Attenuation relations of ground motion for rock and soil sites in eastern United States

E L S E V I E R P l I : S 0 2 6 7 - 7 2 6 1 ( 9 7 ) 0 0 0 1 6 - X

Soil Dynamics and Earthquake Engineering 16 (1997) 363-372 © 1997 Elsevier Science Limited

Printed in Great Britain. All rights reserved 0267-7261/97/$17.00

Attenuation relations of ground motion for rock and soil sites in eastern United States

Howard Hwang & Jun-Rong Huo Center for Earthquake Research and Information, The Universio, of Memphis, 3890 Central Avenue, Box 526590, Memphis,

TN 38152-6590, USA

(Received 22 April 1997; accepted 24 April 1997)

This paper presents the attenuation relations of peak ground acceleration and spectral accelerations for rock and soil sites in the central and eastern United States (CEUS). For the bedrock site condition, 56 pairs of moment magnitude M and epicentral distance R are used to simulate ground motion, and for each pair of M and R, 550 samples of ground motion parameters are generated using a seismological model together with random vibration theory and distribution of extreme values. From the regression analyses of these data, the attenuation relations of ground motion parameters for the bedrock site are established. With the aid of appropriate site coefficients, these attenuation relations are modified for the site categories specified in the 1994 NEHRP Provisions. These attenuation relations are appropriate for the assessment of seismic hazards at far-field rock and soil sites in the CEUS. © 1997 Elsevier Science Limited.

1 I N T R O D U C T I O N

In the western United States (WUS), the attenuation relations of ground motion parameters, such as peak ground acceleration (PGA) and spectral accelerations (SA) are based on observed strong motion data. However, such attenuation relationships cannot be used to predict the ground motion in the central and eastern United States (CEUS), because many researchers, for example Nuttli 1, have suggested that the characteristics of ground motion in the CEUS are quite different from those in the WUS.

Estimating strong ground motion in the CEUS is quite challenging because the strong motion data are scarce. In recent years, many researchers, for example, Hanks and McGuire 2 and Boore and Atkinson 3, have used seismological models to predict the characteristics of ground motion in California and in eastern North America (ENA). In this study, we also use a seismological model together with random vibration theory and distribution of extreme values to simulate ground motion parameter values for the bedrock (BR) site, which consists of rock with a shear-wave velocity of 3.5 km s -l. From the regression analyses of simulated data, the attenuation relations of ground motion parameters for the bedrock site in the CEUS are established. Furthermore, with the aid of appropriate site factors, these attenuation relations are modified

for various site conditions specified in the 1994 NEHRP Provisions 4.

363

2 M O D E L F O R E S T I M A T I N G G R O U N D M O T I O N FOR BEDROCK SITES

In the seismological model, the Fourier amplitude spectrum of bedrock acceleration is expressed as follows 3"

A(f) = CS(f)O(f) (1)

where C is the scaling factor, S(t') is the source spectral function, and D(f) is the diminution function. The source spectral function S(J) used in this study is the acceleration source spectrum proposed by Brune 5,6

S(f) = (27rf) 2 M° 1 -b (f/~o) 2 (2)

where fo is the corner frequency and Mo is the seismic moment. The corner frequency is related to the stress parameter by

= 4 . 9 × 106 /3(~) 1/3 (3) f0

in which Aa is the stress parameter, and/3 is the shear-wave velocity at the source region and is taken as 3.5 km s -t. The

364 H. Hwang, J.-R. Huo

scaling factor C is

C - {R°e~)FV 1

47rpf l 3 r (4)

where r is the hypocentral distance, (Roe) is the radiation coefficient averaged over an appropriate range of azimuths and take-off angles, F accounts for the amplification of the seismic wave at the free surface, V accounts for the par- tition of a vector into horizontal components, and P is the crustal density of the continental crust at the focal depth. In this study, the crustal density 0 is taken as 2.7 g cm

The diminution function D(f) represents the anelastic attenuation that accounts for the damping of the earth's crust and a sharp decrease of acceleration spectra above a cut-off frequency fm

-~f~ Dq) =exp [ Q~] Pq,fm) (5)

where Q(/) is the frequency-dependent quality factor of the medium in the study region, and P ~ f m ) is the high-cut filter to account for the observation that the acceleration spectra often show a sharp decrease above a cut-off frequency J;,,, which cannot be attributed to path attenuation. The high-cut filter is taken as

