Seismic Hazard Assessment of Tianwan Nuclear Power Plant Site in China

 

Pentti Varpasuo

Fortum Engineering Ltd

Finland

 

Absract

 

Ground accelerations during strong-motion earthquakes are generally extremely irregular, resembling random time functions; however, these irregularities show some common features. The motion is highly oscillatory and aperiodic, it is initiated with small amplitudes that rapidly build up until they reach an intensity that remains almost stationary for a certain time and then decay, steadily, until the end of the record. The 5 % bedrock field ground spectra according to HAF 0101(1) were adopted for targets for ground motion simulation. The horizontal ground motion spectrum was anchored to 0.2 g and the vertical ground motion spectrum was anchored to 0.1 g. The numerical simulation method used in this study based on the fact that any periodic function can be expanded into a series of sinusoidal waves. The power spectral density function is generated from target response spectra. The evolutionary character of seismic ground motion is accounted for by using time and frequency dependent modulation of stationary motion. In the simulation process the match of the generated motion is improved by iterative process where the spectral density function is corrected by the response spectrum match ratio. The match is evaluated against multiple damping target spectra. The generated time histories shall have the following characteristics:

1. The mean of the zero-period acceleration (ZPA) values (calculated from the individual time histories) shall equal or exceed the design ground acceleration.

2. In the frequency range 0.5 to 33 Hz, the average of the ratios of the mean spectrum (calculated from the individual time history spectra) to the design spectrum, where the ratios are calculated frequency by frequency, shall be equal to or greater than 1.

3. No one point of the mean spectrum (from the time histories) shall be more than 10 % below the design spectrum. When responses from the three components of motion are calculated simultaneously on a time-history basis, the input motions in the three orthogonal directions shall be statistically independent. Two time histories shall be considered statistically independent if the absolute value of the correlation coefficient does not exceed 0.3.

As a result of the study the design acceleration time histories compliant with HAF 0101 (01) target response spectra were generated. The compliance of generated design time histories with HAF 0101 (01) design spectra was evaluated and shown according to the rules enumerated in the previous section.

 

1      Introduction

The limitations and paucity of recorded acceleration time histories together with the widespread use of time-history dynamic analysis for obtaining structural and secondary systems’ response are the primary motivations for the development of simulation capabilities. Individual real earthquake records are limited in the sense that they are conditional on a single realization of a set of random parameters (magnitude, focal depth, attenuation characteristics, frequency content, duration, etc.), a realization that will likely never occur again and that may not be satisfactory for design purposes.

It is the purpose of this investigation to design a stochastic model that will generate artificial ground acceleration time histories fitting to the pre-determined ground response spectra.

2      Basic concepts

The derivations and terminology presented in this section follow the reference [[1]].

A function x(t) is called deterministic if for each value t=t1 it takes a specified value x1 = x(t1). A function x(t) such that for each value t=t1 behaves like a random variable x1 = x(t1) is called non-deterministic function and the ensemble of all possible forms of x(t) define a random process with each form of x(t) being called member of the process. This definition can be applied to records of strong-motion earthquakes if, for example, we let x(t) be the ground acceleration at time t after the motion begun. In this context existing records of actual earthquakes can be considered to be members sampled from the random process. Random process x(t) is said to be strongly stationary if its probability law is independent of time shift t , i.e. the joint probability law of the set of random variables  x(t1), x(t2), ..., x(tn) is the same as that of x(t1+t), x(t2+t), ..., x(tn+t). If this joint probability law Gaussian, the joint probability law is Gaussian, the process is said to be Gaussian random process. In this study it will always be assumed that the mean value of the random process x(t) is zero at all times. Thus a Gaussian process becomes completely described by its covariance function

 

Equation 1        Covx(t1,t2)=E[x(t1)x(t2)]

 

In Equation 1 the symbol E[.] represents an average across the whole ensemble. The stationary characteristics of the random process x(t) are reflected in that the covariance function is not a function of both time co-ordinates, t1 and t2 , but only on their difference t=t2-t1. For stationary random process, the covariance function is called auto-correlation function

 

Equation 2        Rx = E[x(t)x(t+t)]

 

Equation 2 completely describes the stochastic characteristics of the Gaussian process. Another statistic frequently used to describe a stationary random process is the power spectral density function

 

Equation 3        Sx(w) = 1/p Rx(t) exp(-iwt)dt

 

The power spectral density function represents the contribution of each frequency component to the mean square value of the process.

