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Soil Dynamics and Earthquake Engineering 31 (2011) 1232–1247

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Soil Dynamics and Earthquake Engineering

0267-72

doi:10.1

n Corr

200092

E-m

journal homepage: www.elsevier.com/locate/soildyn

Effects of moment magnitude, site conditions and closest distance ondamping modification factors

Anmin Hao a,n, Deyuan Zhou a, Yaming Li b, Hui Zhang b

a Research Institute of Structural Engineering and Disaster Reduction, Tongji University, Shanghai 200092, Chinab Shanghai Institute of Architectural Design & Research Co. Ltd, Shanghai 200092, China

a r t i c l e i n f o

Article history:

Received 22 December 2010

Received in revised form

15 March 2011

Accepted 1 May 2011Available online 23 May 2011

61/$ - see front matter & 2011 Elsevier Ltd. A

016/j.soildyn.2011.05.002

espondence to: Room 602, Building No. 4, Lan

, China. Tel.: þ86 21 6598688.

ail address: [email protected] (A. Hao).

a b s t r a c t

Damping modification factors (DMF) are used to adjust response spectral values corresponding to

damping 5% of critical to other damping levels. Ground motions recorded are orderly grouped according

to moment magnitude, site conditions and closest distance. Near-fault motion records with closest

distance closer than 10 km are not included in this paper. Based on the classification, the effects of the

three seismological parameters on the median DMF are investigated. Consequently, the influence of site

class reduces with increasing earthquake magnitude, and the effect of closest distance generally can be

neglected with closest distance closer than 100 km except for rock sites. Except for soft soil sites,

moment magnitude has a more significant effect than closest distance and site conditions, and the

median DMF from acceleration spectra are most sensitive to seismological parameters. For soft soil

sites, the median DMF only vary a little with moment magnitude and closest distance.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Different damping elastic response spectra in structure engi-neering are required for the design of base-isolated structuresand structures with supplementary damping devices, as well asfor performance-based design approaches that use equivalentlinearization.

The damping modification factors (DMF) are usually defined asfunctions of the damping ratio and, in some cases, the responseperiod [1–8]. Some of these have been adopted in seismic codes(e.g., Newmark and Hall [1] formulation adopted in the ATC-40[9] and FEMA-356 [10]; Bommer et al. [6] equation adopted in theEC8 [11]; Ramirez et al. [7] expression adopted in the NEHRP[12,13]). Recently, Lin et al. [14] evaluated five different models ofthe DMF [1,3,4,15,16] using 216 ground motions recorded on firmsites in California. Cardone et al. [17] evaluated seven differentformulations of the DMF [1,4–7,16,18] based on the European,Californian and Japanese earthquake strong-motion databases.

Recently, considering the effects of seismological parameterson the DMF, several scholars further studied DMF. Lin and Chang[16] investigated the effects of site classification (site Classes A–Daccording to the NEHRP [12]) on the mean DMF. As for the dampingmodification factors derived from displacement response spectra(DMFd), the DMFd for site Classes AB and D are very similar, whereasthe DMFd for site Class C is generally slightly greater than those for

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the site Classes AB and D. As for the damping modification factorsderived from true acceleration response spectra (DMFa), The DMFa

are more sensitive to site conditions than DMFd. Bommer andMendis [19] showed the DMFd reduce with increasing earthquakemagnitude and site-to-source distance using predictive equationsand stochastic simulations, which further reflects the dependence ofDMF on duration. Besides, the effect of site conditions does not showa consistent pattern. Nevertheless, Bommer and Mendis, taking therecordings from Mexico City of the 1985 Michoacan earthquakeas an example, stressed that site effect on the DMF was verypronounced in some cases. The DMFd proposed by Cameron andGreen [20] varied as a function of general site classification, earth-quake magnitude and tectonic setting when damping ratios aregreater than 2%, whereas the DMFd for x¼1% also depended on site-to-source distance.

Recently, Stafford et al.[21] proposed equations, as a func-tion of significant duration and number of cycle, to estimateDMF for various damping ratios. The results indicate theduration measures are more efficient than the numbers ofcycles for predicting DMF, and that significant errors may beintroduced if one uses the DMF recommended in codes whenconsidering either very short or very long duration motions aswell as for motions containing low or high numbers of equiva-lent load cycles. Hatzigeorgiou [22] proposed expressions forDMFd, DMFv and DMFa. The results show that effect of thesource distance can be practically ignored, and that The DMFdecrease for site conditions from hard rock to soil. Besides, Hubbardand Mavroeidis [23] proposed a conservative model for the DMFsubjected to near-fault ground motions with distinct velocity pulses.