P(f,J;n) = 1 + (6)

In this study, the strong-motion segment of an acceleration time history a(t) is considered as a stationary Gaussian process with a mean of zero. Under this condition, the one-sided power spectrum S~([) can be derived from the Fourier amplitude spectrum as follows:

S,~(f) = 21A0")i2 (7) td

where Td is the strong-motion duration. Given the power spectrum S~(f), the standard deviation of ground acceleration o. can be determined as

2 [ % = S ~ q ) d f (8) 0

In addition, the mean peak bedrock acceleration PA and its standard deviation cr~,A can also be determined as follows 7.

PA = Pmo, (9)

O p A ---- q o .

where

10)

r,m = ¢ 2 rn(vcrd) + 0.5772

V/2 ln(vJd) 11)

q - - 1.2 5.4

V/2 ln(v~Td) 13 + [2 ln(v~Td)] 32 12)

and

{ max(2.1,28v0Td) 0.00 < 6 --< 0.10

v,,T d : (1.638 o.45 - 0.38)v0Td 0.10 < 8 < 0.69

VoTd 0.69 <~ 8 < 1.00

(13)

where 6 is the shape factor and v0 is the mean zero-crossing rate of the stationary process over the duration Td.

A response spectrum is a representation of the maximum response (acceleration, velocity, or displacement) to an earthquake ground motion for all possible simple oscilla- tors, The equation of motion for a simple oscillator with frequency coo and damping ratio ~" is

5(+ 2~'coo2 + cooX = - a(t) (14)

where X(C%,t) is the relative displacement of the oscillator. For a given frequency coo, the spectral displacement SD(c%) is defined as the maximum absolute value of X(coo,t),

SD (c%)= maxlx(ooo, t) I (15)

Since earthquake ground acceleration a(t) is a stationary Gaussian process, the relative displacement X(COo,t) is also a stationary Gaussian process with zero mean and the power spectrum S~x(W) as

S~x(W) = [nx(w)12Saa(C0) (16)

where H~(c0) is the frequency response function of the oscillator. Given the power spectrum S~(w), the mean and standard deviation of the maximum value, that is. spectral displacement SD(w0), can be determined from eqn (9) and eqn (10) with the power spectral function S~q) in eqn (8) replaced by S~0q. Given SD(coo), the spectral acceleration SA(coo) can be computed as

SA(wo) = torSI (c%) (I 7)

3 UNCERTAINTIES IN SEISMIC PARAMETERS

Given a moment magnitude M and an epicentral distance R, some seismic parameters such as the crustal density 0 and shear=wave velocity/3 appear to have less influence on the resulting ground motion. On the other hand, the stress parameter Ao, strong-motion duration Td, cut-off frequency fro, quality factor Q0'), radiation coefficient (Ro,}, and focal depth H, have significant effects on the resulting earthquake ground motion. Uncertainties in these seismic parameters are taken into account in the estimation of ground motion.

In this study, the stress parameter Ao is considered as constant and independent of magnitude. Boore and Atkinson 3, Toro and McGuire s, and Somerville et al. "~ suggested an average Ao of 100 bar for earthquakes in the CEUS. The stress parameter for the 1988 Saguenay earthquake determined by Atkinson and Boore m is about 200 bar. Frankel et al. i J used 150 bar to estimate ground motion in the CEUS for generating the new version of the national

Attenuation relations of ground motion 365

Table 1. Uncertainties in seismic parameters

Parameters Distributions Range

Ao Uniform 100-200 bar .f~, Uniform 20-40 Hz

(17o,) Unitbrm 0.48-0.64 H Uniform 6-15 km 3'0 Uniform 0.0006-0.0008 r/ Uniform 0.25-0.55 Tj Lognormal eqn (21)

Table 2. Ranges of epicentral distance used in this study

Moment magnitude M Epicentral distance R (kin)

5.0 5-200 5.5 15-200 6.0 25-200 6.5 35-200 7.0 40-200 7.5 45-200

seismic maps of the United States. In this study, the range of stress parameter is taken as 100-200 bar.