2.1           White Noise

White noise is the mathematical idealisation of stationary random process in which all frequencies contribute with equal intensity to the mean square value of the process. Such process is characterised by constant power spectral density function, S0, over entire frequency range. Or, equivalently, by the auto-correlation function

Equation 4        R(t) = pS0d(t)

In Equation 4 d(t) is the Dirac delta function.

This auto-correlation function indicates that the process has an infinite has an infinite variance, due to contribution of entire frequency range, and is completely non-correlated at different times. White noise can also be interpreted as a superposition of random pulses arriving randomly in time in which arrival times are outcomes from homogeneous Poisson process. This process can be physically interpreted as the arrival of the train of seismic waves.

2.2           Shot noise

A non-stationary counterpart of white noise is called shot noise. The physical interpretation of the shot noise process is as a superposition of random pulses arriving randomly in time according to non-homogeneous Poisson process. In other words, it is a superposition of random pulses whose rate of arrivals is random with probabilistic characteristics varying with time. These characteristics allow the inclusion of the initial build up and decay towards the end in the intensity of the arriving pulses. A Gaussian shot noise is fully described by its covariance function

 

Equation 5        Cov(t, t+t) = f(t)d(t)

 

In Equation 5 f(t) is the variance intensity function of the process. In Equation 5 again the process shows an infinite variance and complete lack of correlation. The shot noise process can be described mathematically as the product of white noise and deterministic function of time, p(t). The variance intensity function of the shot noise process then becomes

 

Equation 6        f(t) = pS0p(t)2

2.3           Second order linear filter

The dynamic behaviour of a linear single degree of freedom system is governed by the classical second order differential equation

 

Equation 7        + 2zw0+w2y = x(t)

 

This equation is sometimes referred to as second order electrical filter due to its analog in electrical circuits. The physical meaning of the parameters z and w0 are well known to represent the damping ratio and the frequency of undamped vibration of the system. The response of a mechanical system to an excitation represented by a random process is another random process usually referred to as the output process. Formally, the output process y(t) can be expressed in the time domain as

 

Equation 8        y(t) = x(t)h(t-t)dt

 

In Equation 8 h(t) is the unit impulse response function of the filter. The response process can also be obtained through the frequency domain in terms of the Fourier transforms of both processes

 

Equation 9        Y(iw) = H(iw)X(iw)

In Equation 9 H(iw) is the complex frequency response function of the filter. The transfer functions h(t) and H(iw) are Fourier transform pairs and either one of them is sufficient to describe completely the steady state behaviour of the system.

If the excitation process is Gaussian, the output process of linear system will also be Gaussian, and fully described by its covariance function

 

Equation 10      Covy (t1, t2) = Cov(t1 ,t2)h(t1-t1)h(t2-t2)dt1dt2

 

The system that is the target of this investigation is the free vibration of single degree of freedom system subjected to a random motion of its support. The excitation process x(t) represents the displacement of the support and the output process y(t) represents the absolute displacement of the system. The governing differential equation for this system is

 

Equation 11      + 2zw0 + w2y = 2zw0 + w02x

 

The unit impulse response transfer function for this system is

 

Equation 12      h(t) = w02/wd exp(-zw0t)sin(wdt + 2a)

 

In Equation 12 wd=w0(1-z2)1/2 and a = arcsin(z).