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A. Hao et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 1232–1247 1233

Based on the Next Generation Attenuation (NGA) database,the objective of this study is to further evaluate the effects ofseismological parameters (i.e., moment magnitude, closest distanceand site conditions) on the median DMFd, DMFv and DMFa. Resultsare compared with existing achievements. The analysis is referred to54 different earthquakes with moment magnitude between 5.6 and7.9, closest distance to fault rupture ranging from 10.3 to 199.9 km,and four site classes according to the definition of the NEHRP [13]provisions based on the average shear-wave velocity in the upper30 m (Vs,30) consisting of Class B (rock with 760 m/soVs,30r1500 m/s), Class C (very dense soil and soft rock with 360 m/soVs,30r760 m/s), Class D (stiff soil 180 m/srVs,30r360 m/s), andClass E (soft soil with Vs,30r180 m/s).

2. Damping modification factors

As we all known, in the seismic analysis and design of structures,the true relative velocity and absolute acceleration are usuallyapproximated by their corresponding pseudo-values. This approachis simple and works well for structures with small damping. Whenthe damping of a structure is enhanced for the purpose of responsereduction, it may result in large analysis and design errors [24]. Inthe current provisions, the prediction of the maximum relativevelocity, which is important in determining the maximum designforce for the design of velocity-dependent damping devices, isapproximated by pseudo-velocity. However, the error of suchapproximation for certain modes with high damping ratios maybe unacceptably large. Ramirez et al. [25] utilized the correct factor,which is the ratio of the exact relative velocity of SDOF systems to

Fig. 1. Moment magnitude versus closest distance.

Table 1Classification of accelerograms based on site class, moment magnitude and closest dis

Moment

magnitude

Site

class

ClstD (km) Record

count

Group

N

5.5–6.5 B 10oRr50 8 1

50oRr100 10 2

C 10oRr50 20 3

50oRr100 20 4

100oRr200 20 5

D 10oRr50 20 6

50oRr100 20 7

100oRr200 15 8

E 50oRr100 19 9

100oRr200 10 10

162

the pseudo-velocity, to obtain better estimates of the relativevelocity in the structures with damping systems. Besides the peakvelocity, the estimation of the peak absolute acceleration is alsoimportant in design of structures with added dampers. For example,damage of nonstructural components is directly related to the peakabsolute acceleration [26], and the seismic design force is deter-mined by the peak absolute acceleration in structures with baseisolation systems [24]. For structures with small damping, the peakabsolute acceleration can be represented by pseudo-accelerationwith good accuracy. Once the damping is significantly large, thisapproximation can be unsatisfactory [27]. So it is of significance tostudy DMF based on displacement, velocity and accelerationresponse spectra for structural design, especially to structures withadded dampers and isolated structures.

The DMF for elastic relative displacement, relative velocity andabsolute acceleration response spectra are defined as

DMFd ¼SdðT ,xÞ

SdðT,5%Þð1Þ

DMFv ¼SvðT ,xÞ

SvðT ,5%Þð2Þ

DMFa ¼SaðT ,xÞ

SaðT,5%Þð3Þ

in which Sd(T,x), Sv(T,x) and Sa(T,x) are the elastic displacement,velocity and acceleration response spectra corresponding to thedamping ratio x and period of vibration T, while Sd(T,5%), Sv(T,5%)and Sa(T,5%) are the elastic displacement, velocity and accelera-tion response spectra corresponding to the 5% damping ratio andperiod T. Response spectra for all the ground motions were com-puted using the numerical algorithm developed by the Newmarkintegration scheme [28].

In this study, DMFd, DMFv and DMFa are computed from linearSDOF systems with ten different damping ratios: 2%, 3.5%, 5%,10%, 15%, 20%, 25%, 30%, 40% and 50%. For each earthquake recordand each damping ratio, the DMF are computed for a set of40 periods of vibration from 0.01 to 6.0 s, with 0.01 s step forT¼0.01�0.05 s, 0.1 s step for T¼0.1�1.0 s and 0.2 s step forT¼1.2�6.0 s.

3. Ground-motion database used

A total of 620 horizontal acceleration-time histories (310seismic motions) from 54 different earthquakes were selectedfrom the NGA database (http://peer.berkeley.edu/nga/index.html)Fig. 1 shows the relation of moment magnitude-closest distancein the study. 310 seismic motions fell into four site classes, every

tance.

Moment

magnitude

Site

class

ClstD (km) Record

count

Group

N

46.5 B 10oRr50 7 11

50oRr100 9 12

C 10oRr50 20 13

50oRr100 20 14

100oRr200 20 15

D 10oRr50 20 16

50oRr100 20 17

100oRr200 20 18

E 10oRr50 7 19

50oRr100 5 20

148

http://peer.berkeley.edu/nga/index.html

Fig. 2. Variation of median DMFd for x¼3.5, 20 and 40% with moment magnitude for site Class B (a) R¼10–50 km, (b) R¼50–100 km.

Fig. 3. Variation of median DMFd for x¼3.5%, 20% and 40% with moment magnitude for site Class C: (a) R¼10–50 km, (b) R¼50–100 km, and (c) R¼100–200 km.

Fig. 4. Variation of median DMFd for x¼3.5%, 20% and 40% with moment magnitude for site Class D: (a) R¼10–50 km, (b) R¼50–100 km, and (c) R¼100–200 km.

