Assessment of Site Amplification Effect from Input Energy Spectra of Strong Ground Motion

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1 Assessment of Ste Amplfcaton Effect from Input Energy Spectra of Strong Ground Moton M.S. Gong & L.L Xe Key Laboratory of Earthquake Engneerng and Engneerng Vbraton,Insttute of Engneerng Mechancs, CEA, Harbn J. Sun Insttute of Cvl Engneerng, Helongjang Unversty, Harbn SUMMARY: To analyze and estmate the amplfcaton effect of dfferent sol stes, the nput energy spectra of strong ground motons at dfferent stes ncludng bed rock, very dense sol and stff sol are computed, and the attenuaton law of nput energy spectra s regressed and obtaned by usng two-stage nonlnear regresson method. The mean nput energy spectra for a gven magntude and dstance for dfferent stes are computed from the attenuaton law, and the nput energy spectra ratos between dfferent sol stes and rock ste are calculated and analyzed. It s found that the mean amplfcaton factors are 1.66 and.43 from the very dense sol and stff sol stes to rock ste respectvely n a wde range of perods. The results of the paper can be referenced by the sesmc hazard analyss, sesmc regonalzaton and related works. Keywords: ste amplfcaton effect, strong ground moton, nput energy spectra, attenuaton law 1. INSTRUCTION The strong ground moton s the basc materal for sesmc desgn n the feld of earthquake engneerng. It s well known that the strong ground moton characterstcs are nfluenced greatly by the ste condtons (Lu et al, 008), and n general, the strong ground moton s amplfed by sol stes. However, the strong ground moton s affected by many parameters such as magntude, source to ste dstance, propagaton medum, etc. The characterstcs of these factors are usually studed by usng attenuaton law for strong ground moton parameters, such as peak ground acceleraton, peak velocty, response spectra and so on. However, such parameters mentoned above are essentally ndependent of the duraton of the strong ground moton. It s wdely held that the duraton plays some mportant role n producng cumulatve damage to structures. The nput energy spectra, establshed by Uang and Bertero (1990), characterze the duraton very well, and are consdered as a convenent sngle-parameter descrptor of strong ground moton duraton and ampltude. Based on 304 strong ground moton records, Chapman (1999) establshed the attenuaton relatonshp of the elastc absolute nput energy spectra, that s, he dd not consder the effect of ductlty. As we all know, structures are generally put nto non-lnear state under the acton of strong ground moton. That s to say, the ductlty must be taken nto account. Chou and Uang (000) establshed the attenuaton model for absorbed energy spectra from the vew of structure damage and they consdered the absorbed energy as the ndex of structure damage, and they also analyzed the effects of ste condtons on absorbed energy spectra from the attenuaton law. In order to analyze the effect of ste condtons, the attenuaton law of strong ground moton nput energy spectra s obtaned by usng two-stage regresson method wth nonlnear Gauss-Newton estmaton based on 66 strong moton records. However, accordng to the study of Uang and Bertero (1990), there are two knds of nput energy spectra, ncludng absolute nput energy spectra and relatve nput energy spectra, and they are very dfferent when the perod of Sngle-Degree-Of-Freedom (SDOF) system s very short or very long. As we all know, the perod of a real structure s often not very long, so dfferences between the two knds nput energy need to be compared necessarly. In ths study, the attenuaton law of the two knds nput energy s nvestgated,

2 and the two knds of nput energy spectra, ncludng absolute and relatve nput energy spectra, are obtaned for a gven magntude and dstance from the attenuaton law. The authors had dscussed the attenuaton of nput energy spectra (Gong et al, 005; 009), so n the paper, the two knds of energy spectra are compared, and the mean effects of sol ste on nput energy spectra are analyzed. Some remarkable conclusons are obtaned at last.. STRONG GROUND MOTION RECORDS A total number of 66 strong ground moton records from 15 sgnfcant earthquakes n Calforna of Amerca are used for the analyss (Gong et al, 005), and each record ncludes two mutually perpendcular and a vertcal corrected acceleraton tme hstores. Heren, the geometrc mean of energy spectra calculated from the two horzontal components of each record s used for the analyss. The local ste condton of each record s classfed based on the average shear-wave velocty (V s ) over up to 30 meters n depth from the ground surface as shown n Table 3.1. Ste classes A (hard rock) and B (rock) are combned to one knd of ste condton for the analyss because the shortage of strong moton records (Chou and Uang, 000). Moreover, the very dense sol and stff sol mean and respectvely as shown n Table 3.1, and three knds of stes condtons are analyzed n the paper,.e., and. The data dstrbuton wth the relatonshp between magntude (M) and fault dstance (D) s shown n Fgure.1. It can be seen that there s some dependence between the magntude and dstance whch presents a tendency that the data of large magntude, long dstance and small magntude, short dstance are more than the data wth large magntude, short dstance and small magntude, long dstance. Ths knd of dependence could affect the regresson results, and n order to avod the effect of dependence on the coeffcents, the two-stage regresson method s adopted for the analyss. Table 3.1. lassfcatons (Chou and Uang, 000) NEHERP General Descrpton V s (m/s ) Ths Study A Hard rock V s 1500 A+B B Rock 1500 V s 760 A+B C Very dense sol and soft rock 760 V s 360 C D Stff sol 360 V s 180 D E Sol V s 180 / F Lquefable sols, senstve clays, collapsble cemented sols V s 180 / M M M D/km (a) (35) D/km (b) (94) D/km (c) (137) Fgure.1. Dstrbuton of the strong ground moton records