 

The complex frequency response transfer function is

 

Equation 13      H(iw) = (1 + 2ziw/w0)/(1-w2/w02 + 2izw/w0)

3      Shot noise model for ground motion simulation

The derivations and terminology presented in this section follow the reference [[2]].

The random fluctuations observed in records of strong-motion earth­quakes usually follow general patterns that can be used in the design of a stochastic model to simulate their effect. They begin with small amplitudes, which increase in time until the stronger shocks occur. When the main shocks are over, the amplitudes decay steadily until the motion ends. It is also observed that real earthquakes do not show components in every frequency. Rather they show predominant frequencies within a relatively narrow hand. Earthquakes recorded on firm soil at moderate epicentral distances show predominant frequencies in the range of 2-5 Hz. These characteristics have led investigators to design various types of stochastic processes for the generation of pseudo-earthquakes.

3.1           Filtered white noise

The power spectral density function of filtered white noise can be written in form

 

Equation 14      Sx(w) = S0|H(iw)|2

 

In Equation 14 H(iw) is the complex frequency response function of the filter and S0 is the power spectral density of the white noise excitation. For a second order linear filter as described in section 2.3, the power spectral of the output process becomes

 

Equation 15      Sy(w) = S0 (1 + 4z2w2/w2)/((1-w2/w02)2 + 4z2w2/w02)

3.2           Shot noise model

The shot noise model appropriate for ground motion simulation is obtained by filtering a shot noise through a second order linear filter. Both the filter and the shot noise is selected so that relevant features of strong-motion records at moderate epicentral distances.

3.2.1      Stochastic model

A Gaussian non-stationary shot noise is used to represent the acceleration at bedrock during an earthquake. This process simulates the effect of random pulses arriving as seismic waves to the bottom of a superficial soil layer. The non-stationary character shows the variability in the random arrival times of these seismic waves. This stochastic process is completely characterized by f(t), the variance intensity function of the shot noise.

3.2.2      Mechanical model

The second order linear filter, used in this investigation, represents a damped single degree of freedom system formed by a mass supported on a spring and a dashpot in parallel. The acceleration at bedrock is used as the acceleration of the support and the absolute acceleration of the mass simulates the acceleration of the ground surface. Roughly, this model simulates the fundamental shear mode response of the ground layer. The behavior of the mechanical model is completely defined by the parameters z and w0.

3.2.3      Simulation procedure

The acceleration at bedrock is simulated by a Gaussian shot noise obtained as the product of a stationary white noise, w(t), of intensity S0 and a deterministic function of time, p(t); thus,

 

Equation 16      ab(t) = p(t)w(t)

 

The shaping function, p(t), must be zero for negative arguments, non­negative e1sewhere, and, in general, a smoothly varying function of time. It is related to the variance intensity function by Equation 6. The filtering effect of a soil layer is simulated by a damped single degree of freedom linear system with damping ratio  z and an undamped circular frequency w0.The ground acceleration ag(t) is obtained as the absolute acceleration of the mass from the set of equations

 

Equation 17      + 2zw0 + w0z = - ab(t)

 

Equation 18      ag(t) = -(2zw0 + w02z)

 

If initial conditions of zero ground velocity and zero ground displacements are assumed, the ground acceleration process can be formally expressed as

 

Equation 19      ag(t) =  ab(t) h(t—t) dt

In Equation 19 the unit impulse response function of the filter, h(t), is given in Equation 12. Through the frequency domain, the ground acceleration process can be obtained in terms of its Fourier transform, as

 

Equation 20      Ag(iw) = H(iw)Ab(iw)

 

In Equation 20 complex frequency response function, H(iw) is given in Equation 13. The stochastic characteristics of the ground acceleration process are represented by the covariance function obtained from Equation 10 and Equation 5, i.e.

 

Equation 21      Cov(t1,t2) = f(t)h(t1 - t)h(t2 - t)dt

 

For the particular case of t1 = t2 , this covariance function becomes the variance function of the process, namely

 

Equation 22      s2(t) = f(t)h(t-t)2dt

 

It can be conclude that the ground acceleration process is Gaussian and is completely defined by filter parameters, z and w0 , and by f(t), the variance intensity function of the shot noise.

