleration), V (maximal velocity or peak ground velocity), D (maximal displacement or peak ground displacement), A/V ratio, CAV (Cumulative Absolute Velocity), Ia (Arias Intensity), T (duration 5% to 95% Ia), GMP α γ δ σ A (m/s²) V (m/s) D (cm) A/V (s-1) CAV (m/s) Ia (m/s) T (s)

8 SMDB regression laws Application of attenuation relationship High magnitude Far field earthquake / Low magnitude near field earthquake M = 7.3 M = 5.5 km Dist = 50 km Ground response spectrum D = 9 km 1.00E+00 T = s D = 3-25 cm A/V = 6-15 s-1 CAV = 4-10 m/s T = 3-9 s D = 1-6 cm A/V = s-1 CAV = 1-5 m/s Pseudo-acceleration (g) 1.00E-01 M=5.5-9 km M = km 1.00E E E E E+02 Frequency (Hz)

9 Simplified RC structure Base model = Single degree of freedom oscillator Non-linearity = Bilinear Takeda s constitutive law Accounting for stiffness degradation Frequency fixed to 5 Hz for this study 2 design levels : 0.05 g and 0.1 g Post-elastic behavior determined to reproduce typical behavior of Wall type RCS / Frame type RCS Ground response spectrum 1.00E+00 Pseudo-acceleration (g) 1.00E-01 SSE - Rock site - M=5.5-9km Design level : 0.1g Design level : 0.05g 1.00E E E E E+02 Frequency (Hz) Computed parameter : Ductility = max NL displ t / Elastic threshold displ t

10 Accelerogram selection Selected case : M = D = 9 km Natural accelerogram selection Criteria 5 < Magnitude < 6 0 < Distance < 20 km Average GRS ~ Regression GRS 26 natural accelerograms selected Artificial accelerograms generation Criteria Average GRS ~ Regression GRS Average Std deviation < GMP < Average + std deviation 30 artificial accelerograms selected Acceleration (cm.s -2 ) Acceleration (g) Umbro-Marchigiano xa.cof Time (s) Time (s)

11 Results and analysis Comparison of accelerogram characteristics Response spectra Comparaison natural / artificial accelerograms Pseudo-acceleration (g) Frequency (Hz) 1 V (m/s) - Natural accelerograms Regression law : Average +/- Std dev. Regression Law Artificial accel. - Average Natural accel. - Average Ground Motion Parameters (regression laws) Natural accelerograms (average) Artificial accelerograms (average) Average value Average val. - Std deviation Average val. + Std deviation T (s) V (m/s) D (cm) A/V (s-1) CAV (m/s) Ia (m/s) V (m/s) - Artificial accelerograms Regression law : Average +/- Std dev

12 Results and analysis Damage calculation on RC structures Ducility (drift) : ratio between maximum NL displacement over elastic threshold displacement Max NL displacement / Elastic threshold displacement Ductility - Wall type RCS Design level = 0.05 g Frame type structure Design level = 0.05 g Frame type structure Design level = 0.1 g Wall type structure Design level = 0.05 g Wall type structure Design level = 0.1 g Ductility - Wall type RCS Design level = 0.05 g Ductility (average result) Natural accelerograms Artificial accelerograms Ductility Natural accelerograms Ductility Artificial accelerograms 5 4 Ductility - Frame type RCS Design level = 0.1 g 5 4 Ductility - Frame type RCS Design level = 0.1 g Ductility 3 2 Ductility Natural accelerograms Artificial accelerograms

13 Results and analysis Main results to be pointed out Ground Motion Parameters Very good agreement between natural and artificial accelerograms in terms of average values Scattering higher for natural accelerograms than for artificial ones For natural ones : High number of accelerograms was needed (to get proper trends) Relatively high variability around M and D was left For artificial ones Variability is not negligible although GMP are input data for generation (especially GRS and Duration in that case) Non linear behavior of RC structures Very good agreement between natural and artificial accelerograms Average value especially The use of GRS and other GMP seems to be a key factor Variability is significant for natural and artificial accelerograms A method to account for scattering is proposed in the next step

14 Content Context and objectives Part 1 - Comparison of natural and artificial time histories Description of main tools and input data Natural and artificial accelerogram selection Results and analyses Part 2 - Considerations on the number of accelerograms to be used for NL calculations and a way to account for variability First case : Impact non-linearity A way to account for variability Application on 2 types of non-linearities Results and analyses Conclusion

