Directivity effect of the 2016 Kumamoto Earthquake on both the ground motion and the damage of wooden house

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1 Dirctivit ffct of th 216 Kumamoto Earthquak on both th ground motion and th damag of woodn hous *Haato Nishikawa 1) and Tomia Takatani 2) 1), 2) Nat l Institut of Tchnolog, Maizuru Collg, Maizuru, Koto , Japan 2) takatani@maizuru-ct.ac.jp ABSTRACT In th 216 Kumamoto Earthquak, a trmndous damag for a Japans-stl traditional framd-basd woodn hous occurrd in Mashiki town, whr th Japan Mtorological Agnc sismic intnsit of 7 lvl succssivl obsrvd twic. Th ruptur propagation ffct of a sismic fault, that is, th dirctivit ffct ma b on of som primar factors causd a grat damag to woodn hous. In this papr, ground motions at locations around this sismic fault in th 216 Kumamoto Earthquak wr analticall valuatd b th mpirical Grn s function mthod, and th ffct of th dirctivit ffct of sismic fault on not onl th ground motion but also th maximum drift angl of woodn hous rprsnting its sismic damag was invstigatd. Morovr, th ffct of th bas shar cofficint of woodn hous on its maximum drift angl was valuatd in ordr to prdict th sismic damag of woodn hous against a strong arthquak ground motion. 1. INTRODUCTION A trmndous sismic damag of collaps to woodn hous was causd b th 216 Kumamoto Earthquak occurrd on both April 14 (M JMA =6.) and 16 (M JMA =7.3) (Building Rsarch Institut, 216). In particular, Mashiki town locatd at nar th hpocntr of ths arthquaks has twic arthquak ground motions with th Japan Mtorological Agnc sismic intnsit of 7 lvl succssivl. In this arthquak, th ruptur of a sismic fault propagatd toward th northast dirction from its hpocntr, and thn th ruptur propagation ffct of th sismic fault, that is, th dirctivit ffct ma b on of som primar factors causd a grat damag to woodn structur. In this papr, th ground motions around this sismic fault causd in th 216 Kumamoto Earthquak ar analticall valuatd b th mpirical Grn s function mthod, and th influnc of th dirctivit ffct of sismic fault on not onl th ground motion but also th maximum drift angl of woodn hous rprsnting its sismic damag is invstigatd in dtail. Morovr, th ffct of th bas shar cofficint of woodn hous on its maximum drift angl is valuatd in ordr to prdict th sismic damag of woodn hous against a strong arthquak ground motion.

2. ESTIMATION OF SEIMIC GROUND MOTION 2.

In this stimation procdur, sismic ground motion can b valuatd basd on th sismic fault modl (Nozu, 21

Noz (216) rportd that th vlocit wav rcords at obsrvation points of K-NET and KiK-nt sstms in shown in Fig.1 ar accuratl rproducd b this stimation procdur. Fig. 1 Location of th picntr (star), Fig.

2 2. ESTIMATION OF SEIMIC GROUND MOTION 2.1 Estimation Mthod In this papr, th sismic ground motion around a sismic fault causd in th 216 Kumamoto arthquak is stimatd b th mpirical Grn s function mthod proposd b Nozu t. al (29). In this stimation procdur, sismic ground motion can b valuatd basd on th sismic fault modl (Nozu, 216) with 3 aspritis locatd at th sismic fault indicatd in Fig.1. Ths aspritis ar shown in Fig.2. Noz (216) rportd that th vlocit wav rcords at obsrvation points of K-NET and KiK-nt sstms in shown in Fig.1 ar accuratl rproducd b this stimation procdur. Fig. 1 Location of th picntr (star), Fig. 2 Distribution of aspritis (squar), stations, small vnts, and fault pak slip vlocit, and hpocntr (squar) (Nozu, 216) (star sign) (Nozu,216) In this papr, th sismic ground motions on both th ground surfac lar and sismic bdrock at locations (b1-k) around this sismic fault in th 216 Kumamoto Earthquak shown in Fig.3 ar analticall valuatd b th mpirical Grn s function mthod basd on th sismic fault modl indicatd in Fig.2. Th signs of A1 to A3 illustratd in Fig.3 rprsnt th aspritis 1 to 3, rspctivl. Asprit 1 has th sam location as an stimation point of 3 for sismic ground motion. Sismic ground motion wavs obsrvd at KiK-nt Mashiki location (KMMH16) for th arthquak with M JMA =4.2 occurrd at : AM on April, 216 wr mplod as a Grn s function in th mpirical Grn s function mthod, and also thir motions ar common to thos of locations. In addition, th sit amplification charactristics rquird in th valuation of sismic ground motion on ground surfac lar ar common to all locations. This papr mplod som valus at KiK-nt Mashiki obtaind b Nagasaka and Nozu (216) shown in Fig.4 as a sit amplification ffct. Also, th nonlinarit of ground surfac lar du to a strong arthquak motion is takn into considration b th multi-non-linarit ffct (Nozu and Morikawa, 23) in th valuation of a sismic motion on ground surfac lar.