3.3           Example of estimation of model parameters

The filter parameters and the variance intensity function of the shot noise are estimated using available earthquake records that are assumed to be sample wave forms generated by the model. In order to obtain significantly consistent results, only records of earthquakes occurring in similar conditions are used. Thus the model will actually simulate earthquake records corresponding to these conditions of soil, epicentral distance, range of magnitude, etc. The records used in the example are the two horizontal components of ground acceleration recorded during the earthquakes:

1.      El Centro, California, December 12, 1934, N and W;

2.      El Centro, California, May 18, 1940, N and W;

3.      Olympia, Washington, April 13, 1949, N80E N10W;

4.      Taft, California, June 21 1952, N69W and S21W.

These records were normalized to a unit spectral intensity as defined by Housner in reference [[3]] and are assumed to be waveforms sampled from the ground acceleration process.

3.3.1      Estimation of filter parameters

The Fourier amplitude transforms of the excitation and output processes of the model are related by Equation 20 as

 

Equation 23      |Ag(iw)|2  = |H(iw)|2|Ab(iw)|2

 

Averaging Equation 23 across the whole ensemble and using the definition of the bedrock acceleration process Equation 16 , the ensemble average becomes from Equation 5

Equation 24      E[|Ab(iw)|2] = f(t)dt = const.

Thus, it may be seen that the ensemble average across the ground acceleration process in Equation 23 has the same shape as the frequency response amplitude, namely

 

Equation 25      E[|Ag(iw)|2] = |H(iw)|2 *const

 

This relation is used in the estimation of the filter parameters by computing E[|Ag(iw)|2] as an average of sample wave forms and estimating the values of z and w0 that give the best fit with

 

Equation 26      |H(iw)|2 = (1 + 4z2w2 /w02)/[(1-w2/w02)2 +4z2w2/w02]

 

Letting Fi(iw) be the Fourier transform of the sample wave form fi(t), the ensemble average is estimated as

Equation 27      E[|Ag(iw)|2] = 1/n |Fi(iw)|2

The best fit was found with parameters z = 0.6 and w0 = 5p

3.3.2      Estimation of variance intensity function

The variance intensity function is estimated from Equation 22 . The Fourier transform of Equation 22 gives

 

Equation 28      S2(iw)  = F(iw) K(iw)

 

In Equation 28 K(iw) is the Fourier transform of  function h(t)2. Substituting the computed expressions for S2(iw) and K(iw) into Equation 28 we obtain an estimate for F(iw), the Fourier transform of the variance intensity function, i.e.

 

Equation 29      F(iw) = S2(iw)/K(iw)

 

An inverse Fourier transform provides an estimate of f(t). The smooth variance intensity fitted to the sample wave form can written as

 

Equation 30      f(t) = 5.11*10-5 sec                 0<t<11.5 sec


f(t) = 5.11*10-5 sec *exp(-0.155 sec-1(t-11.5 sec))      t>11.5 sec

3.4           Generation of artificial accelerograms

First, samples of white noise are generated, then these samples are shaped using the shaping function and passed through the filter to obtain the wave forms representing ground acceleration.

3.4.1      Generation of white noise

A sequence of independent random numbers uj with uniform distribution in the interval (0,1) is generated. A new sequence of independent random numbers wj with Gaussian distribution having zero mean and unit variance is obtained with transformation

 

Equation 31      wj =  (-2 ln uj)1/2cos (2puj+1)     j=odd

Equation 32      wj+1 = (-2 ln uj )1/2sin (2pu­­­j+1)   j=odd

 

This sequence of white numbers is now spaced at intervals Dt with the origin time randomly sampled from uniform distribution in the interval (0,Dt). Repeating this procedure a sufficient number of times, an ensemble of random waveforms w(t) is obtained. If the ordinates w­­j of each of wave forms are multiplied by (pS0/Dt)1/2 , the autocorrelation of the process becomes