A. Hao et al. / Soil Dynamics and Earthquake Engineering 31 (2011) 1232–12471234


site classification was subdivided based on moment magnitudes[20] and closest distance [20,29]. Table 1 shows the classificationof accelerograms according to site class, moment magnitude andclosest distance in sequence. However, for site Class E, it shouldbe pointed out that most of the ground motions recorded withmoment magnitude from 5.9 to 7.9 and closest distance from 40to 152 km come from 1999 Chi-Chi, Taiwan earthquake, which gives

Fig. 5. Variation of median DMFd for x¼3.5%, 20% and 40% with moment

magnitude for site Class E and R¼50–100 km.

Fig. 6. Variation of median DMFd for x¼3.5% and 20% with closes



rise to biased phenomena: the ground motions recorded are mainlyobtained from great earthquakes and long closest distance.

4. Results of statistical study

The median values for the DMFd, DMFv and DMFa of each group(see Table 1) are obtained, and then comparisons are performedbased on different classifications of accelerograms. In the followingthree sub-sections, the influences of moment magnitude, closestdistance and site conditions are explored, respectively. The sum-mary of the effects is presented in the last subsection.

4.1. DMF derived from displacement

4.1.1. Moment magnitude

Figs. 2–5 show the variation of the median DMFd for x¼3.5%,20% and 40% with moment magnitude for site Classes B–E,respectively. A consistent pattern can be observed from Figs. 2–4:for periods greater than about a critical period (T0)–for site Class B,T0¼3.5 s for R¼10–50 km and T0¼2.8 s for R¼50–100 km; for siteClass C, T0¼1.0 s for both R¼10–50 and R¼50–100 km, T0¼3.5 s forR¼100–200 km; for site Class D, T0¼1.4 s for R¼10–50 km,T0¼1.8 s for R¼50–100 km and T0¼3.5 s for R¼100–200 kmthe moment magnitude has a significant effect on the median

t distance for site Class B: (a) Mw¼5.5–6.5 and (b) Mw46.5.

t distance for site Class C: (a) Mw¼5.5–6.5 and (b) Mw46.5.

t distance for site Class D: (a) Mw¼5.5–6.5 and (b) Mw46.5.


DMFd. Further, the influence of moment magnitude increases whendamping ratios and periods increase, and the median DMFd forlower-magnitude earthquakes are closer to unity than those for

Fig. 9. Variation of median DMFd for x¼3.5% and 20% with clo

Fig. 10. Variation of median DMFd for x¼3.5% and 20% with site conditions for

Fig. 11. Variation of median DMFd for x¼3.5% and 20% with site conditions fo

larger-magnitude earthquakes. Considering the ratio of the medianDMFd for Mw46.5 to the median DMFd for Mw¼5.5–6.5 corre-sponding to x¼20% at the given site class and closest distance, the

sest distance for site Class E (a) Mw¼5.5–6.5, (b) Mw46.5.

Mw¼5.5–6.5: (a) R¼10–50 km, (b) R¼50–100 km, and (c) R¼100–200 km.

r Mw46.5: (a) R¼10–50 km, (b) R¼50–100 km, and (c) R¼100–200 km.


minimum values of the ratios are 0.61 for site Class B, 0.67 for siteClass C and 0.71 for site Class D. The more significant the momentmagnitude has affects on the median DMFd, the further the ratiosare away from unity. For ToT0, the median DMFd for Mw¼5.5–6.5and Mw46.5 are generally quite close for site Classes B–D. Fig. 5show the effect that the moment magnitude has on the median DMFd

for site Class E is not distinct and does not follow a consistent pattern.Generally, the effect of moment magnitude on the median

DMFd for site Class C are more prominent than those for site ClassD within R¼10–100, whereas the effect of moment magnitude forsite Class B are more prominent than those for site Class D withinT¼4–6 s. However, the moment magnitude has the similar effectson the median DMFd for site Classes C and D corresponding to

Fig. 12. Variation of median DMFv for x¼20% with moment magn

Fig. 13. Variation of median DMFv for x¼20% with moment magnitude for s

Fig. 14. Variation of median DMFv for x¼20% with moment magnitude for si

R¼100–200 km. In brief, the moment magnitude has notableeffect on the median DMFd for high damping ratios and longperiods except for soft soil conditions.

4.1.2. Closest distance

Figs. 6–9 show the variation of the median DMFd for x¼3.5% and20% with closest distance corresponding to site Classes B–E, respec-tively. From Fig. 6, the median DMFd slightly increase with closestdistance from R¼10–50 to 50–100 km for x¼20% and T4�3.0 s.From Figs. 7 and 8, for a given moment magnitude and siteconditions, the median DMFd for R¼10–50 and 50–100 km aregenerally similar. For site Class C with T¼1.0–6.0 s and site Class Dwith T¼1.0–4.0 s, the median DMFd for R¼100–200 km are different

itude for site Class B (a) R¼10–50 km and (b) R¼50–100 km.

ite Class C (a) R¼10–50 km, (b) R¼50–100 km, and (c) R¼100–200 km.

te Class D: (a) R¼10–50 km, (b) R¼50–100 km, and (c) R¼100–200 km.


from those for R¼10–50 and50–100 km for lower-magnitude earth-quakes. The median DMFd for Mw46.5 vary slightly with closestdistance for site Classes C and D. For soft soil sites, the effect ofclosest distance generally can be neglected except for Mw¼5.5–6.5and T4�4.0 s. Lastly, the closest distance has a less effect on themedian DMFd than the moment magnitude.

