Simulation of earthquake ground motion for generation of artificial accelerograms

Transcription

1 Earthquake Resistant Engineering Structures V 83 Simulation o earthquake ground motion or generation o artiicial accelerograms J. A. Abdalla & Y. M. ag-elhassan Department o Civil Engineering, American University o Sharjah Formerly, University o Khartoum, Sudan Abstract The determination o strong ground motion acceleration-time history is vital or the evaluation o the dynamic response o existing structures and also or the earthquake resistant design o new structures. The determination o such strong ground motion records is usually obtained by using accelerometers to record the strong motion parameters in the event o earthquakes. The lack and scarcity o accelerometers or recording strong ground motion acceleration-time history in some seismically vulnerable mega-cities necessitates the use o simulation or artiicial generation o these records. This paper simulates ground motion acceleration-time history using stochastic processes. The ground acceleration is modelled as a Gaussian stationary process and the non-stationary accelerationtime history is obtained by applying an envelope or shape unction to the stationary process. The power spectral density used or this process is a unction o the earthquakes magnitudes, epicentral distances, and sites soil condition. The generated acceleration-time history can be used to assess the vulnerability o existing buildings to earthquakes and also or the earthquake resistant design o new buildings. Keywords: artiicial accelerogram, simulation o ground motion, stochastic processes. Introduction Earthquakes are among the most destructive natural disasters. The lie and economic loss which may result rom a severe earthquake striking a densely populated area, is a direct consequence o damage and collapse o buildings. There are several densely populated mega-cities that are located in a sot deposit 005 WIT Press

2 84 Earthquake Resistant Engineering Structures V and are not ar rom seismically active aults. As scientiically proven, sot deposit tends to magniy earthquake accelerations several times even i the epicentral distance is several hundreds o km away as was the case with Mexico City 985 earthquake. Unless the buildings were designed to resist earthquake orces, such magniied ground acceleration may result in severe damage to buildings causing many atalities and casualties. The problem o earthquake resistant design o structural rameworks has been recognized by engineers or many years, but it is only recently 950 s that the most signiicant progress has been made. These advances resulted rom many actors including: increasing availability o strong ground motion records in some parts; the introduction o statistical approaches in analysis and design; 3 improved understanding o the dynamic behavior o heavily loaded structures; and 4 increasing availability o high-speed digital computers and powerul sotware or nonlinear dynamics analysis o structures. Unortunately the availability o strong motion records does not apply to many seismically active areas. An earthquake is usually deined by a collection o responses acceleration, velocity or displacement in time known as response history or time history. I the observations can be predicted, the process is called deterministic. I however, the observations can only be deined in terms o probability statements, the process is reerred to as non-deterministic or stochastic. The truly random nature o earthquake phenomena can be realistically represented only by statistical mathematical models. Analyses that have used actual recorded data o particular earthquakes are equivalent to a deterministic approach, and provide an unsatisactory basis or developing response statistics. Although the deterministic aspects o these analyses become less restrictive when eects o a large number o past earthquakes are studied, the opportunity to investigate response or a spectrum o reconstructed earthquakes is limited by the relatively small number o existing records o strong motion earthquakes and their total absence in some cases. These concerns give rise to the use o simulated earthquakes time histories to represent ground motion. As a recommended alternative, simulation o earthquake ground motion has the advantage that they can produce as many sample records as desired. The simulations can be devised to be consistent statistically with past earthquakes, or varied to emphasize particular adverse aspects in anticipation o uture earthquakes or relects the local site condition. This paper simulates earthquake excitation in Khartoum and artiicially generates ground acceleration time histories o earthquakes using spectral analysis. Although simulation o earthquakes time histories becoming less important due to increase in availability o earthquakes records and the wide spread o strong ground motion accelerograms, this is not the case in many part o the world where there is still moderate earthquake activity rate. Thereore, the necessity and importance o such research stem rom the lack o strong ground motion records or Khartoum as a megacity with moderate seismic activity rate. The rest o the paper is organized as ollows. In the ollowing sections, characterization o earthquake ground motion models will be presented, ollowed by power spectral density 005 WIT Press