3 3. INPUT ENERGY SPECTRA Two knds of nput energy spectra, absolute and relatve energy spectra, are adopted n the paper. For a vscous damped Sngle-Degree-Of-Freedom (SDOF) system subjected to a horzontal strong ground moton, the dfferental equaton of moton can be expressed as the followng Eqn v cv fs 0 (3.1) m t Where m s the mass of SDOF system, v t (v t =v+v g, v g s the dsplacement of ground) s the absolute dsplacement of the system, v s the relatve dsplacement of the system respect to the base, c s the vscous dampng coeffcent, and f s s the restorng force. Substtutng v t =v+v g nto Eqn. 3.1, t can be rewrtten as the followng Eqn. 3.. mv cv f m (3.) s v g Therefore, the structural system under the exctaton of ground moton can be equvalent to the system wth fxed base and subjected to an effectve horzontal dynamc force wth magntude of mv. g Although both systems gve the same relatve dsplacement, two knds dfferent energy response defntons, absolute and relatve nput energy, can be derved from Eqn. 3.1 and Eqn. 3. respectvely (Uang and Bertero, 1990). The equatons of absolute and relatve nput energy can be expressed as the followng Eqn. 3.3 and Eqn Absolute nput energy: E mv dv (3.3) a t g Relatve nput energy: E r g mv dv (3.4) The absolute nput energy defnton as Eqn. 3.3 shows s physcally meanngful n that the term mv t represents the nerta force acted on the system. The force, whch s equal to restorng force plus dampng force, s the same as the total force acted on the system foundaton. Therefore, the E a represents the work done by the total base shear at the foundaton on the foundaton dsplacement v g. The relatve nput energy defnton as Eqn. 3.4 shows physcally represents the work done by the equvalent force mv on relatve dsplacement of the equvalent fxed-base system. g The nput energy equvalent velocty whch s defned by Uang and Bertero (1990) s adopted for the analyss n order to elmnate the effect of mass and analyze convenently because the defnton ncludng the unt are consstent wth velocty. The nput energy s converted to an equvalent velocty by the followng Eqn. 3.5 and Eqn V E m (3.5) a a V E m (3.6) r r In ths way, the absolute and relatve nput energy spectra can be obtaned by calculatng the response of Sngle-Degree-Of-Freedom (SDOF) systems wth dfferent perods. The author had analyzed the attenuaton law of the constant-ductlty nput energy spectra wth dfferent ductlty level (Gong et al, 005). In the paper, to analyze the effects of stes on nput energy spectra, the two knds of nput

