İstanbul ve çevresi için sismik risk analizi ve hedef spektrumuna uygun yapay deprem ivme kaydı üretilmesi

Abstract

Deprem tehlikesi altında bulunan ülkemizde önemli yapıların inşa edilmeye başlanması ile bunların inşa edilecekleri yerlerde deprem tehlikesinin niceliksel büyüklüklerinin öngörülen ekonomik ömre göre olasılık yön temleri ile rasyonel olarak belirlenmesi ve yapının dinamik deprem hesabı için gerekli spektrumlar veya deprem ivme kaydının üretilmesi bu çalışmanın esas amacıdır. Bunun için yerleşik nüfusu, ekonomik ve sosyal potansiyeli ile ülkede çok önemli yer tutan İstanbul kentimiz bir durum çalışması olarak ele alınmıştır. Bu anlamda çalışmanın ilk aşamasında, İstanbul'u etkileyen deprem kaynaklarının yerleri, büyüklükleri, tipleri, İstanbul'a olan uzaklıkları ve manyitüdleri geçmiş deprem verilerinden toplanmış, daha sonra genelde Türkiye ve özelde İstanbul için uygun azalım ilişkisi belirlenmiş tir. Bölgenin jeolojik yapısından kaynaklanan zemin yapı sına uygun manyitüd-sıklık ilişkisinin belirlenmesinin ardından depremlerin oluşumu için Poisson modeli benimsenerek ve zemin hareketi parametresi olarak en büyük zemin ivmesi değeri alınarak, İstanbul için sismik risk analizi yapılmıştır. Sismik risk analizi sonuçları bölüm 2'de çeşitli tablolarda özetlenmiş ve sonunda İstanbul için %5 ve %15 aşılma olasılıklarına karşılık, kayalık ve sağlam olmak üzere iki ayrı zemin türü için ivme spektrum eğrileri oluşturulmuştur. Çalışmanın ikinci aşamasında, oluşturulmuş olan spektrum eğrileri, hedef spektrumlar ı olarak belirlenmiş ve Dursunbey 1979 D-B depremi ivme kayıtlarından yola çıkılarak İstanbul için yapay deprem ivme kaydı, 0.02 saniyelik zaman aralıklarıyla zaman alanında oluşturulması için bir yöntem ve buna yönelik bir program geliştirilmiştir. Çalışmada varılan sonuçlar ise 5. bölümde bir dizi öneriyle birlikte yer almaktadır.Earthquake risk, is the most essential criterion for the design of structures, especially for nuclear po wer plants, suspension bridges, industrial pipes and tall buildings. That's why designing a structure means to determine the earthquake response of the structure, which requires strong motion earthquake records to be used as earthquake inputs. Recent development in seismology gives an idea on a destructive earthquake and its magnitude which may occur in the near future. The calculation meth ods for the above purpose depends on probability theorems and some statistical distributions which the expert should select according to the conditions. Such a study requires a set of data such as the se i smo- tectonic properties of the province, the ground conditions, recent earthquake events, intensities, mag nitudes, epicenter and hypocenter distances, the type of earthquake sources, and finally a suitable attenuation relationship, defining the correlations between an event and the ground motion characteristics. Then using pro bability theorems, makes us come to the probability of exceeding of the ground motion parameter across a specific value at a predicted time interval and that is called "seismic risk analysis". In the first part of this study, a seismic risk analysis for the structures, which will be projected in Istanbul, is made. The peak ground acceleration value is used as the ground motion parameter, and the probabi lity of exceeding is calculated. For this, a 200x380 km2 zone, which is bordered across 25.90~31.05<' Eastern meridians and 39.95~41.35° Northern paralles, in which the west end of the North An atolian Fault is sited from Marmara Sea through Saroz bay, is taken and the recent earthquake events taking place in the period 1901~1986 are collected according to their dates, magnitudes and hypocentral distances. So, the most important three random variables, earthquake magnitude, M, ix the epicentral distance, R, and the number of earth quakes at a certain time interval N, is yet determined. After specifying the types of earthquake sources as point, line and circular sources, the next step is to calculate the probability distributions of these earth quake magnitudes which can be derived from the recurrence relations of magnitudes and their frequencies in time. According to this, the average number, N(m), of earth quakes with magnitude greater than M at a certain time interval is developed by Guttenberg and Richter and is equal to; logN(m) = a - b-M which can also be written as; N(m) = a-e-B-M Here; a = 10a ; 13 = b-lnlO and a presents the total number of earthquakes that can occur at a site while B is mainly related with the tecto nic property of the zone. In this study, 4.6 is selected as the value mo, below which earthquakes are not of engi neering importance. For instance, the magnitude - recur rence relationships for the North Anatolian Fault which is defined as a combination of six line sources is; -logN = 1.181 + 0.406-M Using the data collected, regression analysis for the determined earthquake sources is made for each source and a and J3 parameters are calculated as regression cons tants. It should be noted that, the maximum value of magnitudes of each year is used in this analysis to re move the lack of knowledge in catalogues. This extreme value distribution enables us to find some characteristic values such as; 1-) The mean value of annual maximum magnitudes: M = Mm in + 1/B 2-) Annual modal maximum: Mm ax = lncr/B 3-) The maximum magnitude which can occur in a re turning period of Tr=85 years: logN = a - b-M + logTV and here N=l as we are searching for the greatest magnitude that can occur in that period for once. 4-) Annual seismic risk: Annual seismic risk is the probability of occur i ng an eartquake having at least a magnitude of M or greater and calculated as; 1 M = -In fî where ; a -ln(l-R) M : Magnitude, R : Seismic risk (for one year) This gives us an idea for designing the structu res according to their importance. The risk value for normal structures is 15~10% while it is 5% for important structures such as hospitals, schools, etc. For nuclear power plants the risk is 0.5%. On