Frequency content indicators of strong ground motions

Transcription

1 Frequency content indicators of strong ground motions F. Pavel & D. Lungu Technical University of Civil Engineering Bucharest, Romania SUMMARY: The frequency content of ground motions seems to be the most important parameter to explain the structural damage experienced during strong earthquakes. The frequency content of ground motions can be characterized using various stochastic and/or deterministic indicators. A comparative analysis of stochastic and deterministic frequency content indicators is applied to a set of famous strong ground motion records having peak ground accelerations from.g to.9g and recorded during the last 7 years. Since T C is an important parameter for structural seismic design in use in many present day codes (Eurocode and others), one main focus of the analyses is the comparison of the various definitions of the control period T C of: Bommer et al. (), Lungu et al. (997), Newmark & Hall (99, 9), ATC - (97) as well as the definitions implicitly contained in ASCE/SEI 7- (). Keywords: earthquake records, stochastic modeling, response spectra, structural design. INTRODUCTION The ground motions recorded worldwide in the last 7 years show various frequency contents, from wide and intermediate frequency bandwidth ground motions (recorded in hard and/or medium soil conditions) to narrow frequency band ground motions (recorded in soft soil conditions). The random frequency contents of ground motions generally depends on both source mechanism and magnitude as well as on epicentral distance and local soil conditions. The frequency contents of the strong ground motions is a key parameter for explaining and understanding structural damage experienced during strong seismic events. Probabilistic-based assessment of the frequency contents of the ground motion records can be done using the Power Spectral Density concept (PSD) and its related dimensionless indicators ε (Cartwright&Longuet-Higgins) and q (Vanmarcke), or the fractile frequencies f, f 5 and f 9 (Kennedy Shinozuka indicators) below which %, 5% and 9% of the total cumulative power of the PSD occurs. The deterministic assessment of the frequency contents of the ground motions records can be based on the concept of the control period of structural response spectra, historically introduced by Newmark & Hall (99, 9), as well as on the evolution of the concept during the last fifty years.. CHARACTERIZATION OF THE GROUND MOTION FREQUENCY CONTENT.. Stochastic indicators for the frequency content of seismic records The definition of the most reliable frequency content indicators of the ground motion records are based on modelling the strong phase of the recorded accelerogram as a stationary stochastic process.

2 The duration D of the stationary part of the motion may be selected as the time interval in which a significant fraction (say 7%, % or 9%) of the total cumulative power of the accelerogram a(t) is released i.e. D.9 = t.5 t.95, D. = t. t.9, etc. Cum. Power = a( t) dt (.) [ ] Consequently, the power spectral density (PSD) of accelerograms considered in the present study was determined for the stationary part of the record modelled to be within the time interval t. t.9. The dimensionless indicators ε and q are defined as a function of the spectral moments of the PSD for the stationary process of the ground acceleration: ε = λ λλ (.) λ q = λλ (.) where λ i is the i-th moment of the PSD. i + i x ( ) λ = ω S ω dω (.) The guidance values for ε indicator in the case of actual ground motion accelerograms might be: /< ε<.5 for a wide frequency band process;.5< ε<.9 for an intermediary band process; ε>.9 for narrow frequency band processes associated wide frequency band noise.. Deterministic indicators for the frequency content of seismic records The deterministic analysis of the frequency content of ground motions is related to the maximum response of a SDOF (single degree of freedom) system to the recorded ground motion. Two control periods of response spectra are T C and T D. T C represents the border between the maximum acceleration branch and the maximum velocity branch of the response spectra and T D is the border between the maximum velocity branch and the maximum displacement branch of the response spectra. In Table. are presented various definitions for control periods T C and T D of the response spectra given in ATC - (97), Newmark & Hall (99, 9), Lungu et al. (997), Bommer et al. () and resulting from the data in ASCE 7- (). There are two categories of definitions for T C the definitions based on the spectral values: acceleration, velocity and displacement given in: ATC - (97), Lungu et al. (997) and ASCE 7- () and the definitions based on the peak values of the seismic ground motion: Newmark & Hall (99, 9) and Bommer et al. (). The definitions based on the spectral values use the effective peak acceleration, velocity and displacement: ATC - (97),