4.1.3. Site conditions

Figs. 10 and 11 show the variation of the median DMFd with siteconditions for Mw¼5.5–6.5 and Mw46.5, respectively. As can beseen: (1) site conditions have an effect on median DMFd for lower-magnitude earthquakes while site conditions have little effect on themedian DMFd for larger-magnitude earthquakes; (2) for Mw¼5.5–6.5,the median DMFd computed from site Class C are slightly closer tounity than those computed from site Classes B and D with R¼10–50

Fig. 15. Variation of median DMFv for x¼20% with moment magnitude for site

Class E and R¼50–100 km.

Fig. 16. Variation of median DMFv for x¼20% with closest di


Fig. 18. Variation of median DMFv for x¼20% with closest

and 50–100 km corresponding to T¼1.0–4.0 s, whereas the medianDMFd for site Classes B–D are closer to unity than those for siteClass E with periods greater than about 1.5 s.

4.2. DMF derived from velocity


Figs. 12–15 show the variation of the median DMFv for x¼20%with moment magnitude for site Classes B–E, respectively. Fig. 12shows, in most cases, the median DMFv for Mw¼5.5–6.5 andMw46.5 are similar for site Class B although the median DMFv forMw¼5.5–6.5 are slightly closer to unity than those for Mw46.5 withT¼3.0–6.0 s and R¼50–100 km. Figs. 13 and 14 show a consistentpattern for periods greater than about a critical period (T0)–for siteClass C, T0¼1.2 s for R¼10–50 km, T0¼1.0 s for R¼50–100 kmand T0¼2.0 s for R¼100–200 km; for site Class D, T0¼1.3 sfor R¼10–50 km, T0¼1.6 s for R¼50–100 km and T0¼3.4 s forR¼100–200 km–that the moment magnitude has a significant effecton the median DMFv. Further, the influence of moment magnitudeincreases with increasing damping ratios, and the median DMFv forlower-magnitude earthquakes are closer to unity than those forlarger-magnitude earthquakes (for x¼3.5% and 40%, not shown inthe plots). Considering the ratio of the median DMFv for Mw46.5 tothe median DMFv for Mw¼5.5–6.5 corresponding to x¼20% at thegiven site class and closest distance, the minimum values of theratios are 0.76 for site Class B, 0.73 for site Class C and 0.75 for siteClass D. So the effect of moment magnitude on the median DMFv isless pronounced than those on the median DMFd. For ToT0, themedian DMFv for Mw¼5.5–6.5 and Mw46.5 are quite close

stance for site Class B: (a) Mw¼5.5–6.5 and (b) Mw46.5.

stance for site Class C: (a) Mw¼5.5–6.5 and (b) Mw46.5.

distance for site Class D (a) Mw¼5.5–6.5, (b) Mw46.5.


regardless of the damping ratios for site Classes C–D. Fig. 15indicates slightly lower DMFv for Mw¼5.5–6.5 than for Mw46.5within T¼1.5–4.0 s, whereas the curves are inverted withinT¼4.5–6.0 s.

Generally, the effect of moment magnitude on the medianDMFv for site Class C are slightly greater than those for site ClassD with R¼10–100, whereas the effect of moment magnitude onthe median DMFv for site Classes C and D is more significant thanthose for site Classes B and E. In brief, the moment magnitude hasa great effect on the median DMFv for systems with high dampingratios and long periods at very dense/stiff soil and soft rock sites.


Fig. 20. Variation of median DMFv for x¼20% with site conditions for Mw¼

Fig. 21. Variation of median DMFv for x¼20% with site conditions for Mw


Figs. 16–19 show the variation of the median DMFv for x¼20%with closest distance corresponding to site Classes B–E, respec-tively. As can be seen, the median DMFv for R¼10–50 and 50–100 km are close to each other except for the median DMFv

computed from Figs. 16(b) and 18(b) with T¼4.0–6.0 s where themedian DMFv for R¼10–50 km are closer to unity than those forR¼50–100 km. From Figs. 17(a) and 18(a), for T¼1.0–5.0 s, themedian DMFv for R¼10–100 km are greatly closer to unity thanthose for R¼100–200 km. Figs. 17(b) and 18(b) indicate that, forx¼20%, the median DMFv computed from the ground motions for

stance for site Class E: (a) Mw¼5.5–6.5 and (b) Mw46.5.

5.5–6.5: (a) R¼10–50 km, (b) R¼50–100 km, and (c) R¼100–200 km.

46.5: (a) R¼10–50 km, (b) R¼50–100 km, and (c) R¼100–200 km.