3 Earthquake Resistant Engineering Structures V 85 unctions and then simulations o earthquake ground motion or Khartoum ollowed by results, discussion and conclusions. Earthquake motion characterization models The recorded accelerograms o earthquakes may be used to represent earthquakes at a site. As indicated, in this study, simulated earthquakes time histories are generated rom an appropriate power spectrum. Over the years acceleration time histories are simulated by several researchers, especially prior to the instrumentation era, using dierent models. Early models or artiicial generation o acceleration ground motions were proposed by ousner [], Kanai [] and Tajimi [3]. White noise stationary random models, based on Kanai- Tajimi models, were then suggested by Bycrot [4] and ousner and Jennings [5]. Non-stationary stochastic models were later introduced by Amin and Ang [6], Iyengar and Iyengar [7], Saragoni and art [8] and su and Bernard [9]. Furthermore, Wong and Triunac [0] proposed a narrow requency band model that can be used in conjunction with an empirical scaling unction or characterization o amplitudes and duration o strong motion acceleration. The model resulted in accelerograms that have non-stationary requency. In this model the requency bands were selected narrow enough such that the group velocity is approximately constant throughout the requency range. Under the assumption that strong motion earthquakes result primarily rom surace waves in a layered medium resting on a semi-ininite rock ormation, Shinozuka et al. [] proposed a method to derive the expression or the Rayligh wave that produces acceleration at the ground surace with a speciied power spectral density. In this method the ground acceleration is modeled as a Gaussian stationary processes and the power spectral densities used or these processes are unction o earthquake's magnitude, and epicentral distance. Pires and Tang [] proposed a model that uses either a Gaussian white noise or a iltered Gaussian white noise with a uniorm power spectral density unction over the entire requency range. They used the Fast Fourier Transorm FFT approach to simulate input support acceleration time history that corresponds to a periodic random process. wang and Jaw [3] had simulated the stationary acceleration time history by the ollowing expression: Roooei et al. [4] proposed a model based on the generalized non-stationary Kanai-Tajimi model in which both the non-stationary amplitude and requency are incorporated into the model. The model was able to accurately capture the non-stationary eatures o actual earthquake accelerograms. 3 Power spectral density unctions Most o the earthquake characterization models presented above have used the Kanai-Tajimi [, 3] Power Spectral Density PSD unction, or its variations, to generate the acceleration time history. The Kania-Tajimi power spectral density unction is in the ollowing orm: 005 WIT Press

4 o G c b c c b a G + + = 4 4 ω ω ω ω ousner and Jennings [5] had used Kania-Tajimi power spectral density unction ω G o equation where ω : is the natural requency o linear oscillator which ranges rom. rad/sec corresponding to natural period T = 3.0 sec. to rad/sec corresponding to natural period T = 0.3 sec.; a = 0.96/t; t = equivalent duration o strong motion earthquake = 30 sec.; b = 0.64; c = Other orms o power spectral density unctions had been suggested by several investigators such as Park et al. [5], Shinozuka et al. [], Lee et al. [6] and Elghadamsi et al. [7], Pires and Tang [], and wang and Jaw [3]. Each orm has dierent parameters and parameters range values. In this study the triple-ilter power spectral density unction suggested by Lee et al. [6] is used. To overcome the singularities o Kanai-Tajimi at small requencies, the Kanai-Tajimi PSD unction has been urther iltered in these low requency regions. One such ilter was proposed by Clough-Penzien and augmented by igh-pass. Lee et al. [6] had used Kanai-Tajimi [, 3], Clough- Penzien [8] and igh-pass ilters to get a new orm o Normalized Power Spectral Density NPSD unction as ollows: G o NPSD 3 = where Kanai-Tajimi ilter is given by: + + = 4 ξ ξ 3 Clough-Penzien ilter is given by: + = 4 ξ WIT Press 86 Earthquake Resistant Engineering Structures V