3 Lungu et al. (997), which represent averaged values, while the American Code ASCE 7- uses the spectral acceleration values at two periods corresponding to the short period range (. s) and to the medium period range (. s). The relationships for the control period T C from Newmark & Hall (99, 9) and Bommer et al. () provide similar values. In the case of the control period T D, the definition given in Bommer et al. (). provides values times larger than the Newmark & Hall (99, 9) definition. Table.. Definitions of control periods T C and T D of the structural response spectra ATC - (97) Lungu et al. (997) Newmark & Hall (99, 9) Bommer et al. () αv PGV TC = π = EPV EPV α TC = π TC = π APGA PGV TC = 5 EPA EPA.5 PGV PGV PGA = π =.9. PGA PGA ASCE 7- () S TC = S D DS - T D EPD = π EPV T D αv PGD = π = α PGV A.9 PGV PGD = π = PGA PGV T D PGD = PGV - ) SA EPA =.5 SV EPV =.5..5s..s EPA = ) max SA..5 max SV EPV =..5 max SD EPD =..5 EPA effective peak acceleration EPV effective peak velocity EPD effective peak displacement PGA peak ground acceleration PGV peak ground velocity PGD peak ground displacement S DS design spectral response acceleration parameter at short periods (. s) given by code; S D design spectral response acceleration parameter at. s given by code; ) Definitions based on a fixed period window for computing EPA (..5 s) and EPV (.. s); ) Definitions based on a mobile period window (of. s width) for getting maximum effective values.. STRONG MOTION DATASET ANALYSIS In this study a dataset of seismic records are used from earthquakes in: Chile, Greece, Iran, Italy, Japan, Mexico, Montenegro, New Zealand, Romania, Taiwan, Turkey and USA. The peak ground acceleration (PGA) of the earthquake records varies between.g (Mexico-City SCT 95 EW) and.9g (Naghan 977 Long). The strong ground motion records are bordered by the narrowest frequency band record - Mexico-City SCT 95 (ε=.99) and by the broadest frequency band record Naghan 977 (ε=.7).

4 T C Lungu et al. (997).5 s Mexico City 95.5 Concepcion Bucharest INCERC 977 Christchurch REHS Athens Sepolia 999 PGA, cm/s Frequency content indicator, ε Mexico City 95 Athens Sepolia 999 L'Aquila 9 Tabas 97 PGA, cm/s Figure.. Control period, T C versus PGA Figure.. Dimensionless indicator, ε versus PGA The distribution of the control period of response spectra T C, stochastic dimensionless indicator ε, earthquake magnitude M W and earthquake depth, h with PGA of the analysed records is respectively given in Fig.., Fig.., Fig.. and Fig... Magnitude, M W Tohoku Maule Michoacan 95 Valparaiso 95 Depth, km Subcrustal Vrancea 977 (9 km) Subcrustal Vrancea 9 ( km) Erzincan 99 Valapraiso 95 Naghan Ano Liosia 999 Naghan 977 PGA, cm/s 5 Friuli 97 PGA, cm/s Figure.. Event moment magnitude, M W versus PGA Figure.. Earthquake depth, h versus PGA The distribution of the number of analysed records with PGA, M W, h, recording station epicentral distance and earthquake occurrence year are respectively given in Fig..5, Fig.., Fig..7, Fig.. and Fig..9. mean = 5 cm/s COV=. 9 Number of events Number of events PGA, cm/s Magnitude, M W Figure.5. Frequency of recorded PGA Figure.. Frequency of event moment magnitude, M W

5 Number of events 7 5 mean = km COV =.9 Number of events mean = km COV = > Depth, km > Epicental distance, km Figure.7. Frequency of earthquake depth, h Figure.. Frequency of recording station epicentral distance Number of events 7 5 < > Year Figure.9. Frequency of earthquake occurrence year The values of the stochastic and of the deterministic frequency content indicators for the strong ground motions selected in the dataset and computed using the definitions from Cap. are shown in Table.. Table.. Stochastic and deterministic indicators for analysis of the frequency content of selected ground motions Stochastic indicators Deterministic indicators T C, s Reference: Earthquake record Frequency content indicator, ε f, Hz f 9, Hz ATC - (97) Newmark &Hall (9) Lungu et al. (997) Boomer et al. () ASCE 7- () Naghan, Naghan Long. L Aquila, Centro Valle EW Ano Liosia, Athens Sepolia Transv. Tabas, Tabas N7E Valparaiso, Llolleo NE