R¼100–200 km are slightly lowest among given closest distanceranges. Fig. 19 shows the closest distance has only a little effecton the median DMFv; however, the effect lacks a clear trend.Finally, the closest distance has a less effect than the momentmagnitude.


Figs. 20 and 21 show the variation of the median DMFv forx¼20% with site conditions for Mw¼5.5–6.5 and Mw46.5,respectively. The following can be observed: (1) for Mw¼5.5–6.5and R¼10–100 km (Fig. 20(a, b)), the median DMFv computedfrom site Class C are slightly closer to unity than those computedfrom site Classes B and D with T¼1.0–6.0 s, whereas the medianDMFv for site Classes B and D are obviously closer to unity thanthose for site Class E with periods longer than 1.0 s, especially to

Fig. 22. Variation of median DMFa for x¼20% with moment magn

Fig. 23. Variation of median DMFa for x¼20% with moment magnitude for s

Fig. 24. Variation of median DMFa for x¼20% with moment magnitude for s

T¼2.0–5.0 s; (2) for Mw46.5 and R¼10–100 km (Fig. 21(a, b)),the median DMFv computed from site Class B are the closest tounity among those computed from site Classes B–E with T¼1.0–6.0 s.From (Fig. 21(a)), the median DMFv obtained from site Class E arethe lowest at except for the very short periods, whereas from(Fig. 21(b)), the median DMFv for site Classes C–E are similar inmost period range; and (3) the effect of site conditions can beneglected when closest distance is greater than 100 km.

4.3. DMF derived from acceleration


Figs. 22–25 show the variation of the median DMFa for x¼20%with moment magnitude for site Classes B–E, respectively. Theclear trend can be observed from Figs. 22–24: for periods greater

itude for site Class B: (a) R¼10–50 km and (b) R¼50–100 km.

ite Class C: (a) R¼10–50 km, (b) R¼50–100 km, and (c) R¼100–200 km.

ite Class D: (a) R¼10–50 km, (b) R¼50–100 km and (c) R¼100–200 km.


than about a critical period (T0)–for site Class B, T0¼4.0 s forR¼10–50 km and T0¼2.8 s for R¼50–100 km; for site Class C,T0¼1.0 s for both R¼10–50 km and R¼50–100 km, T0¼3.5 s forR¼100–200 km; for site Class D, T0¼1.8 s for both R¼10–50 kmand R¼50–100 km, T0¼3.5 s for R¼100–200 km–the momentmagnitude has a significant effect on the median DMFa, and thevalues of T0 for the median DMFa and median DMFd are similar.Further, the influence of moment magnitude on the DMFa

increases when damping ratios and periods increase (forx¼3.5% and 40%, not shown in the plots). Considering the ratioof the median DMFa for Mw46.5 to the median DMFa forMw¼5.5–6.5 corresponding to x¼20% at the given site class andclosest distance, the minimum values of the median DMFa are0.37 for site Class B, 0.39 for site Class C and 0.51 for site Class D.So the effect of moment magnitude on the median DMFa is moresignificant than that on the median DMFd. For ToT0, the median

Fig. 26. Variation of median DMFa for x¼20% with closest dis

Fig. 25. Variation of median DMFa for x¼20% with moment magnitude for site

Class E and R¼50–100 km.



DMFa for Mw¼5.5–6.5 and Mw46.5 are generally quite close forsite Classes B–D. Fig. 25 shows the moment magnitude only has alittle effect on the median DMFa for site Class E. In brief, the effectof moment magnitude on the median DMFa derived from siteClass C is most prominent among four site Classes when theclosest distance is closer than 100 km. The median DMFa are moresensitive to earthquake magnitude than the median DMFd.


Figs. 26–29 show the variation of the median DMFa for x¼20%with closest distance corresponding to site Classes B–E, respec-tively. From Fig. 26, for Mw¼5.5–6.5, the median DMFa forR¼10–50 km are slightly lower than those for R¼50–100 kmwhen periods are longer than 2.0 s. But for Mw46.5, the curvesare inverted. Fig. 27(a) shows that the median DMFa forboth R¼10–50 and 50–100 km are closer to unity than thosefor R¼100–200 km when periods are greater than about 1 s,whereas the median DMFa for both R¼10–50 and 50–100 kmare very close. Fig. 27(b) indicates the median DMFa for R¼

10–50 km are generally highest with T¼1.0–6.0 s while themedian DMFa for R¼50–100 and 100–200 km are similar,and the similar results can be obtained from Fig. 28(b) forT¼2.0–6.0 s. Fig. 28(a) shows, in most cases, the median DMFa

slightly decrease with increasing closest distance. For site Class E,the results derived from Fig. 29 are similar to those derived fromFig. 9 for DMFd.


Figs. 30 and 31 show the variation of the median DMFa forx¼20% with site conditions for Mw¼5.5–6.5 and Mw46.5,

tance for site Class B: (a) Mw¼5.5–6.5 and (b) Mw46.5.

tance for site Class C: (a) Mw¼5.5–6.5 and (b) Mw46.5.

tance for site Class D: (a) Mw¼5.5–6.5 and (b) Mw46.5.