 

Equation 33      R(t) = 0                                                                       if          t<2Dt
R(
t) = pS0/Dt(4/3 + 2(t/Dt) + 1/6(t/Dt)3)                                           if    -2Dt<t<-Dt
R(t) = pS0/Dt(2/3 - (t/Dt)2 -1/2(t/Dt)3)                                               if          -Dt<t<0
R/t) =
pS0/Dt(2/3 - (t/Dt)2 + 1/2(t/Dt)3)                                             if          0<t<Dt
R(t) =
pS0/Dt(4/3 - 2(t/Dt) + 1/6(t/Dt)3)                                            if          Dt<t< 2Dt
R(t) = 0                                                                                                if         
t< 2Dt

 

Equation 33 in the limit, as Dt approaches zero, approaches the form

 

Equation 34      R(t) = pS0d(t)

 

This limiting case corresponds to a white noise with constant power spectral density S0.

3.4.2      Shaping white noise

The non-stationary shot noise chosen to represent the bedrock acceleration process is obtained multiplying a white noise of intensity S0 times a shaping function p(t). The shaping function p(t) is obtained in terms of variance intensity function as follows

 

Equation 35      p(t) = [f(t)/p/S0]1/2

 

For purposes of numerical calculations, the shaping function can be lumped with the scaling factor. Thus bedrock acceleration wave forms become

 

Equation 36      ab(t) = (f(t)/Dt)1/2w(t)

3.4.3      Filtering the acceleration at bedrock

The waveforms of the bedrock acceleration ensemble were filtered trough second order linear filter to obtain the ground acceleration ag(t) from the differential equation

 

Equation 37      + 2zw0 + w02 z = -ab(t)

 

ag(t) = -2zw0 - w02z

 

The solution of this equation is obtained step-by-step procedure with piecewise linear acceleration assumption.

4      Fitting the synthetic ground motion to match target single spectrum

The derivations and methodology described in this section follow the reference [[4]].

4.1           Design response spectra

The 5% bedrock field ground spectra according to HAF 0101(1) were adopted for targets for ground motion simulation. The horizontal ground motion spectrum was anchored to 0.2g and the vertical ground motion spectrum was anchored to 0.1g.

In the following Table 1 the spectral ordinates as functions of frequency are given in tabular form:

 

Horizontal spectrum

Frequency

0.25 HZ

3.3 HZ

14.3 HZ

25 HZ

33.3 HZ

50 HZ

Horizontal

0.062g

0.610g

0.538g

0.346g

0.2g

0.2g

Vertical spectrum

Frequency

0.25 HZ

4 Hz

14.3 Hz

25 Hz

33.3 Hz

50 HZ

Vertical

0.084g

0.262g

0.294g

0.182g

0.1g

0.1g

 

Table 1 Tabulated values of vertical and horizontal design spectra

4.2           Acceleration time histories

The limitations and paucity of recorded acceleration time-histories together with the widespread use of time-history dynamic analysis for obtaining structural and secondary systems' response are the primary motivations for the development of simulation capabilities. Individual real earthquake records are limited in the sense that they are conditional on a single realisation of a set of random parameters (magnitude, focal depth, attenuation characteristics, frequency content, duration, etc.), a realisation that will likely never occur again and that may not be satisfactory for design purposes.