For the cut-off frequency fro, Toro and McGuire 8 sug- gestedf , , of 40 Hz for rock sites in the eastern United States. From the investigation of the 1988 Saguenay earthquake, Chen and Hwang 12 found that fm of 20 to 30 Hz are appropriate for rock sites at epicentral distances less than 100 km. Thus, the range of cut-off frequency is taken as 2 0 - 4 0 Hz. The range of focal depth is 6 -15 km based on the hypocentral locations of instrumentally recorded micro-earthquakes in the New Madrid seismic zone.

The radiation coefficient (Ro,) is related to fault type, rupture velocity, and rupture direction. Boore and Boat- wright ~3 determined the P- and S-wave radiation coefficients considering three types of faults and various fault orientations. The S-wave radiation coefficient they obtained varies from 0.48 to 0.64. This range also covers the results indicated by other researchers 14. Thus, the range of (Ro,) is considered as 0 .48-0.64.

The quality factor Q(¢) describes the attenuation of seismic waves and is related to the coefficient of anelastic attenuation of seismic energy "Y~9 by

7rf 70]el r / ( 18 ) 3'(/) = Q(f)~ =

where Y0 is the value of 3'(/) at 1 Hz and r / is a coefficient.

From a study on the attenuation of shear and Lg waves in the central United States, Dwyer et al. 15 determined r /and Y0 as follows:

r~ = 0 . 4 0 ± 0.15 (19)

3/0 = 0.0007 ± 0.0001 (20)

The strong-motion duration Ta is determined using the following formula proposed by Huo and Hu J6.

ln(Td) = -- 5.222 + 0.7511M + 0.5815 ln(R + 10) + e

(21)

where e is a normal random variable with a mean of zero and the standard deviation of 0.37. The strong-motion duration Td is modeled as a lognormal distribution (eqn (21)), while other parameters Ao, fro, (Ro,), H, Q0, r /are modeled as a uniform distribution. The random seismic parameters are summarized in Table 1.

4 A T T E N U A T I O N R E L A T I O N S FOR B E D R O C K SITES

The ranges of epicentral distance R shown in Table 2 are used to generate the ground motion data. The lower bound of the epicentral distance in Table 2 is taken as the limit of

Table 3. Regression coefficients of attenuation relations for bedrock sites

Period (s) Ci C2 C3 C~ %~VSRI

0.05 --I.831 0.910 - i . 244 -0.00440 0.307 0.10 -2.312 0.924 -1.233 -0.00317 0.311 0.15 -2.671 0.938 -1.227 -0.00265 0.317 0.20 -2.968 0.952 -1.219 -0.00240 0.326 0.25 -3.224 0.966 -1.213 -0.00221 0.337 0.30 -3.461 0.981 -1.208 -0.00210 0.343 0.35 -3.690 0.997 -1.201 -0.00204 0.349 0.40 -3.911 1.013 -1.195 -0.00199 0.357 0.50 -4.344 1.048 -1.180 -0.00200 0.365 0.60 -4.764 1.084 -1.165 -0.00203 0.375 0.70 -5.176 1.120 -1.149 -0.00211 0.383 0.80 -5.578 1.157 -1.134 -0.00219 0.388 1.00 -6.362 1.231 -1.100 -0.00243 0.404 1.20 -7.103 1.302 -1.069 -0.00267 0.416 1.50 -8.135 1.404 -1.024 -0.00302 0.431 2.00 -9.652 1.556 -0.961 -0.00354 0.451 2.50 -10.94 1.687 -0.912 -0.00392 0.459 3.00 -12.05 1.802 -0.875 -0.00267 0.466 PA -2.904 0.926 -1.271 -0.00302 0.309

366 H. Hwang, J,-R. Huo

the near field as suggested by Kriniztsky et al. 17, while the upper bound is taken as 200 km. In the process of simula- tion, the increment of epicentral distance is 0.2 in logarithmic scale and the increment of moment magnitude M is 0.5 in the range of 5.0 to 7.5. Thus, 56 pairs of M and R are used to generate the ground motion data.

For each pair of M and R, 50 samples of each random seismic parameter (Table 1) are generated according to the distribution, and these samples are then combined to create 50 sets of seismic parameters. For each set of seismic

parameters, the mean value and standard deviation of the ground motion parameters are determined by the aforementioned procedure. Assuming the ground motion parameters follow a lognormal distribution, 11 samples of the ground motion parameters are generated within the mean minus and plus three standard deviations. Thus, for each pair of M and R, 550 (50 × 11) samples are generated, Since 56 pairs of M and R are considered, a total of 30800 (550 × 56) samples are created for each ground motion parameter.