Fig. 29. Variation of median DMFa for x¼20% with closest distance for site Class E (a) Mw¼5.5–6.5, (b) Mw46.5

Fig. 30. Variation of median DMFa for x¼20% with site conditions for Mw¼5.5–6.5: (a) R¼10–50 km, (b) R¼50–100 km, and (c) R¼100–200 km.

Fig. 31. Variation of median DMFa for x¼20% with site conditions for Mw46.5: (a) R¼10–50 km, (b) R¼50–100 km, and (c) R¼100–200 km.


respectively. From Fig. 30, for Mw¼5.5–6.5, the median DMFa arethe highest for site Class C and, in most cases, the lowest for siteClass E. However, the median DMFa for site Classes C–E are closeto each other when R¼100–200 km. From Fig. 31, for Mw46.5,the effect of site conditions on the median DMFa can be neglectedexcept for site Class B corresponding to R¼10–50 km where themedian DMFa for site Class B are higher than those for the otherthree site classes when periods are longer than 1.2 s. In brief, theeffect of site conditions on the median DMFa decreases withincreasing earthquake magnitude and closest distance.

4.4. Summary of results

The following can be obtained from the above-mentionedthree sub-sections:

(1)
Except for soft soil sites, moment magnitude has a moresignificant effect on the median DMF than closest distanceand site conditions. Furthermore, the effect of momentmagnitude on the median DMFa is most prominent, thesecond for the median DMFd and the lowest for the median

Fig.DMF


DMFv. For example, For x¼20%, the median DMFa for lower-magnitude earthquakes are notably greater than unity withincreasing periods while those for larger-magnitude earth-quakes are in most cases smaller than unity.

(2)
It is a clear trend that the median DMF for x45% greatlyreduce with increasing moment magnitude except for soft soilsites. Furthermore, For site Class C and D, moment magnitudehas a significant effect on the median DMF for T4�1.0 s(when R¼10–100 km)/T4�3.5 s (when R¼100–200 km).For rock sites, the median DMF forx45%, in most cases,reduce with increasing moment magnitude for T43.0–4.0 s.For soft soil sites, the moment magnitude usually has only alittle effect on the median DMF.
(3)
The effect of closest distance on the median DMF does notdisplay a consistent pattern. For rock sites, in particular, theeffect of closest distance is more apparent for larger-magni-tude than lower-magnitude earthquakes except for shortperiods. For soft soil sites, the closest distance has apparenteffect on the median DMFd and DMFa only when Mw¼5.5–6.5and T4�4.0 s, otherwise the closest distance has little effecton the median DMFd, DMFv and DMFa. For site Classes C andD, the median DMF are similar for closest distance from 10 to100 km while the median DMF reduce for lower-magnitudeearthquakes when the closest distance is greater than 100 km.
(4)
The effect of site conditions on the median DMF does notfollow a systematic trend. The influence of site conditionsis more significant for lower-magnitude earthquakes thanfor larger-magnitude earthquakes when T¼1.0–6.0 s. ForMw¼5.5–6.5 and R¼10–100 km, the median DMF computedfrom site Class C are generally closest to unity while thosederived from site Class E are the highest (for xo5%)/lowest(for x45%); For Mw46.5 and R¼10–50 km, the medianDMFv and DMFa computed from site Class B are the closestto unity while those derived from site Class E are the lowest(for x45%), and the median DMFd for site Class B are slightlyclosest to unity while those for site Classes C–E are similar.For Mw46.5 and R¼50–100 km, the DMFv computed fromhigh damping ratios are the highest for site Class B. For therest, the effect of site conditions usually can be neglected.
(5)
For given damping ratios, the peak (for xo5%)/dip (forx45%) values of the median DMF are almost not changedregardless of moment magnitude, site conditions and closestdistance. Besides, it should be point out that, for soft soil sites,the effects that the moment magnitude and closest distance
32. Variation of median DMF for T¼2.0 s with damping ratio for different moment mag

v and (c) for DMFa.

have on the median DMF are not obvious, and the medianDMF for high damping ratios are smaller than unity.

5. Discussion and comparsion with other studies

Bommer and Mendis [19] showed the DMFd reduced withincreasing earthquake magnitude for sites located at rock, whichis basically consistent with the results for site Classes B–D in thispaper. Cameron and Green [20] classified ground motion recordedas rock motions (site Classes A–C in the NEHRP [13]) and soilmotions (site Classes D–E in the NEHRP [13]), and showed thatthe DMFd for lower magnitude earthquakes were closer to unitythan those for larger-magnitude events. However, it can bereferred that the effect of moment magnitude on the DMFd forsite Class E was not specially considered in [20]. However, for siteClass E, the authors show that the moment magnitude has lessinfluence on the median DMF, and that the variation of themedian DMF with moment magnitude does not display a con-sistent pattern (see Figs. 5, 15 and 25). It should be pointed outthat the ground motion records for site Class E are mainly fromthe 1999 Chi-Ch, Taiwan earthquake just as stated in part ofSection 3.