The intent herein is to focus on one commonly used method of numerical simulation, the one based on the fact that any periodic function can be expanded into a series of sinusoidal waves:

Equation 38      x(t)  = Ai sin(wi t + fi)     

Ai is the amplitude and fi is the phase angle of the ith contributing sinusoid. By fixing an array of amplitudes and then generating different arrays of phase angles, different motions which are similar in general appearance (i.e., in frequency content) but different in the local details, can be generated. The computer uses a "random number generator" subroutine to produce strings of phase angles with a uniform distribution in the range between 0 and 2p. The total power of the steady state motion, x(t) is (A2i/2).  Assume now that the frequencies wi in Equation 38 are chosen to lie at equal intervals Dw. Figure 3 shows a function G(w) whose value at wi is equal to Ai2 /2Dw so that G(wi)Dw = Ai2/2. Allowing the number of sinusoids in the motion to become very large, the total power will become equal to the area under the continuous curve G(w), which is in effect the spectral density function.  When G(w) is narrowly centred around a single frequency, then Equation 38 will generate nearly sinusoidal functions. On the other hand, if the spectral density function is nearly constant over a wide band of frequencies, components with widely different frequencies will compete to contribute equally to the motion intensity, and the resulting motions will resemble portions of earthquake records. Of course, the total power and the relative frequency content of the motions produced by using Equation 1 do not vary with time. To simulate in part the transient character of real earthquakes, the stationary motions, x(t), are usually multiplied by a deterministic intensity function such as the exponential compound function.

 

The most widely used equation form for power spectral density function is so called filtered white-noise spectral density function expressed by Equation 2 is as follows:

 

Equation 39     

 
                     

In Equation 39 the filtered white noise power spectral density function is depicted with the following arbitrary parameters: G0=100, wg=50,  zg=0.5. In actual simulation task the parameters are so selected that the power spectral density function corresponds as closely as possible the given target response spectrum. Theoretical spectral density shapes such as Equation 39 are obtained by examining, smoothing and averaging of the squared Fourier amplitudes |f(w)|2 of actual strong motion records. This stems from the basic fact that, for stationary random processes, the expected value of |f(w)|2 and the spectral density functions G(w) are proportional.

In summary, the problem in simulation with the model represented by  Equation 38 is, then, one of selecting a proper shape and intensity of either the power spectral density function or the Fourier amplitude spectrum and estimating the duration of the motion. Development of design criteria has evolved along different paths, however. In the nuclear industry, for example, a set of smooth response spectra has been adopted for use in seismic design. In this practice the power spectral density function is generated from smooth target response spectra. In the simulation generation process the match of the generated motion is improved by iterative process where the spectral density function is corrected by the response spectrum match ratio as follows:

 

Equation 40      G(w)i+1 = G(w)i (St(w)/Si (w)) 

 

In Equation 40 St(w) is the target response spectral value.

The generated time histories shall have the following characteristics:
1. The mean of the zero-period acceleration (ZPA) values (calculated from the individual time histories) shall equal or exceed the design ground acceleration.
2. In the frequency range 0.5 to 33 Hz, the average of the ratios of the mean spectrum (calculated from the individual time history spectra) to the design spectrum, where the ratios are calculated frequency by frequency, shall be equal to or greater than 1.
3. No one point of the mean spectrum (from the time histories) shall be more than 10% below the design spectrum. When responses from the three components of motion are calculated simultaneously on a time-history basis, the input motions in the three orthogonal directions shall be statistically independent. Two time histories shall be considered statistically independent if the absolute value of the correlation coefficient does not exceed 0.3.

The generated time histories and corresponding response spectra together with target spectra are depicted in following figures:

 

 

 

Figure 1            Horizontal x-axis ground acceleration time history

Figure 2            Horizontal x-axis ground response spectrum fit

Similar figures can be constructed for y-axis and vertical acceleration time histories and target ground response spectra.

4.3           Correlaton coefficients between ground acceleration time history components and other validity tests

According to reference [[5]] the input motion time histories should meet the following requirements:

1.      One or more recorded, modified recorded or synthetic earthquake ground motion time histories may be used to calculate seismic response of safety related structures.