1 - - '

tm v 6

5 ¢--

.O 4 3

2 0 o o < 0.1

O 5 ~ 4

~ a

0 .01 1

i i I i i I i I i I

0.3 second

2 3 4 5 6 7 8 2 3 4 5 6 7 8 10 1 0 0

Epicentral Distance (kin)

0 10 8

6

4

g 10-1 _ _

. ~ 1 0 -~

n ~O

--

1.0 second " ~

\ \ \

- 3 i i 1 i i i J i J = , i I I I I I J i 1 0 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2

1 10 1 0 0

Epicentral Distance (km)

Fig. 1. Median attenuation curves of spectral acceleration for bedrock site condition.

Attenuation relations of ground motion

Table 4. Site categories specified in 1994 NEHRP provisions

367

Category Description

A B C

D

E

F

Hard rock with measured shear wave velocity, ~s > 1500 m s -~ (~s > 5000 fi s -j) Rock with 7 6 0 m s J < ~s -< 1500ms -i (2500fts -j < 9s-----5000fts -j) Very dense soil and soft rock with 360 m s -~ -< ~s --< 760 m s -j (1200 ft s -t -< ~s -< 2500 ft s -j) or with either N > 50 or ~u --> 100 kPa (2000 psi) Stiff soil with 180 m s -I -< ~ -< 360 m s -~ (600 ft s -I -< ~s -< 1200 ft s -l) or with either 15 -< F/-< 50 or 50 kPa -< ~u -< 100 kPa (1000 psf -< ~u -< 2000 psf) A soil profile with i~ < 180 m s -~ (600 ft s -r) or any profile with more than 3 m (10 ft) of soft clay defined as soil with PI > 20, w --< 40%, and su < 25 kPa (500 psf) Soils requiring site-specific evaluations 1. Soils vulnerable to potential failure or collapse under seismic loading such as liquefiable soils, quick and highly sensitive

clays, collapsible weakly cemented soils 2. Peats and/or highly organic clays (H > 3 m (10 ft) of peat and/or highly organic clay where H is thickness of soil) 3. Very high plasticity clays (H > 8 m (25 ft) with PI > 75) 4. Very thick soft/medium stiff clays (H > 36 m (120 ft))

In this study, the fol lowing funct ional form is used for the at tenuat ion of ground mot ion parameter:

In(YBR) : C1 + C2 M + C3 In[ ~ + Ro(M)]

-~- C 4 V / ~ -t- H 2 q'- e (22)

where YBR is the ground mot ion parameter at the bedrock sites, which is in the unit of g, R0(M) is used to account for very little a t tenuat ion of accelerat ion within the source region and is taken as 0 .06exp(0.7M) as suggested by Campbel l J8, H is the focal depth, which is usual ly taken as 10 km in the CEUS; Cl, C2, C3 and C4 are regression coefficients, e is a normal r andom variable with a zero mean and standard devia t ion 13r~R to represent the vari- abil i ty of ground mot ion parameter. F rom the regression analyses of s imulated data, the at tenuat ion relat ions of ground mot ion parameters for bedrock sites are de termined and the regression coefficients are listed in Table 3. Fig. 1 shows the median at tenuat ion curves for various momen t magni tudes .

5 A T T E N U A T I O N R E L A T I O N S F O R O T H E R SITE C O N D I T I O N S

Past earthquakes have demonstra ted that local site con- dit ions have significant effects on the characteristics of ground motion. The site effect is usually incorporated into bui ld ing codes by specifying several site categories and ass igning site coefficients for each site category. The site categories specified in the 1994 N E H R P Provisions are shown in Table 4.