Amplification factor Fig. 3 Location of valuating sits and aspritis for sismic ground motion 1 1 1.1.1 1 1 Frqunc(Hz) Fig. 4 Sit amplification ffct at KMMH16 2.2 Estimation Rsults Figs.

3 Amplification factor Fig. 3 Location of valuating sits and aspritis for sismic ground motion Frqunc(Hz) Fig. 4 Sit amplification ffct at KMMH Estimation Rsults Figs. and 6 show vlocit wavs at c3, g1, g and j3 points on both th sismic bdrock and th ground surfac, rspctivl. j3 point is locatd at th ruptur dirction of sismic fault, and c3 point is don at th opposit dirction to th ruptur dirction of sismic fault. g1 and g points ar locatd at th prpndicular to th ruptur dirction of sismic fault. Thr is not a significant diffrnc btwn th vlocit amplituds at c3, g1 and g points, and th priods of vlocit wavs at g1 and g locations ar longr than that at c3 point. Pak ground vlocit (hraftr rfrrd as PGV) at j3 point is almost

4 Vlocit(cm/s) Vlocit(cm/s) Vlocit(cm/s) Vlocit(cm/s) Vlocit(cm/s) Vlocit(cm/s) Vlocit(cm/s) Vlocit(cm/s) Tim(s) Tim(s) (1) c3 (2) g Tim(s) Tim(s) (3) g (4) j3 Fig. Bdrock vlocit wavforms calculatd b mpirical Grn s function mthod Tim(s) Tim(s) (1) c3 (2) g Tim(s) Tim(s) (3) g (4) j3 Fig.6 Surfac vlocit wavforms calculatd b mpirical Grn s function mthod

thr tims thos at c3, g1 and g3 points, and th amplitud of puls wav at j3 point is much largr. In th sam mannr as th vlocit wavs on th arthquak bdrock shown in Fig.

5 thr tims thos at c3, g1 and g3 points, and th amplitud of puls wav at j3 point is much largr. In th sam mannr as th vlocit wavs on th arthquak bdrock shown in Fig., PGV at j3 point on th ground surfac indicatd in Fig. 6 is almost thr tims thos at c3, g1 and g3 points. PGV on th ground surfac is almost 1 tims thos on th sismic bdrock. It is found from Figs. and 6 that th sismic wavs at ground surfac ar gratl amplifid with surfac lars on th sismic bdrock. To invstigat th spatial charactristics from PGV valus at locations on both th arthquak bdrock and th ground surfac, Figs.7 and 8 indicats th PGV distribution map of both th arthquak bdrock and th ground surfac. It is found from Fig.7 that PGV valus at th north-ast sid from th Asprit 3 trnd to b largr than othr locations. On th othr hand, PGV valus at th south sid of th sismic fault ar largr than othr locations in comparison with thos on th arthquak bdrock illustratd in Fig.7, and also vn PGV valus at som locations around th Asprit 1 ar ovr 1cm/s. To invstigat th rlationship btwn th ruptur propagation dirction and PGV valu, a rlationship btwn th cosin valu of thta,, shown in Fig.9 and ~cm/s ~1 1~ ~ (1) componnt (2) componnt Fig. 7 Distribution of PGV on sismic bdrock (1) componnt (2) componnt Fig.8 Distribution of PGV on surfac

6 PGV m (cm/s km) PGV m (cm/s km) Fig. 9 Dfinition of cosθ cosθ (1) sismic bdrock (2) surfac Fig. 1 Rlationship btwn cos and PGV m th indx of PGV m multiplid th distanc X from th Asprit 1 b PGV valu is shown in Fig.1. Thta,, can b obtaind from normalizing th compass valu of a masuring point with th ruptur dirction (2 dgrs) of sismic fault. In this papr, th ffct of th distanc attnuation on PGV valu is corrctd b multipling th distanc X b PGV valu. As can b obvious from Fig.9, th smallr th distanc btwn obsrvation point and th ruptur dirction of sismic fault is, th larg PGV valu is. It should b notd that th ffct of th ruptur propagation of sismic fault on PGV valu significantl appars. 3. EFFECT OF RUPTURE PROPAGATION ON WOODEN STRUCTURE RESPOE In this sction, th ffct of th ruptur propagation of sismic fault on th rspons of woodn structur is invstigatd. Th maximum drift angl is usd as an indx valuating th rspons of woodn structur du to sismic motion.

Maximum drift angl R of woodn hous is valuatd b th prformancquivalnt acclration rspons spctrum, which was proposd b Saratani t al. (26) and Haashi t al. (28).