4 energy equvalent velocty, V a and V r, of elastc SDOF system wth 5% dampng rato n the perod (marked as T) range 0.1 to 3.0 second are consdered and analyzed, for the effects of stes on elastc energy spectra and nelastc energy spectra are very smlar accordng to the authors study before. 4. ATTENUATION MODEL To select a proper attenuaton model s an mportant work n the attenuaton study of strong ground moton parameters. The model must be physcally meanngful, and also makng the regresson error to be small. The followng regresson model proposed by Boore et al (1993) as Eqn. 4.1 shows s ftted to the nput energy equvalent velocty V a and V r. lgy 1/ a b( M 6) c( M 6) d lg( D h ) eg fg (4.1) c d r e where Y, M and D are the response varable (geometrc mean of the two horzontal components), moment magntude and fault dstance respectvely of the -th strong ground moton record. G c and G d are the ste effect factors of the -th record (G c =1 for and zero otherwse; G d =1 for and zero otherwse). For each perod T, unknown coeffcents a, b, c, d, e, f, h, and varance lgy of random errors r and e are determned usng the two-stage regresson procedure. The most common method to solve the coeffcents of attenuaton model s the two-stage regresson procedure orgnally proposed by Joyner and Boore (1993). The method s proposed because there s some dependence between the magntude and dstance as shown n Fgure.1. If the coeffcents of magntude, dstance, and local ste are solved smultaneously, errors n measurng the magntude would affect the other coeffcents. However, n the two-stage analyss procedure, the coeffcents of magntude M and dstance D are solved separately and successvely, and the method can be vewed as a remedy to decouple the dependence between magntude and dstance through ntroducng the dummy varables. In the study, the two-stage regresson analyss wth Gauss-Newton method s adopted to determne the unknown coeffcents of the attenuaton model Eqn. 4.1, and the coeffcents could be found n the authors other paper (Gong et al, 005). 5. RESULT ANALYSIS 5.1. Results of absolute nput energy spectra V a Accordng to the above attenuaton model, the nput energy spectra can be computed for the gven magntude and dstance. For example, the absolute energy spectra V a for M=7.0 and D=5.0km on three knds of stes are shown n Fgure 5.1(a). To estmate the amplfcaton of sol ste, the energy spectra ratos of sol stes to rock ste are calculated and shown n Fgure 5.1(b). From Fgure 5.1, t can be concluded that the ste class has a sgnfcant effect on absolute nput energy spectra V a, and the absolute nput energy spectra V a of and are much hgher than that of for a gven perod, magntude and dstance. The amplfcaton of absolute nput energy spectra V a from to and s shown n Fgure 5.1(b). It can be observed that the mean ncrease of V a s about 66.7% and 151.6% for and respectvely for all the perods. That s to say, the strong moton ground moton s amplfed about 1.67 tmes and.5 tmes for and respectvely compared wth rock ste. The maxmum ncrease of V a s about 79.6% and 19.1% for and respectvely at perod 1.8s, and the amplfcaton coeffcents are a lttle bt small for the short perods (T<0.3s) as shown n Fgure 5.1(b). Furthermore, the amplfcaton factor s same for other magntude and dstance because the effect of sol ste n Eqn. 4.1 only depends on the factor e and f for and respectvely. The concluson can be proved by usng the exponent transformaton to the both sdes of Eqn. 4.1 and then

5 calculatng the rato of dfferent ste condtons to. V a (cm/s ) V a /V a(a+b) (a) Absolute nput energy spectra (M=7.0, D=5.0km) (b) Spectra rato to rock ste (M=7.0, D=5.0km) Fgure 5.1. Effects of ste condtons on absolute nput energy spectra V a 5.. Results of relatve nput energy spectra V r The effect of ste class on relatve nput energy spectra V r s very smlar to that on absolute nput energy spectra V a as Fgure 5. shows. Fgure 5.(a) shows the relatve energy spectra for M=7.0 and D=5.0km on three knds of ste classes and Fgure 5.3(b) shows the amplfcaton factors for dfferent perod. From Fgure 5., we can see that V r spectra of and are much hgher than that of for a gven perod, magntude and dstance. It can be observed that the mean ncrease of V r s about 65.4% and 134.4% for and respectvely for all the perods. It means that the strong moton ground moton s amplfed about 1.65 tmes and.34 tmes for and respectvely compared wth rock ste. The maxmum ncrease of V r s about 79.% and 174.5% for and respectvely at perod 1.8s as shown n Fgure 5.(b). As same as absolute energy spectra, the amplfcaton factor s same for other magntude and dstance because the effect of sol ste n Eqn. 4.1 depends on the factor e and f for and respectvely. Consderng the two knds of nput energy spectra V a and V r together, the average amplfcaton factors are 1.66 and.43 from the and to ste A+B respectvely from the pont of nput energy spectra. That means the ste condtons must be consdered very well when the ste sesmc hazard analyss, structural sesmc desgn and related works are carred out. V r (cm/s) (a) Relatve nput energy spectra (M=7.0, D=5.0km) V r /V r(a+b) (b) Spectra rato to rock ste (M=7.0, D=5.0km) Fgure 5.. Effect of ste condtons on relatve nput energy spectra V r