Hwang et al. 19 carried out a study to establish the site coefficients for these site categories using the ground mot ion expected to occur in the CEUS. Hwang et al. excluded the site category F (Table 4), which requires site-specific evaluations, and added a site category BR to represent the bedrock site. For the site categories BR, A, and B (rock sites), synthetic acceleration t ime histories were generated using a seismological model. For the site categories C, D, and E (soil sites), the acceleration t ime histories at the ground surface were generated from non- l inear site

Table 5. Regression coefficients for various site categories

Period Site category A Site category B Site category C Site category D Site category E (s)

a b ~FS a b ~FS a b /3FS a b fiFS a b t3~- s

0.1 0.00 0.35 0.05 0.00 0.46 0.09 -0 .93 0.74 0.24 -4 .04 1.05 0.53 -4 .46 1.11 0.43 0.2 0.00 0.37 0.05 0.00 0.55 0.10 -0 .63 1.03 0.17 -2 .74 1.23 0.39 -3 .24 1.46 0.37 0.3 0.00 0.37 0.05 0.00 0.58 0.11 0.17 0.84 0.13 -1 .97 1.30 0.32 -2 .16 1.59 0.31 0.4 0.00 0.36 0.05 0.00 0.58 0.12 -0 .24 0.93 0.10 - 1.65 1.46 0.27 -2 .02 1.79 0.27 0.5 0.00 0.35 0.05 0.00 0.58 0.12 -0 .15 1.02 0.10 -0 .74 1.40 0.23 -1.31 1.78 0.24 0.6 0.00 0.34 0.05 0.00 0.57 0.14 0.10 1.02 0.10 -0 .42 1.39 0.22 -0 .82 1.75 0.22 0.7 0.00 0.33 0.05 0.00 0.54 0.14 0.26 0.96 0.09 -0 .48 1.46 0.20 -0 .57 1.75 0.20 0.8 0.00 0.32 0.05 0.00 0.52 0.14 0.40 0.86 0.08 -0 .17 1.48 0.21 -0 .09 1.72 0.19 0.9 0.00 0.30 0.05 0.00 0.49 0.14 0.28 0.79 0.09 0.08 1.44 0.20 0.33 1.62 0.17 1.0 0.00 0.29 0.05 0.00 0.47 0.13 0.25 0.73 0.07 0.41 1.35 0.18 0.73 1.48 0.17 1.2 0.00 0.26 0.04 0.00 0.42 0.12 0.19 0.62 0.08 1.04 1.09 0.19 1.27 1.17 0.19 1.5 0.00 0.22 0.04 0.00 0.35 0.11 -0.01 0.51 0.08 1.02 0.84 0.20 1.16 0.89 0.20 2.0 0.00 0.17 0.04 0.00 0.28 0.09 -0.01 0.37 0.08 0.71 0.60 0.19 0.71 0.64 0.16 2.5 0.00 0.15 0.03 0.00 0.23 0.08 -0 .18 0.32 0.08 0.29 0.49 0.17 0.26 0.53 0.17 3.0 0.00 0.13 0.04 0.00 0.20 0.07 -0 .19 0.28 0.07 0.13 0.40 0.15 0.11 0.43 0.15

PGA 0.00 0.34 0.05 0.00 0.46 0.08 -0 .96 0.77 0.22 -2.71 1.00 0.32 -3.01 1.19 0.27

368 H. Hwang , J.-R. Huo

response analyses. At a selected period T, the ratio of the spectral acceleration value of a site category to that of the bedrock site was calculated. This ratio is called the site coefficient and denoted as Fs(T). To include uncertainties in modeling of seismic source, path attenuation, and local site conditions, a total of 250 runs were performed for each site category. From the regression analyses of simulated data, the site coefficient for each site category is expressed as follows:

In [Fs(T) ] = a(T)Pa + b(T) + e (23)

where a(T) and b(T) are regression coefficients, PA is the peak bedrock acceleration in the unit of g, and e is a zero- mean normal random variable with the standard deviation firs to represent the variability of site coefficient. Table 5 lists the regression coefficients a and b and/3FS for A, B, C, D, and E site conditions. The median site coefficients for various site conditions are shown in Fig. 2.

For a site category, the ground motion parameter PGA or SA(T), denoted as Ys(T), can be determined from multiply- ing the bedrock ground motion parameter YBR(T) by an appropriate site coefficient Fs(T):

Ys(T) = YBR(T)Fs(T) (24)

Since both YBR(T) and Fs(T) are lognormal variables, Ys(T) is also a lognormal variable with the median value Ys and

t - 4 ._~ ._o

~oa

. . . . Site A

/ . - - _ ~ . . . . Site B

/ . . . . ." ' , , . ~ . . . . . . Site C

/ / - - - - Site 0

PA = 0.1g

I i I

0 0.5 1 1.5 2 2.5

Period (second)