7 Maximum drift angl R of woodn hous is valuatd b th prformancquivalnt acclration rspons spctrum, which was proposd b Saratani t al. (26) and Haashi t al. (28). B a contraction mthod, a two-stor woodn hous is assumd to b a singl dgr of frdom with an quivalnt hight, H, and quivalnt mass, M. Th quivalnt-prformanc acclration rspons spctrum mans an quivalnt rspons spctrum with a sismic prformanc capacit of woodn hous and can b givn b th following quation. S πh R T F (1) 2 a (2 / ) / h whr, S is an quivalnt-prformanc acclration rspons spctrum (m/s 2 ), a H is an quivalnt hight (m) in th contraction sstm from a two-stor woodn hous to a singl dgr of frdom, R is a maximum drift angl, T is an quivalnt priod (s), F is a rduction rat function of acclration rspons spctrum. Th hstrsis h charactristics of woodn hous modl ar assumd to b a bi-linar tp, and th ilding shar forc can b givn b M gc for th maximum drift angl R (=1/1) at ilding stag as shown in Fig.11. T corrsponding to th maximum drift angl R at ilding stag is givn b th following quation..7 (1 9( R / R ) ) /1 R H / C g ( R R ) T 2 RH / C g ( R R ) T (2) is a ratio of an quivalnt mass to actual mass, and C is a ilding shar forc cofficint. Th rduction rat function F and th damping factor h h ar givn b th following quations. Fh 1./ (1 1 h) h..2 ( 1 (1/ R R / )) (4) In this papr, and H ar assumd to b.9 and 4.m, rspctivl, basd on th rsarch papr b Saratani t al.(26). C ar assumd to b.1,.2,.3,.4,.,.6 and S can b calculatd for ths C a valus. (3) Fig. 11 Analsis modl of woodn hous (Haashi t al., 28)

8 Sa, Sa(m/s 2 ) Sa, Sa(m/s 2 ) Sa, Sa(m/s 2 ) Sa.Sa(m/s 2 ) Fig.12 shows th acclration rspons spctrum, S a, and th quivalnt prformanc acclration rspons spctrum, S a obtaind from th sismic motions on ground surfac for th vlocit wavs at four location of c3, g1, g3 and j3. Sa for R =.1,.2,.3,.,.1 and.2 ar indicatd in Fig.12, and an intrsction point btwn S a and S a is th maximum drift angl R. In th componnt of both S a and S a at c3 and j3 locations, th maximum drift angl of c3 location is ovr.1 in C =.2 to.4 and also is largr in C >.. On th othr hand, th maximum drift angl of j3 location is lss than.3 for an C. Th maximum drift angl of.3 mans a larg dstruction of woodn structur. Th maximum drift angl in componnt of both S a and S a is largr than that in componnt. In both and componnts of both S a and S a at g1 and g locations, th maximum drift angl is a larg valu of about.1 in C =.1 and.2, and is.2 to 3 in C >.3. This implis that th sismic damag of woodn structur is rducd b th improvmnt of sismic prformanc of woodn structur itslf R= Priod(s) Sa(C=.1) Sa(C=.2) Sa(C=.3) Sa(C=.4) Sa(C=.) Sa(C=.6) c3 j Priod(s) Sa(C=.1) Sa(C=.2) Sa(C=.3) Sa(C=.4) Sa(C=.) Sa(C=.6) g1 g 2 (1) componnt 2 Sa(C=.1) Sa(C=.1) R=.2 Sa(C=.2) Sa(C=.3) Sa(C=.4) 1 Sa(C=.2) Sa(C=.3) Sa(C=.4).1 Sa(C=.) Sa(C=.6) Sa(C=.) Sa(C=.6) c3 g Priod(s) j Priod(s) g (2) componnt Fig.12 Acclration rspons spctrum and quivalnt prformanc acclration spctrum

9 Fig.13 indicats th maximum drift angl valus for componnt at locations in C =.1 to.6. As can b sn from Fig.11, th maximum drift angl valus at almost all locations in th north sid of sismic fault in C =.1 and.2 ar ovr.7 and ar rd markrs. Th locations with rd markr dcras with an incras of C, and thr is no rd markr in C =. and.6. ~.3.3~..~.7.7~ (1) C =.1 (2) C =.2 (3) C =.3 (4) C =.4 () C =. (6) C =.6 Fig.13 Maximum drift angl R for componnt

10 Fig.14 illustrats th maximum drift angl valus for componnt at locations in C =.1 to.6. Th distribution of th maximum drift angl for componnt is almost th sam tndnc as that for componnt. Thr ar man locations with larg maximum drift angl valu in C >=.4 in comparison with componnt. ~.3.3~..~.7.7~ (1) C =.1 (2) C =.2 (3) C =.3 (4) C =.4 () C =. (6) C =.6 Fig.14 Maximum drift angl R for componnt