the other hand, there is a relation between the returning period and the annual seismic risk as; Tr = 1/R which makes us come to; R - 1 - q- a. T d - e x p i - B - M ) In the next step, the most widespread and the most used attenuation relationship, offered by Esteva, Rosenblueth and Kana i, is also used in this study. The expression is; y = bi «eb2 *M. (r + c)- XI b3 where ; m : Earthquake magnitude, r : Epicenter distance, y : The greatest ground acceleration created by the earthquake, bi,b2,b3,c : Constants depending on observations. Here, the values for bi, b2, b3 and c are taken as 5000, 0.8, -2 and 25 respectively, that make the attenuation relationship suit generally to Turkey's data. Now, the equation becomes as; y = 5000-e°-8'M-(r+25)-2 In this study, the occurance of earthquakes in time is taken as a Poisson process accepting that; - Earthquake events are statistically independent from each other across time, - The probability of an earthquake occurance at a small time interval is proportional to the length of the time interval, - The probability of more than one earthquakes occur- ing at a small time interval is negligiable to the probability of one. According to these assumptions, the probability of an earthquake at a specific time interval, t, having a mag nitude value of engineering importance (m>mo), and a num ber of n is; Pr(N=n|v,t) = e- v. t. (vt)n/n! where. v : The average value of the number of earthquakes in unit time at the site (generally one year), N : The total number of earthquakes at a specific time interval, t. The probability of the maximum ground acceleration to be greater than a specific value, is obtained from; s Pr(Y>y|Di) = 2 Pr(Y>y IDi ) -Pr(Di ) i=l Xli where, Y y Di Random variable of the maximum ground acceleration, Specific value of ground acceleration, Occurance of an earthquake having a magnitude greater than mo in source i, number of seismic sources. Using a computer program, the probabilities of ground acceleration versus annual seismic risks are computed and the results are listed below. The next step is to form the response spectrum which can be used for dynamic analysis of structures. Kat ay ama, Iwasaki and Saeki offer some tables which con tain the factors of magnitude, epicenter distance, soil type and amplification. So that predicted absolute acc eleration response spectral amplitudes for given natural periods and damping factors are calculated from these tables and acceleration response spectra versus period curves are obtained for 5 and 15% annual exceeding prob abilities and for two types of soil such as tertiary or older rock (Type I) and dilivium with H>10 m. or alluvium with H<10 m.CType II). The concept of the second part of this study is to generate a time history compatible with the design spectra which have already been calculated from Ka tayama tables. The method for simulating earthquake ground mo tions is developed by Lilhanand and Tseng and also by Watabe and Hirasawa, and has the assumption that, if small corrective time history is added to the original time history, then the occurence time of the maximum re sponse to the resultant time history is close to it of the original time history and the resultant maximum Xiii response can be approximately evaluated by the sum of maximum responses to the original and corrective time histories. As it is clear, the simulation of earthquake ground motions is made in time domain in this new method, According to the above assumption, we can write; ti öRik = öR(wı,flk) = 1 SaOO-hikCti-^.d'fc where, Wi 5Rik=5R(wi,Bk) 6a(t) a(t) hik(t) ti response spectral Bk, Spectral frequency, Spectral damping, Small change in the ace. value at wi and Small adjustment, Initial input acceleration time history, Acceleration impulse response function for a SDOF oscillator with frequency wi and damping ratio Bk, Time at which spectral response occurs, Time lag. The target in here, is to solve 5a(t) for given SR(wi.Bk) which can be expressed as a set of MxN linear algebraic equations where M is the number of spectral damping ra tios and N is the number of spectral frequencies, by letting 5a(t) be; M N 5a(t) =2 S bji -f ji(t) j=ll=l where bj ı are unknown constant coefficients to be deter mined. From the above equations, we come to; M N 5Rtk = 2 2 Ci jki -bj i j=ll=l and here, Ci jki ti = J hikCti-C)-fji (£)-d«£ if f j i (*£)=hj i (t j-£> selection is made, then Cijki matrix becomes symmetric and computed by; xiv ti Ci jki -l hik(ti-t)-hji(tj-t).dt ; tiltj The elements of Cijki matrix is caluculated for elements having the same spectral damping and different spectral frequencies, and for having the same spectral frequencies and different spectral damping from the equation given above. The solutions are listed in chapter three. As Cijki matrix is computed, then to calculate bj ı and therefore Sa(t). So earthquake time history can be calculated ai (t) = a0(t) + 5ao(t) it is possible the synthetic from; where, ax(t) ao(t) The adjusted time history for each iteration, The time history of previous iteration. 1979 Dursunbey earthquake's acceleration record of East-West component is used to apply this method for Istanbul. But when the response spectrum of the earth quake is computed, than ti 1 at ions gration general BENDEP. it's seen that 1 1 is not always less which makes an important difference on the calcu- of the elements of matrix Cijki. So the inte- is also computed for tt>ti situation, and for iteration a computer program is made, called The iteration of the simulation depends very much on fiRik. In this study, the spectral acceleration differ ences between Istanbul and Dursunbey earthquakes are so big that, we formed an envelope function to limit the var iations of amplitudes in the simulated earthquake accele ration data. Also in each iteration step, we normalized the data with the maximum acceleration value and finally got the data whose response spectrum is the most suit- we able cord one with is given our target in chapter spectrum four. The acceleration re-