5

4 o

0=3 o

~ a

. . . . Site A

/ .- . . . . . . . \ . . . . Site B / . , ' ~ ' , , ' X x . . . . . . Site C

/ , / " " - , ' ~ , - - - Site D

.-" . . . . . . . . . . . 2 :-:-_: :_-_: : - .- .2_.:_--_. --._- : - -~. __. ~..:__..~ . . . = _ . ~

PA = 0.3g I I I I I

0.5 1 1.5 2 2.5 3

Period (second)

Fig. 2. Median site coefficients for various site conditions.

logarithmic standard deviation fl vs. The median value and logarithmic standard deviation of Ys(T) can be determined from eqns (22) and (23) as follows:

~'s = PBRPS = exp(Cl + C 2 M + C 4 V / ~ - } - H 2

+ aPA + b)[v/R 2 + H 2 + 0.006 exp(0.7M)] & (25)

/32s = fi2r, R + fi2- s (26)

where the peak bedrock acceleration PA has the following expression (Table 3):

PA = exp( - 2.904 + 0.926M - 0 . 0 0 3 0 2 ~ )

× [ V/R2 + H2 + 0.06 exp(0.7M)] 1.271 (27)

Using the aforementioned procedure, the attenuation relation for each site condition can be determined. Taking the moment magnitude as 6.0, the attenuation curves of spectral accelerations at 0.3 and 1.0 s for various site conditions are shown in Fig. 3.

6 C O M P A R I S O N W I T H O T H E R S T U D I E S

Toro and McGuire ~, Atkinson and Boore 20.2~, and EPRI 22 also used seismological models to establish attenuation relations of bedrock ground motion in the eastern North America (ENA). Dahle et al. 23 developed empirical attenuation relations of ground motion in rock sites using the records of intraplate earthquakes around the world. In the following, the results from these studies are compared to the attenuation relation of bedrock ground motion established in this study.

The attenuation relation of bedrock ground motion proposed by Atkinson and Boore 2{} is as follows:

log(Y) = a + b ( M - 6) + c ( M - 6) 2 - log(r) + dr (28)

and

r = C R 0 + H 2

where Y represents the bedrock PGA and SA(T), Ro is the closest distance from the site to the projection of the fault (km), and a, b, c, d are constants determined from simulated ground motion data. Atkinson and Boore 21 developed a new attenuation relation for bedrock PGA and SA(T). In their later approach, they adopted the source spectral function with two corner frequencies and included the effect of the 'Moho bounce'. The results are given in a tabulate form for various magnitudes, distances, and periods.

The attenuation relation of bedrock PGA and SA(T) developed by EPRI 22 is as follows:

In(Y) = C 1 + C 2 ( M - 6) + C3(M - 6) 2 - - C 4 In(RM)

-- (C5 - C4) max [In(RM/IO0),O] -- C6R M (29)

Attenuat ion relations o f ground motion 369

and

where Y represents the bedrock PGA or SA(T), and CI through C7 are coefficients determined from simulated ground motion data.

The bedrock attenuation relation established by Toro and McGuire 8 is

In(Y) = a + bmlg + cln(r) + dr (30)

where mlg is the lg magnitude. For comparison, ml~ is converted to M using the formula suggested by Boore and Atkinson 8

Dahle et al. 23 developed an empirical attenuation relation of PGA and SA(T) for rock sites using the data from intraplate earthquakes recorded around the world. The data set consists of 87 recordings from 56 earthquakes with surface- wave magnitude Ms mainly from 3.5 to 5.5. The empirical attenuation relationship determined by Dahle et al. is as follows:

1 | ! ! ! ! |

: ~ - 6.0 4 O .

3 B

2 B R

o.1 . . . . . . . . . . . . . . !

- ! 2

n n l ~ l i i i i i i I . . . . 2 3 4 5 6 7 s 9 1 0 0 2


: L . _ ' ' ' ' ' ' i ' t 3 S i t e E " ' M=6.0 "1

g o.1 . . . . . . . .

~ 2 B. :

°"°17 " ~1.0

l O O

Epicentral Distance (km) Fig. 3. Median attenuation curves of spectral acceleration for various site conditions.