6 Table.. (continued) Vrancea, Petresti Focsani EW Duzce, Lamont 75 NS Imperial Valley, El Centro NS Tohoku, Takahagi EW Aegion, Aegion Transv. Montenegro, Petrovac Hotel Oliva NS Friuli, Gemona EW Maule, Concepcion Long. Chi-Chi, CHY NS Kobe, Kobe Takatori NS Erzincan, Erzincan N9E Northridge, Sylmar Converter NE Lytlletton, Christchurch REHS N9E Vrancea, Bucharest INCERC NS Michoacan, Mexico-City SCT EW Absolute acceleration and dynamic amplification factor (DAF) response spectra for the two extreme narrow frequency bandwidth ground motions Mexico-City, SCT, 95, EW comp and Bucharest, INCERC, 977, NS comp are plotted in Fig.. and Fig.. The relative velocity response spectra are represented in Fig. and Fig.. SA, cm/s 95 Michoacan, Mexico 5 β SA, cm/s Vrancea, Romania.5.5 β Tᴄ, Newmark&Hall (9) Tᴄ, Lungu et al. (997) Tᴄ, Newmark&Hall (9) Tᴄ, Lungu et al. (997) Tᴄ, Bommer et al. () Tc, ASCE 7 () Tᴄ, Bommer et al. () Tc, ASCE 7 () Figure.. Acceleration response spectra and T C definitions for Mexico-City, SCT, 95, EW comp Figure.. Acceleration response spectra and T C definitions for Bucharest, INCERC, 977, NS comp

7 5 95 Michoacan, Mexico 977 Vrancea, Romania 5 SV, cm/s 5 5 SV, cm/s Tᴄ, Newmark&Hall (9) Tᴄ, Lungu et al. (997) Tᴄ, Bommer et al. () Tc, ASCE 7 () Tᴄ, Newmark&Hall (9) Tᴄ, Lungu et al. (997) Tᴄ, Bommer et al. () Tc, ASCE 7 () Figure.. Velocity response spectrum and T C definitions for Mexico-City, SCT, 95, EW comp Figure.. Velocity response spectrum and T C definitions for Bucharest, INCERC, 977, NS comp In Fig.. and Fig..7 are shown the absolute acceleration and dynamic amplification factor (DAF) response spectra for two interesting wide frequency bandwidth ground motions Naghan, 977, Long comp. and L Aquila, Centro Valle, 9, EW comp. The relative velocity response spectra are represented in Fig.. and Fig..9. SA, cm/s 977 Naghan, Iran Tᴄ, Newmark&Hall (9) Tᴄ, Lungu et al. (997) Tᴄ, Bommer et al. () Tc, ASCE 7 () β SV, cm/s 9 L'Aquila, Italy Tᴄ, Newmark&Hall (9) Tᴄ, Lungu et al. (997) Tᴄ, Bommer et al. () Tc, ASCE 7 () Figure.. Acceleration response spectra and T C definitions for Naghan, 977, Long. comp Figure.5. Acceleration response spectra and T C definitions for L Aquila Centro Valle 9 EW comp 977 Naghan, Iran 9 L'Aquila, Italy SV, cm/s SV, cm/s Tᴄ, Newmark&Hall (9) Tᴄ, Lungu et al. (997) Tᴄ, Bommer et al. () Tc, ASCE 7 () Tᴄ, Newmark&Hall (9) Tᴄ, Lungu et al. (997) Tᴄ, Bommer et al. () Tc, ASCE 7 () Figure.. Velocity response spectrum and T C definitions for Naghan, 977, Long. comp Figure.7. Velocity response spectrum and T C definitions for L Aquila Centro Valle 9 EW comp

8 Table. and Fig...7 demonstrate the unexpected sensibility of the computed T C values according to different authors definitions, in spite of the fact that the T C values are extremely important input parameters controlling structural design. A surprisingly large variability of the values obtained for the control period T C has been observed, especially for the narrow frequency bandwidth ground motions characterized by ε.9 and according to various definitions and authors. The normalized power spectral density (PSD) functions of the narrowest frequency bandwidth ground motion and of the broadest frequency bandwidth ground motion from the dataset analyzed are displayed in Fig.. and Fig..9. One should note that earthquake engineering education might consider in parallel for structural analysis and design such opposite extremes of seismic input as well as its consequences on structural design. s(ω) Michoacan Mexico Mexico City SCT st. EW comp. ε=.99 f 5 =. Hz f 9 =.5 Hz T C =. s s(ω) Naghan, Iran Naghan st. Long.comp. ε=.7 f 5 =. Hz f 9 = Hz T C =. s..5. Frequency, Hz. Frequency, Hz Figure.. Normalized PSD for Mexico-City, SCT, 95, EW comp Figure.9. Normalized PSD for Naghan, 977, Long comp The influence of the strong motion duration on stochastic frequency content indicators is shown in Fig.. and Fig... The two figures suggest that the influence is negligible. Frequency content indicator ε f 9, Hz Frequency content indicator ε.d ε.7d ε.9d f 9.D, Hz f₉₀.7d f₉₀.9d Figure.. Influence of strong ground motion duration on ε dimensionless indicator Figure.. Influence of strong ground motion duration on f 9 fractile frequency