Considering the important effect of moment magnitude andvarious damping ratios, Figs. 32 and 33 show the variation of themedian DMF for T¼2.0 and 6.0 s with damping ratio for differentmoment magnitude ranges located at site Class C and R¼

50–100 km, respectively. For intermediate and long responseperiods, the influence of moment magnitude on the median DMFa

increases with increase in the damping ratio, whereas theinfluence of moment magnitude on the median DMFd and DMFv

only vary a little with increasing damping ratio when dampingratios are greater than 25%. Considering the dependence of themedian DMF on periods reduces with increasing moment magni-tude, Fig. 34 shows the variation of median DMF for larger-magnitude events with damping ratio corresponding to T¼2.0,4.0 and 6.0 s located at site Class C and R¼50–100 km. As can beseen, for intermediate and long period range, the median DMFd

weakly depend on periods while the median DMFa still stronglydepend on periods, whereas the median DMFv depend on periodsto a certain extent. On the other hand, the DMF recommended inthe EC [11] and NEHRP [12–13] only depend on damping ratioswhen periods longer the lower limit of the period of the constantspectral acceleration branch, which is similar to the result about

nitude ranges located at site Class C and R¼50–100 km: (a) for DMFd, (b) for

Fig. 33. Variation of median DMF for T¼6.0 s with damping ratio for different moment magnitude ranges located at site Class C and R¼50–100 km: (a) for DMFd, (b) for

DMFv, and(c) for DMFa.

Fig. 34. Variation of median DMF for larger-magnitude events with damping ratio corresponding to T¼2.0, 4.0 and 6.0 s located at site Class C and R¼50–100 km: (a) for

DMFd, (b) for DMFv, and(c) for DMFa.


the median DMFd for larger-magnitude earthquakes. However,the period-dependence of the DMF should be adopted for lower-magnitude earthquakes according to the results in this paper. Itshould be notice that the same expression for the DMF is adoptedin the EC [11] although two types of spectra (Type 1 for regions ofhigh seismicity and Type 2 for regions where surface-wavemagnitude not greater than 5.5) are adopted, which maybe implythat significant errors may be introduced if the period-indepen-dence of the DMF are used for lower-magnitude earthquakes. Sothe authors contend the DMF in seismic codes may be betterconvincing when the effect of moment magnitude is taken intoaccount.

For x45%, the median DMFd and DMFa computed from siteClasses B and E slightly increase with increasing closest distancewhen periods are longer than about 3.0 s (see Figs. 6, 26(a) and29(a)), which is incompatible with the conclusion in [19]. Theresults should be interpreted with some caution due to the follow-ing reasons: (I) the ground motion records for the Groups 2, 9 and10 in the Table 1 were almost obtained from the 1999 Chi-Ch,Taiwan earthquake, which obviously lacks representative; (II) Leeet al. [30] showed that the ground motion records from the 1999Chi-Ch, Taiwan earthquake are unreliable because of their poor

quality. For example, these records were excluded by Campbelland Bozorgnia [29] when they developed a new empirical groundmotion model based on the NGA database. So far no unanimousagreement has yet been reached about the effect of closestdistance on the DMF [19,20,22]—partly because different earth-quake records and research methods were utilized by differentscholars, and partly because the effect of closest distance on theDMF is complex. However, the authors consider that the peakground accelerations of ground motions recorded from lower-magnitude earthquakes at closest distance greater than 100 kmare very small; therefore, our interest for lower-magnitude earth-quakes should mainly focus on closest distance closer than100 km. Consequently, the effect of closest distance generallycan be neglected except for rock sites.

Expressions proposed by Lin and Chang [16] indicated themean DMFd and DMFa for site Class C are generally slightlygreater than those for site Classes AB and D (Fig. 35), which isonly applicable to lower-magnitude earthquakes with closestdistance closer than 100 km in this paper. It should be pointedout that the influence of moment magnitude was not consideredin [16]. However, expressions derived from Hatzigeorgiou [22]showed that the proposed DMFd and DMFv for rock site are closer

Fig. 36. Variation of the proposed DMF in [22] for site Classes A, B, C and D based on the United States Geological Survey (USGS): (a) for DMFd and (b) for DMFv.

Fig. 37. Variation of the median DMFd for site Classes B–E without considering the

influences of moment magnitude and closest distance.