In(Y) = C 1 -~ C2M s + ln[G(r, ro)] - C3r (31)

- I r for r --< r 0 (32)

G(r, ro) = ro l ( r0)5/6 for r > r 0 F

in which r is the hypocentral distance (km) and r0 is taken as 100 km. For comparison, Ms is converted to M using the M s - M relationship established by Johnston 24

The comparison of the attenuation curves of peak bedrock acceleration from the aforementioned studies to those established in this study has been performed for moment magnitudes 5.0, 6.0 and 7.0. As an example, the comparison for the moment magnitude 6.0 is shown in Fig. 4. Although the attenuation curves from various studies are scattered signif- icantly, the attenuation curve established in this study is

within the results from all other studies. Furthermore, for moment magnitudes of 5, 6 and 7, and epicentral distances of 30 km and 100 km, the attenuation curves of bedrock spectral accelerations at 0.3 and 1.0 s from various studies are also compared. Fig. 5 shows the comparison for the moment magnitude 6.0. Once again, the results from various studies show a large scatter. The acceleration response spectra from this study are close to the upper bound but within the range of the curves from other studies.

7 C O N C L U S I O N S

In this paper, we have presented the attenuation relations of ground motion parameters, PGA, and SA(T), for rock and soil sites in the CEUS. The attenuation relations for the

8 t , ' ' ' ' ' ' ' 1

7 r .... . . . . . . . . . . . . . . . . .~ 6 :°,, 5 : . . . . . i '='='---.= • ~.'- ~ "%

' ' ' ' ' ' ' ' 1

M = 6.0

v

t - O . I

<

Q .

0.191

0.01

This study ............. Atkinson & Boore (1990) ....... Atkinson & Boore (1995)

. . . . Toro & McGuire (1987) . . . . . . EPRI ( 1 9 9 3 )

- - D a h l e et al . ( 1 9 9 0 )

~ . ~

2 3 4 5 6 7 2 3 4 5 6 7

1 10 100


\ \

Fig. 4. Comparison of attenuation curves of peak bedrock acceleration (M = 6).

Attenuation relations of ground motion 371 ,oo;L, I I I I I I I i [ I I I I I I I I

f P

f %

M = 6.0

| ! I I ! i

O) V

¢- .o

<

.0=.m

CO

10 -1

10 .2

/ . . . . R = 30 km ':':..~"~,

1 •

s J .

R = 100 km

This S t u d y

............. Atkinson & Boore (1990) ...... Atkinson & Boore (1995)

Toro & McGuire (1987) EPRI (1993)

- - Dahle et al. (1990)

1 0 - 3 I ~

0.01 2 3 4 5 6 2 3 4 5 6 2

0.1 1

Per iod (sec) Fig. 5. Comparison of bedrock spectral acceleration (M = 6).

, %

3 4 5 6 10

bedrock site condition are first derived from the regression analyses of ground motion data generated using a seismological model together with random vibration theory and distribution of extreme values. Then, the attenuation relations for other site categories specified in the NEHRP Provisions are established by modifying the attenuation relations for bedrock sites with appropriate site coefficients (site amplification factors) established by Hwang et al. L9 The proposed attenuation curves for bedrock sites are within the range of the attenuation curves from other studies. It is noted that the ground motion simulated in this study is for far-field condition; thus, the attenuation relations of ground motion parameters established in this study are appropriate for the assessment of seismic hazards at far-field rock and soil sites in the CEUS.

ACKNOWLEDGEMENTS

This paper is based on research supported by the National Center for Earthquake Engineering Research (NCEER) under contract no. NCEER 954102B (NSF grant no. BCS- 9025010). Any opinions, findings, and conclusions expressed in the paper are those of the authors, and do not necessarily reflect the views of the NCEER or the NSF of the United States.

REFERENCES

1. Nuttli, O.W., Similarities and differences between western and eastern United States earthquakes, and their consequences


fl)r earthquake engineering, in: J. Beavers (Ed.), Earthquakes and Earthquake Engineering--Eastern United States, Vol. 1, Ann Arbor Science Publishers, Ann Arbor, M1. 1981, pp. 25-51.

2. Hanks, T.C. & McGuire, R.K. The character of high- frequency strong ground motion. Bulletin (~/ the Seismo- logical SocieO' o1 Ameriea, 198 I, 71, 2071-2095.

3. Boore, D.M. & Atkinson, G.M. Stochastic prediction of ground motion and spectral response parameters at hard- rock sites in eastern North America. Bulletin ~?[ the Seismo- logical Society gf America, 1987, 77, 440-467.