9 . CORRELATIONS OF FREQUENCY CONTENT INDICATORS Several correlations between the control periods T C determined according to the definitions given by various authors are plotted in Fig.., Fig.., Fig.. and Fig....5 s r=.9.5 s r=.5 T C ASCE 7 ().5 T C Lungu et al. (997).5.5.5s T C ATC (97).5.5s T C Newmark & Hall (99, 9) Figure.. T C ASCE 7- versus T C ATC - Figure.. T C Lungu et al. versus T C Newmark & Hall.5s r=.5.5s r=. T C Lungu et al. (997).5 T C Lungu et al. (997).5.5.5s T C Bommer et al. ().5.5s T C ASCE 7 () Figure.. T C Lungu et al. versus T C Bommer et al. Figure.. T C Lungu et al. versus T C ASCE 7- The degree of reliability of the results in Fig... is controlled and explained by the value of the correlation coefficient r. Fig... may also suggest the definitions to be used in practical design. Frequency content indicator ε r=.7.5.5s T C Lungu et al. (997) Figure.5. ε dimensionless indicator versus T C Lungu et al.

10 Fig..5 shows the fact that the increase in the value of the deterministic frequency content indicator T C is accompanied by an increase of the value of the stochastic frequency content indicator ε. 5. CONCLUSIONS The values for the control period T C given by Newmark & Hall (9) or Bommer et al. () and the values given by Lungu et al. (997) are clearly well correlated; The mobile window procedure - Lungu et al. (997) is considered the most adequate instrument for computing the values of the control period T C of the response spectra; The values for the control period T C based on two clearly different procedures for computing effective peak values (EPA, EPV, etc.) in Lungu et al. (997) and ATC - (97) are not well correlated; The values for the control period T C given in ATC - (97) and ASCE 7- () produce similar results; The control period T C of the response spectra and the frequency content indicator ε seem to be well correlated; The influence of the strong motion duration on the values of the probabilistic frequency indicators is negligible. REFERENCES ASCE/SEI 7- (). Minimum design loads for buildings and other structures. ASCE, American Society of Civil Engineers. ATC -, Special Publication 5/NSF (97). The tentative provisions for the development of seismic regulations for buildings. Prepared by ATC (Applied Technology Council) associated with the Structural Engineers Association of California. Bommer, J. et al. (). Compatible acceleration and displacement spectra for seismic design codes. Proceedings of the th World Conference on Earthquake Engineering, Auckland. New Zealand. Paper no. 7. Eurocode (). Design of structures for earthquake resistance, Part : General rules, seismic actions and rules for buildings. CEN, European Committee for Standardization. Lungu, D., Cornea, T. (97). Power and response spectra in Bucharest for Vrancea earthquakes. Institutul de Constructii Bucuresti, (in Romanian). Lungu, D. et al. (99). Frequency bandwidth of Vrancea earthquakes and the 99 edition of seismic code in Romania. Proceedings of the th World Conference on Earthquake Engineering, Madrid, Spain. vol. X: 5-5. Lungu, D. et al. (99). Structural response spectra to different frequency bandwidth earthquakes. th International Conference on Structural Safety and Reliability. vol. II: -7. Lungu, D. et al. (997). Basic representation of seismic action. In Design of structures in seismic zones: Eurocode worked examples. TEMPUS PHARE CM Project 9: Implementiong of structural Eurocodes in Romanian civil engineering standards Edited by D. Lungu, F. Mazzolani and S. Savidis, S. Bridgeman Ltd. Lungu, D. et al. (). Advanced structural analysis. Conspress, TUCEB. Naeim, F., Anderson, J. (99). Classification and evaluation of earthquake records for design. EERI Report, Earthquake Engineering Research Institute. Newmark, N., Hall, W.J. (99). Seismic design criteria for nuclear reactor facilities. th World Conference on Earthquake Engineering, Santiago de Chile, Chile. vol. II: B5.-. Newmark, N., Hall, W.J. (9). Earthquake spectra and design. EERI Monograph, Earthquake Engineering Research Institute.