5 Earthquake Resistant Engineering Structures V 87 igh-pass P ilter is given by: = 3 + A 5 where: = cyclic requency o vibration; is Kanai-Tajimi ground cyclic requency o vibration; ξ is Kanai-Tajimi ground damping ratio; is Clough-Penzien cyclic requency o vibration; ξ is Clough-Penzien damping ratio; A is igh-pass constant; and G o is normalized white noise ground intensity. The values o the above parameters depends on the type o soil whether sot, intermediate or hard. Site located on alluvium or other low velocity deposit will be classiied as "sot", site located in sot type rock are classiied as "intermediate" and site located on solid basement rock will be classiied as "hard". Lee et al. [6] had developed requencies, damping ratios and other parameters or dierent types o soils. These values are used in this study. 4 Simulation o earthquakes ground motion or Khartoum The acceleration-time history consists o two modes, stationary and nonstationary. The non-stationary acceleration-time history mode is more comprehensive and the acceleration has variable spectral density. In this study the stationary acceleration model proposed by wang and Jaw [3] is used to generate the non-stationary acceleration time history. A normalized triple iltered power spectral density unction proposed by Lee et al. [6] is used with wang and Jaw [3] stationary model. A normalized non-stationary acceleration time history is then generated by normalizing the stationary acceleration time history and then multiplying it by the peak ground acceleration at expected locations where histograms are going to be generated. wang and Jaw [3] simulation or the stationary acceleration time history is as ollows: N as t = k = S ω ω cos ω t + φ k where the parameters has been adjusted to relect local site conditions. S ω k is the power spectral density unction, herein we used the triple-ilter Normalized Power Spectral Density NPSD as given in equation ; N is number o requency interval = 5; = ω π is the natural cyclic requency; ω = ω u N is circular requency, which is uniormly distributed between. and rad/sec as suggested by ousner and Jennings [5], ω =., k n WIT Press

6 88 Earthquake Resistant Engineering Structures V requency increment; ω u is the cut o requency; ω k = k ω, k =,.375,.750,.5,..., 0; th φ n = n = random phase angle, uniormly distributed between 0 and π. The normalized non-stationary time history a m t, is obtained by applying an enveloped unction t by a stationary time history t, and then normalized by the absolute maximum o the acceleration time history a t as given in equation 7 max a s max as t t am t = 7 a where: a max t is the absolute maximum o a s t ; t is an envelope unction. Several envelope unctions had been suggested by Preumon [9], Orabi et al. [0] and Austin et al. [], among others. In this study a unction suggested by Orabi et al. [0] which o the ollowing orm is used. where: ct eote t 0 t = 8 0 t 0 or non - stationary analysis e = 0.54sec o and c = 0.sec Finally, the non-stationary acceleration time history a g t is obtained rom the product o a speciied peak ground acceleration a p t and the normalized non-stationary acceleration time history a m t as shown beore in equation 9 ag t = a p t* am t 9 A computer program is written to generate acceleration-time history or several earthquakes in Sudan as shown in Figure and Figure. 5 Results and discussion Table shows the predicted peak ground acceleration at Khartoum area due to several earthquake events with dierent magnitudes and epicentral distances. Figure and Figure acceleration-time histories or two earthquakes as artiicially generated in Khartoum area. Although the artiicially generated acceleration-time history is sensible, however, there is a great deal o statistical 005 WIT Press

7 Earthquake Resistant Engineering Structures V 89 uncertainty in the results due to the limited sample and lack o recorded acceleration-time histories to veriy the results. Table : Peak ground acceleration at Khartoum due to several earthquakes. Earthquake Location Earthquake date Epicentral Distance to Khartoum Local Magnitude Scale Peak Ground Acceleration amrat 0/08/ Elshiekh Juba 0/05/ Jabal 09/0/ Dumbier Suakin /05/ ala El xx/0/ Jadida Wadi ala Acceleration g Time second Figure : Acceleration-time history at Khartoum or amrat Elsheikh 993 earthquake. 6 Conclusions From this study it can be concluded that: Artiicial strong motion ground acceleration-time histories can be generated rom a product o normalized stationary excitation whose power spectral densities are unction o time, an envelope unction and peak ground acceleration. 005 WIT Press