4. FEMA, NEHRP Recommended Provisions for Seismic Regulations for New Buildings, 1994 ed., Federal Emergency Management Agency, Washington, DC, 1995.

5. Brune, J.N. Tectonic stress and spectra of seismic shear waves from earthquakes. Journal (?/' Geophysieal Research, 1970, 75, 4997-5009.

6. Brune, J.N. Correction. Journal ~?/ Ge(q~hysical Research. 1971, 76, 5002.

7. Der Kiureghian, A., Sackman, J.L. & Nour-Omid, B. Dynamic analysis of light equipment in structures: response to stochastic input. Journal ~?/ Engineering Mechanics Division, ASCE, 1983, 109(EMI ), 90-110.

8. Toro, G.R. & McGuire, R.K. An investigation into earthquake ground motion characteristics in eastern North America. Bulletin ~?[ the Seismological Socieo' <?/ Ameriea, 1987, 77, 468-489.

9. Somerville, P.G., McLaren, J.P., LeFevre, L.V., Burger. R.W. & Helmberger, D.V. Comparison of source scaling relations of eastern and western North American earthquakes. Bulletin of the Seismological Society (?/ America, 1987, 77, 322-346.

10. Atkinsom G.M., Boore, D.M., Preliminary analysis of ground motion data from the 25 November 1988 Saguenay, Quebec earthquake, Abstract of 84th Annual Meeting, Seismology Society of America, 1989.

11. Frankel, A., Mueller, C., Barnhard, T,, Perkins, D., Leyen- decker, E., Dickman, N., Hanson, S., Hopper, M., National Seismic Hazard Maps, U.S. Geological Survey Open-lile Report 96-532, 1996.

12. Chen, C.H., Hwang, H., Direct evaluation of earthquake

response spectra from seismological models, in: Proceedings of the Fourth U.S. National Conference on Earthquake Engineering, Vol. 1, Earthquake Engineering Research Institute, Oakland, CA, 1990, pp. 427 436.

13. Boore, D.M. & Boatwright, J. Average body-wave radiation coefficients. Bulletin (?/the Seismological Society ~?[Ameriea, 1984, 74, 1615-1621.

14. Aki, K., Richards, P.G., Quantitative Seismology: Theory and Method, W.H. Freeman and Co., New York, 1980.

15. Dwyer, J.J., Herrmann, R.B. & Nuttli, O.W. Spatial attenuation of the Lg wave in the central United States. Bulletin ~?/ the Seismological Society (?f Ameriea, 1983. 73, 781-796.

16. Huo, J.-R., Hu, Y., Magnitude and distance dependent envelope function of acceleration time history, in: Proceed- ings of the 5th US National Conference on Earthquake Engineering, Vol. 111, Earthquake Engineering Research Institute, Oakland, CA, 1994, pp. 169-178.

17. Kriniztsky, E.L., Gould, J.P., Edinger, P.H.. Fundamentals of Earthquake-Resistant Construction, Wiley, New York, 1993.

18. Campbell, K.W. Near-source attenuation of peak horizontal acceleration. Bulletin of the Sei.smoh>gieal Society g[ America, 1981, 71, 2039-2070.

19. Hwang, H., Lin, H. & Huo, J.-R. Site coefficients for design of buildings in eastern United States. Soil Dy,amics a,d Earthquake Enj4ineering, 1997, 16(I), 27-40.

20. Atkinsun. G.M. & Boore, DM. Recent trends in ground motion and spectral response relations for North America. Earthquake Spectra, 1990, 6(1 ), 15-35.

21. Atkinson, G.M. & Boore, D.M. Ground-motion relations for eastern North America. Bulletin (?/the Sei.v, oh>~,,ical Society (?/Ameriea, 1995, 85, 17-30.

22. EPRI Guidelines for Determining Design Basis Ground Motions, Vol. 1, Technical Report TR-102293, Electric Power Research Institute, Palo Alto, CA, 1993.

23. Dahle, A., Bungum, H. & Kvamme. L.B. Attenuation models inferred from intraplate earthquake recordings. Earthquake Engineering and Structural Dynamics, 1990, 19, 1125- 1141.

24. Johnston, A.C. Moment magnitude estimation for stable continental earthquakes. Seismoh~gieal Research Letter.s, 1989. 60(I). 13.

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Attenuation relations of ground motion for rock and soil sites in eastern United States