6 5.3. Comparson of two knds of nput energy spectra Uang and Bertero (1990) had already explaned, the absolute nput energy spectra and relatve nput energy spectra are very dfferent at the very short or very long perod range by usng sngle strong moton record. The dfferences of absolute nput energy spectra V a and relatve nput energy spectra V r constructed from the attenuaton model are compared n the study as shown n Fgure 5.3. It can be observed that the absolute nput energy spectra V a are almost equal to the relatve nput energy spectra V r at perods n the range of s for all the ste classes (for, the cross pont of two knds of nput energy spectra s at around 0.6s, for, the cross pont s at around 0.7s, and for, the cross pont s at around 1.1s). The absolute nput energy spectra V a s much larger than relatve nput energy spectra V r n very short perod range and some less than relatve nput energy spectra V r n long perod range. The dfference trend s smlar as the results computed by usng sngle strong ground moton, for the attenuaton law s obtaned from large number of energy spectra of strong ground motons. The dfference between absolute and relatve nput energy spectra for sngle strong ground moton must result n the smlar dfference trend between the two knds of energy spectra constructed from the attenuaton law. The nput energy spectrum s the most mportant parameter of strong ground moton, and t should be the most approprate parameter for structure sesmc desgn, sesmc hazard analyss and related works. However, consderng almost all of the sesmc desgn methods are based on strength presently, the sesmc desgn method based on energy s stll needed to be studed and dscussed n future, and there are too many scentfc and techncal problems needed to be solved urgently. If the nput energy were adopted as a parameter for sesmc desgn and smlar works, the dfference between absolute nput energy spectra and relatve nput energy spectra n short and long perod range should be consdered very well by the sesmc engneers, earthquake engneerng researchers and structure desgners. V a or V r (cm/s ) V a Spectra V r Spectra Fgure 5.3. Comparson of V a and V r spectra (M=7.0, D=5.0km) 6. CONCLUSIONS The effects of ste condtons on two knds of nput energy spectra constructed from attenuaton law are analyzed, and the dfferences between the absolute and relatve nput energy spectra are compared n the paper. The man conclusons are summarzed as below. (1) The absolute nput energy spectra of strong ground moton s amplfed approxmately about 1.67 tmes from to, and.5 tmes from to n the perod range s, and the components wth perod of 1.8s are amplfed maxmally about 1.80 tmes and.9 tmes for and respectvely.

7 () For the relatve nput energy spectra, they are amplfed approxmately about 1.65 tmes from Ste C to, and.34 tmes from to n the perod range s, and the components wth perod of 1.8s are amplfed maxmally about 1.79 tmes and.75 tmes for and respectvely. (3) The ste class has sgnfcant effect on strong ground moton, and almost all components of dfferent perods are amplfed by sol ste, and the mean amplfcaton factors are 1.66 and.43 for very dense sol ste () and stff sol () ste from the drecton of nput energy spectra. The ste condtons must be consdered very well n the work of sesmc hazard analyss, sesmc regonalzaton, and other related sesmc dsaster reducton programs. (4) The absolute nput energy spectra are almost equal to relatve nput energy spectra at perods n the perod range of around s for all the ste classes, but much larger than relatve nput energy spectra n very short perod range, and less than relatve nput energy spectra n long perod range. The smlar pont s that the peak values of absolute nput energy spectra and relatve nput energy spectra appear at the perod around 0.5 second for all the ste classes. AKCNOWLEDGEMENT The work s supported by Natonal Key Technology R&D Program of Chna under Grant No. 009BAK55B01, Natonal Natural Scence Foundaton of Chna under Grant No , Natural Scence Foundaton of Helongjang under Grant No. QC010005, and Scentfc Research Starng Foundaton for the Returned Overseas Chnese Scholars. The supports are gratefully apprecated. Moreover, the authors would lke to acknowledge Prof. Cha-Mng Uang at Unversty of Calforna for provdng the processed strong ground moton records and the constructve suggestons for the paper. REFERENCES Boore, D.M., Joyner, W.B., and Fumal, T.E. (1993). Estmaton of response spectra and peak acceleraton from western North Amercan earthquakes: An nterm report. U.S. Geol. Survey Open-Fle Report, Chapman, M.C. (1999). On the use of elastc nput energy for sesmc hazard analyss. Earthquake Spectral. 15:4, Chou, C.C., and Uang, C.M. (000). Establshng absorbed energy spectral-an attenuaton approach. Earthquake Engneerng and Structural Dynamcs. 9:10, Gong M.S. Xe L.L, and Sun J. (009). Effect of ondton on Input Energy Spectra of Strong Ground Moton. Journal of Harbn Insttute of Technology, 16:S1, Gong, M.S., and Xe, L.L. (005). Study on comparson between absolute and relatve nput energy spectra and effects of ductlty factor. ACTA Sesmologca Snca. 18:6, Joyner, W.B., and Boore, D.M. (1993). Method for regresson of strong-moton data. Bulletn of the Sesmologcal Socety of Amerca. 83:, Lu Y.J., et al. (008). Some key problems about ste effects on sesmc ground moton parameters. Technology for Earthquake Dsaster Preventon. 3:, Uang, C.M., and Bertero, V.V. (1990). Evaluaton of sesmc energy n structures. Earthquake Engneerng and Structural Dynamcs. 19:1,