11 R R R R Fig. shows th rlationship btwn cosin of and th maximum drift angl, R. Th maximum drift angl, R, in C =.1 to.4 trnds to incras with cosin of. Th maximum drift angl, R, in C =. and.6 ar almost th sam for an cosin of. Th maximum drift angls at all locations ar smallr in comparison with C =.1 to.4, and th sismic rspons of woodn structur sms to b rducd b th improvmnt of sismic prformanc of woodn structur. Th maximum drift angls at all locations for componnt trnd to b largr in comparison with thos for componnt, bcaus th amplitud of vlocit wav with th priod of about 2 scond in th acclration rspons spctrum for componnt is largr than that for componnt as shown in Fig.1.. CONCLUSIO In th 216 Kumamoto Earthquak, a trmndous damag for a Japans-stl.12.1 C=.1 C=.2 C= C=.4 C=. C= cosθ cosθ (1) componnt C=.1 C=.2 C= C=.4 C=. C= cosθ cosθ (2) componnt Fig. Rlationship btwn cos and R

12 traditional framd-basd woodn hous occurrd in Mashiki town, whr th Japan Mtorological Agnc sismic intnsit of 7 lvl succssivl obsrvd twic. Bcaus th ruptur propagation of a sismic fault causd toward th northast dirction from th hpocntr of this arthquak, th ruptur propagation ffct of th sismic fault, that is, th dirctivit ffct ma b on of som primar factors causd a grat damag for woodn hous. In this papr, th ground motions at locations around this sismic fault in th 216 Kumamoto Earthquak ar analticall valuatd b th mpirical Grn s function mthod, and also th influnc of th dirctivit ffct of sismic fault on not onl th ground motion but also th maximum drift angl of woodn hous rprsnting its sismic damag is invstigatd in dtail. Morovr, th ffct of th bas shar cofficint of woodn hous on its maximum drift angl is valuatd in ordr to prdict th sismic damag of woodn hous against a strong arthquak ground motion. Th summar of this papr is as follows, (1) Thr is a significant diffrnc btwn th ground surfac vlocitis in th ruptur propagation dirction and its opposit on of a sismic fault in th 216 Kumamoto Earthquak. Th pak ground surfac vlocitis at svral locations in th ruptur propagation dirction ar mor than cm/s. (2) Basd on th ground motions at locations, th maximum drift angl of woodn hous with th bas shar cofficint of.1 to.6 was valuatd. As a rsult, it was found that th maximum drift angl of woodn hous ma hav a tndnc to b larg in th ruptur propagation dirction of sismic fault. (3) Th largr th bas shar cofficint is, th smallr th maximum drift angl of woodn hous is. It was, consquntl, vrifid that th improvmnt of sismic prformanc of woodn hous has a significant ffct in rducing th sismic rspons of woodn hous. In this papr, sismic motion wavs obsrvd at KiK-nt Mashiki location (KMMH16) for th arthquak with M JMA =4.2 occurrd at : AM on April, 216 wr mplod as a Grn s function in th mpirical Grn s function mthod, and also thir motions ar common to thos of locations. Thrfor, sismic motion wavs wr obsrvd at Mashiki location for th forshock arthquak with M JMA =6. occurrd at 21:26 PM on April 14 in th 216 Kumamoto arthquak, and th dirctivit ffct of sismic fault on not onl th ground motion but also th maximum drift angl of woodn hous against ths sismic wavs will b invstigatd in nar futur. In addition, som dirctivit analss with changing of both th sit amplification charactristics and small sismic wavs usd as a Grn s function ma b ndd to mak som concrt conclusions. REFERENCES Haashi, Y., Nii, A., and Morii, T. (28). Evaluation of building damag basd on quivalnt-prformanc rspons spctra, Procdings of th 14th WCEE. Nagasaka, Y. and Nozu, A. (216), rsarch_jpn/rsarch_jpn_216/jr_48.html, Accssd 8 Ma 217 (in Japans).

13 Nozu, A. and H. Morikawa (23), An mpirical Grn's function mthod considring multipl nonlinar ffcts,zisin, Th Sismological Socit of Japan, (4), (in Japans). Nozu, A., Nagao, T and Yamada, M. (29), Simulation of strong ground motions using mpirical sit amplification and phas charactristics-modification to incorporat causalit-, Journal of Civil Enginring A, JSCE, 6(3), (in Japans). Nozu, A. (216), jr_46.html, Accssd 8 Ma 217 (in Japans). Saratani, A., Morii, T., and Haashi, Y. (26), Fragilit function with pak ground vlocit of wood houss considring agd dtrioration, Procdings of th 12th Japan Earthquak Enginring Smposium, -3.

MAXIMUM RESPONSE EVALUATION OF TRADITIONAL WOODEN HOUSES BASED ON MICROTREMOR MEASUREMENTS

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