15 Part 2 Number of accelerograms and scattering First case : Impact nonlinearity High number of accelerograms : 500 (population = 500) + Selection of sets of 50 accelerograms (among the population) + Evolution of average value depending on + Sets of accelerograms + Number of accelerogram within each set High variability especially for low number of accelerograms (depending BASIC DESIGN DEPARTMENT on (SEPTEN) sets) Average impact force Impact non-linearity - Average value Dependence on accelerograms Average (population) Number of accelerograms used to calculate average value Set n 1 Set n 2 Set n 3 Set n 4 Set n 5 Set n 6 Set n 7

16 Part 2 Number of accelerograms and variability A way to account for variability : Student-Fisher estimator Objective Conservative estimation of a parameter D base on results obtained from non-linear calculations with a set (sample) of N accelerograms Results can be expressed in terms of average value D av and standard deviation S D Use of Student-Fisher estimator Student-Fisher estimator allows to estimate the average value of the population with a given confidence level, based on results obtained on a sample of reduced size 0.05; N 1 D 95% = DAV +. t N With t 0.05;N-1 is the student parameter taken for N-1 degree of freedom and for 95% confidence level S D

17 Part 2 Number of accelerograms and scattering Application (1/2) Previous case : impact non-linearity Impact force Average value (sample) Estimation of the average value of the population Dependence on accelerograms Student-Fisher Estimator Use of Student-Fischer estimator Evolution with accelerograms (95% confidence level) Average (population) Number of accelerograms Set n 1 Set n 2 Set n 3 Set n 4 Set n 5 Set n 6 Set n 7 Impact force Average (population) Number of accelerograms Set n 1 Set n 2 Set n 3 Set n 4 Set n 5 Set n 6 Set n 7 Conservative estimation, based on N (number of accelerograms) and σ (standard deviation of the results)

18 Part 2 Number of accelerograms and scattering Application (2/2) Application on simplified RC structure (part one) : Plastic non-linearity 10.0 Frame type RCS (5 Hz) - Design level = 0.05g Ductility - Student estimator 5.0 Frame type RCS (5 Hz) - Design level = 0.1 g Ductility - Student estimator 8.0 Accel. 1 to 13 - Student 4.0 Accel. 1 to 13 - Student Ductility Accel. 14 to 26 - Student Average 26 accel. Ductility Accel. 14 to 26 - Student Average 26 accel Natural accelerograms Natural accelerograms 10.0 Wall type RCS (5 Hz) - Design level = 0.05 g Ductility - Student estimator 5.0 Wall type RCS (5 Hz) - Design level = 0.1 g Ductility - Student estimator 8.0 Accel. 16 toà 30 - Student 4.0 Accéel. 1 to 15 - Student Ductility Accel. 1 to 15 - Student Average 30 accel. Ductility Accel. 16 to 30 - Student Average 30 accel Artificial accelerograms Artificial accelerograms

19 Results and analysis Main results to be pointed out In most cases The use of Student-Fisher estimator (95% confidence level) lead to conservative prediction of the average value of the population Even with a low number of accelerograms Confirmed with two types on non-linearities The higher the number of accelerogram is, the more accurate the prediction is A relative freedom is left for engineering purpose

20 Content Context and objectives Part 1 - Comparison of natural and artificial time histories Description of main tools and input data Natural and artificial accelerogram selection Results and analyses Part 2 - Considerations on the number of accelerograms to be used for NL calculations and a way to account for variability First case : Impact non-linearity A way to account for variability Application on 2 types of non-linearities Results and analyses Conclusion

21 Conclusion and perspectives Main conclusions Ground motion should be characterized with more than one parameter! GRS, PGV, PGD, Duration, CAV, Ia Natural and artificial time histories may lead to equivalent damage If they are generated or selected based on (or compared to) ground response spectrum and other ground response parameters In that context, attenuation relationships are proposed to determine GMP based on earthquake characteristics (Magnitude and focal distance) from a European SMDB A method to account for variability of results is also proposed Based on Student-Fisher estimator Conservative evaluation of a design parameter (95% confidence level) A relative freedom is left (concerning number of accelerograms) for engineering purpose Perspectives Extension of the study is planed : With other earthquake characteristics (low magnitude near field earthquakes, high magnitude far field earthquakes) With other types of non-linearities (uplift )