Fig. 35. Variation of the proposed DMF in [16] for site Classes AB, C and D based on NERHP [12]: (a) for DMFd and (b) for DMFa.


to unity than those for soil site (Fig. 36). However, as can be seenfrom Table I–IV in [22], the median PGA are 0.14 g for rock site,0.27 g for very dense soil site, 0.27 g for stiff soil site and 0.18 g forsoft soil, which may be further inferred that moment magnitudeselected by Hatzigeorgiou for rock site is lower than that for soilsite, whereas the median DMF for lower-magnitude earthquakesshould be closer to unity than those for larger-magnitude earth-quakes according to the results in this paper. So the results fromHatzigeorgiou would be better convinced if the effect of momentmagnitude had been considered. Lin [31] showed the proposedDMFd computed from larger-magnitude 1999 Chi-Chi earthquakeare lower for site Class III (i.e., soft soil, in accordance withTaiwan’s seismic design provision for buildings with isolationsystems [32]) than for the other site classes when periods longerthan 2.0 s, which has certain differences from the result that theinfluence of site conditions on the median DMFd is generally notobvious for larger-magnitude earthquakes in this paper. Besides,Bommer and Mendis [19] discussed the effect of site condi-tions on the DMF based on the predictive equations, and aclear trend cannot be obtained. It is worthwhile to note thatmoment magnitude and closest distance were not furtherclassified when the effect of site condition was investigated in

the above researches [16,19,22,31]. Similarly, Fig. 37 shows thevariation of the median DMFd for site Classes B–E provided that theinfluences of moment magnitude and closest distance are notconsidered. It is very interesting to note the clear trend that themedian DMFd reduce with site classes from rock to soft soil exceptfor short periods. Similar results, not shown in this paper, have beenobtained for DMFv. However, considering the conclusion in thepaper that moment magnitude usually has a significant effect on themedian DMF and the influence of closest distance sometimes cannotbe neglected, so it is more convincing that the effect of siteconditions should be discussed for the given ranges of momentmagnitude and closes distance. As a result, the effect of site class forlower-magnitude earthquakes is more significant than that for larger-magnitude earthquakes when the different ranges of moment mag-nitude are considered, and other detail achievements can be seenin the above Section 4.4(4) in this paper.

Besides, Bommer and Mendis [19] showed that the durationof ground motions is the underlying cause of the variation ofthe DMF, whereas strong-motion duration is generally notfound to be strongly dependent on site classification which isclassified only by the nature of the uppermost layers at the site[33]. In the NGA database, the classification of ground motionsrecorded is determined based on the average shear-wavevelocity of the upper 30 m profiles (Vs30), which maybe partlyinterpret the lack of clear trend for the influence of classifica-tion on the DMF. In addition, the complex communicationmedia of ground motions and different earthquake rupturetypes (e.g., bilateral and unilateral ruptures [34]) maybe, tosome extent, affect response spectra, and further make theinfluences of seismological parameters on the DMF complex.

6. Conclusions

This paper investigated the effects of seismological parameters onthe median DMF. Then the results are discussed and compared withexisting achievements. Near-source ground motions (i.e. closest


distance is closer than 10 km) are not included in this paper and assuch the conclusions presented below are not applicable to suchconditions. The key conclusions in this paper are as follows:

(1)
The effect of site class is more significant for lower-magnitudeearthquakes than for larger-magnitude earthquakes while,except for rock sites, the effect of closest distance generallycan be neglected with closest distance closer than 100 km.The minimum values of the median DMF for high dampingratio nearly remain unaffected by seismological parameters.
(2)
For site Classes B–D in accordance with the NEHRP 2003Provisions, Moment magnitude has a more significant effecton the median DMF than closest distance and site conditionswhile these seismological parameters have more significanteffects on the median DMFa than those on DMFd and DMFv.For larger-magnitude earthquakes, the structural displace-ment and velocity responses can be effectively controlled byadding damping while the structural acceleration responsesometimes increases when damping ratios are greater than20%. For example, for x¼20%, the median DMFa for T4�3.4 sare greater than unity when sites located at rock with closestdistance closer than 50 km. It is noteworthy for lower-magnitude earthquakes that the acceleration response of thebase-isolated structures and structures with supplementarydamping devices maybe increase if the adding dampingdevices are too much although the displacement and velocityresponses are effectively controlled.
(3)
For site Classes B–D in accordance with the NEHRP 2003Provisions, the dependence of the median DMF on periodsreduces with increasing moment magnitude. For lower-magni-tude earthquakes, the median DMFd and DMFv become closer tounity with increasing period. However, for larger-magnitudeearthquakes, the median DMFd are nearly independent ofperiods in the intermediate and long period range while themedian DMFa still strongly depend on periods, whereas themedian DMFv depend on periods to a certain extent.
(4)
For soft soil sites, the median DMF only vary a little withmoment magnitude and closest distance. Further, the medianDMFd and DMFa are nearly independent of periods in theintermediate and long period range while the median DMFv
are also nearly independent of periods in the intermediateperiod rang and dependent on periods in the long periodrange to a certain extent. Besides, for base-isolated structuresand structures with supplementary damping devices, thestructural displacement, velocity and acceleration responsescan be effectively controlled by adding damping.

Acknowledgements

The authors greatly acknowledge the support for this study bythe Key Projects in the National Science & Technology PillarProgram (Grant no. 2009BAJ28B00). We would like to expressour sincere appreciation to the anonymous reviewers for theirinsightful comments, which have greatly aided us in improvingthe quality of the paper.

Appendix A. Supplementary material

Supplementary data associated with this article can be foundin the online version at doi:10.1016/j.soildyn.2011.05.002.

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