8 90 Earthquake Resistant Engineering Structures V 6 x Acceleration g Time second Figure : Acceleration-time history at Khartoum or Juba 990 earthquake. Although this artiicially generated accelerograms are simply simulations o acceleration-time histories based on the known parameters, nevertheless, they are acceptable to be adopted as the ground acceleration time history. This is mainly due to the lack o recorded acceleration time history or earthquakes in Sudan. Accelerograms are constructed or amrat Elshiekh 993 earthquake and or Juba 990 earthquakes. The constructed accelerograms are or the eect o the above earthquakes in Khartoum. Although the general characteristics o the earthquakes are similar, their peak ground accelerations are dierent. Dynamic Response Spectra can be constructed rom the abovegenerated accelerograms. These response spectra, with some adjustment, can serve as design spectra or seismic assessment o existing buildings and or seismic design o new buildings in Khartoum. Although this study had laid the oundation or simulation o earthquakes eects in buildings in Khartoum, there are many areas and topics that need urther study and more data need to be collected or more elaborate investigation. Also, the best way or generation o accelerograms is through recording using strong motion recorders which are widely available. Reerences [] ousner, G.. Properties o strong ground motion earthquakes, Bulletin o the Seismological Society o America, 45:97-8, WIT Press

9 Earthquake Resistant Engineering Structures V 9 [] Kanai, K. Semi-empirical ormula or the seismic characteristics o the ground motion, Bulletin o Earthquake Research Institute University o Tokyo 35:309-35, 957. [3] Tajimi,. A. A statistical method o determining the maximum response o a building structure during an earthquake, Proceedings o the Second World Conerence in Earthquake Engineering WCEE, Science Council o Japan, , 960. [4] Bycrot G. N. White noise representation o earthquake, ASCE Journal o Engineering Mechanics, 86:-6, 960. [5] ousner, G.. and Jennings, P. C. Generation o artiicial earthquakes, ASCE Journal o Engineering Mechanics, 90 : 3-50, 964. [6] Amin, M. and Ang, A.. S. Nonstationary stochastic model o earthquake motions. ASCE Journal o Engineering Mechanics, 94: , 968. [7] Iyengar, R. N. and Iyengar K. Non-stationary random process models or earthquake accelerograms, Bulletin o the Seismological Society o America, 59:63-88, 969. [8] Saragoni, G. R. and art, G. C. Simulation o artiicial earthquake, Journal o Earthquake Engineering and Structural Dynamics, :49-67, 974. [9] su, T. I. and Bernand, M. C. A random process or earthquake simulation. Journal o Earthquake Engineering and Structural Dynamics, 64: , 978. [0] Wong,. L. and Triunac, M. D. Generation o strong motion accelerograms, Journal o Earthquake Engineering and Structural Dynamics, 7: , 979. [] Shinozuka, M., Kameda,. and Koike, T. Ground strain estimate or seismic risk analysis, ASCE Journal o Engineering Mechanics, 09: 75-90, 983. [] Pires, J. A., Tang, M. Statistic o hysteretic energy dissipated under random dynamic load ASCE Journal o Structural Engineering Division, 68: 706-7, 990. [3] wang,.. M. and Jaw, J. W. Probabilistic damage analysis o structures. ASCE Journal o Structural Engineering, 67: , 990. [4] Roooei, F. R., Mobarake, A. and Ahmadi, G. Generation o artiicial earthquake records with a nonstationary Kanai-Tajimi model, Engineering Structures 3: , 00. [5] Park, Y. J., Wen, Y. K. and Sang, A.. Random vibration o hystertic systems under bi-directional ground motion Journal o Earthquake Engineering and Structural Dynamics, 4: , 986. [6] Lee, C-T, Elghadamsi, F. E. and Mohraz, B. Smooth power spectral density o accelerograms and its application to multi-degree-o-reedom system. NSF Report, School o Engineering and Applied Science, SMU, Dallas, Texas, WIT Press

10 9 Earthquake Resistant Engineering Structures V [7] Elghadamsi, F. E., Mohraz, B. Lee, C. T. and Moayyad, P. Timedependent power spectral density o earthquake ground motion, Journal o Soil Dynamics and Earthquake Engineering, 7: 5-, 988. [8] Clough, R. W and Penzien, J. Dynamic o Structures. McGraw-ill, 993. [9] Perumont, A. The generation o spectrum compatible accelerograms or the design o nuclear power plants, Journal o Earthquake Engineering and Structural Dynamics, : , 984. [0] Orabi, I. I., Goodarz, A. and Lin, S. ysteretic column under earthquake excitations, ASCE Journal o Engineering Mechanics, 5: 33-5, 989. [] Austin, M. A., Pister, K. S. and Mahin, S. A. A methodology or computer-aided design o earthquake resistant steel structures, Earthquake Engineering Research Center, University o Caliornia at Berkeley, EERC Report No. 853, WIT Press