2.      Time histories shall be so selected or developed that they reasonably represent the duration of strong shaking conditions expected for the site. For analysis shorter time segments may be used if they satisfy the conditions given below:

3.      The developed time histories shall have following characteristics:

·        the mean of the zero-period acceleration (ZPA) calculated from the individual time histories shall equal or exceed the design ground acceleration

·        in the frequency range 0.5 t0 33 Hz the average of the ratios of the mean spectrum ( calculated from the individual time history spectra) to the design  spectrum, where the ratios are calculated frequency by frequency shall be equal, shall be equal to or greater than 1.

·        no one point of the mean spectrum (from the time histories shall be more than 10% below the design spectrum

Spectral values from the time history shall be calculated at sufficient frequency intervals to produce accurate response spectra. The following table provides suggested frequencies at which spectral ordinates may be calculated:

Frequency range (Hz)

Increment(Hz)

0.5-3.0

0.10

3.0-3.6

0.15

3.6-5.0

0.20

5.0-8.0

0.25

8.0-15.0

0.50

15.0-18.0

1.0

18.0-22.0

2.0

22.0-34.0

3.0

 

Table 2 Suggested frequencies for calculating of response according to reference [5].

Another acceptable method to choose the frequencies is such that each frequency is within 10% of the previous frequency. When responses from the three components of the motion are calculated simultaneously on a time history basis the input motion in the orthogonal directions shall be statistically independent, and the time histories shall be different. Shifting the starting time of single time history does not constitute the establishment of different time history. Two time-histories shall be considered statistically independent if the absolute value of the correlation coefficient does not exceed 0.3.

4.3.1      Correlation coefficients

Correlation coefficients between synthetic excitation components were developed using EXCEL [[6] ] data analysis software. The resulting matrix of correlation coefficients is given in the following table:

 

 

Table 3 Table of correlation coefficients between synthetic excitation components

As can be seen from the Table 3 that the correlation coefficients between vertical and horizontal components are less than 0.05 and the correlation coefficient between two horizontal components is 0.18. All these coefficients are less than 0.3 and the requirement of statistical independence of components is fulfilled.

Summary statistics of the time series representing the earthquake components are given in the following table:

 

Table 4 Summary statistics of synthetic earthquake excitation components

From the Table 4 it is seen that the ZPA values of the components are in g units are 0.2001447 for both horizontal components and 0.100 for vertical component and so the first requirement of reference [5] is fulfilled.

4.3.2      Fit to the target spectrum

The fit to reference [[7]] target spectrum corresponding to 5% damping is given the following table:

 

Table 5 Fit to HAF 0101 (01) 5% damping target spectra

As it can be seen from Table 5 all ASCE 4-86 spectral fit criteria all fulfilled for synthetic time histories developed.

5      Conclusion

The match of Tianwan Nuclear Power Plant design acceleration time histories with HAF 0101 (01) Design spectra is studied. The compliance of design time histories with HAF 0101 (01) design spectra according to ASCE 4- 86 [5] rules are shown.

 

6      References



[[1]]        Y.K. Lin, "Probabilistic theory of structural dynamics", Robert E. Krieger Publishing Co., Florida, 1967.

[[2]]        P. Ruiz and J. Penzien, " PSEQN - Artificial generation of earthquake accelerograms", Earthquake Engineering Research Center, Report No EERC 69-3, University of California, Berkeley, California, March 1969.

[[3]]        Housner G.W., "Behavior of Structures During Earthquakes, Journal of Engineering Mechanics Division, ASCE, 85, No EM4, pp 109-129, October 1969.

[[4]]        D. A. Gasparini, E. H. Vanmarcke, "Simulated earthquakes compatible with prescribed response spectra",  Massachusetts Institute of Technology, Publication No. R76-4, Cambridge, Massachusetts, January 1976.

[[5]]        ASCE STANDARD 4-86, "Seismic Analysis of Safety Related Nuclear Structures", American Society of Civil Engineers, September 1986.

[[6]]        Microsoft­â Excel, Users' Guide, Version 7.0, ă 1997 Microsoft Corporation.

[[7]]        Contract LYGNPP-R-97-002/85-265-47/100, Appendix 1/2, Standard Response Spectra.