表層地盤における地震波のエネルギーフローの検討

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1 SH

2 E E V t k e V t t d d Ek = ρv 0 t d = ρv t dt dt E e t γ d e = 0 τ γ = γ = ρ E V t d V t V t dt () E E k d E = Ek + Ee = ρv t e dt

3 E t = de dt Seimogragh Layer No. rond A rface h d E de dt = ρv E h dt Srface layer B E A m B m m h E E m t de t d d E = dt = ρ t V dt dt t dt C A n n B n E E d z Bae layer z i( ω t+ kz) i( ωt kz) = Ae + Be t ω A, B k k = ρω ρ D D = ( + id) A, B A B m m m+, m+ km m kmm ikmh k m m m km m ikmhm e e Am + km m km m+ Am Am T = = m Bm k B + + m m kmm ikmh k m m m kmm ik m B m mh m e e km+ m+ km+ m+ 3

4 h m n z iωt iωt m = Ume = ( Am + Bm) e iωt iωt n = Une = ( An + Bn) e T m+ An Am Am T T m [ Tn][ Tn ] T m+ T A = = n, m+ = B n B m B T T m Bm Tnm, + = [ Tn][ Tn ] T m+ T, T, U, U m n Un T + T T + T Am Am P = = nm, + Um B m Bm Am Un An Un P nm,, + Tnm, + P = nm, + B = m Um B n Um ω ω D 4

5 (a) PI L-0m S L-4.0m CH (c) TKS L-0m A WL (m 40 C L-00m Damping ratio D (%) SF L-.5m M L-5m D epth 60 A B L-6.4m 0 B S L-3.4m 40 S ) (m 60 CH D epth 80 C L-83.4m M S CH ) Seimogragh Damping ratio D (%) WL 80 S-wave velocity V (m/) (b) SK Damping ratio D (%) A L-0m SF WL 0 L-.0m M B SF L-5m 0 ) CH (m 40 S CH D epth 60 CH 00 C L-97m CH Seimograph S-wave velocity V (m/) Seimograph S-wave velocity V (m/) (d) KNK Damping ratio D (%) L-0m A S WL M 0 L-.0m S V-initial M 0 B V-inv.NS S L-5m V-inv.EW C M ) 40 D-inv.NS SF (m D-inv.EW M M 60 F D epth M 80 Rock C L-00m Seimograph CH 80 S-wave velocity V (m/) 5

6 6

7 E E d E E w 7

8 ( de dt) L 8.4 ( de dt) L 3.4 de dt ( de dt) max E 8

9 (a) z ρ V A Ep Layer bondary A E E B d ρ V (b) Ed E ρ ρ V V k = ω V k = ω V i( t kz) = Ae ω i( ωt kz ) i( ωt+ kz ) = A e + B e z = 0 A A B α = ρv ρv E p E α = ρv ρv 9

10 ( ) A A = + α ( ) ( ) B A = α + α ( ) E E = 4α + α p d ( ) ( ) E E = α + α V /(+ ( d dt) ρ V z z = 0 A B A B i( ωt kz) i( ωt+ kz) = Ae + Be i( ωt kz) i( ωt+ kz) = Ae + Be ikh B A = e A = A B A = ( + α ) + ( α ) ( α ) + ( + α ) ( + α ) + ( α e )e ik H ik H e ik H z, ρ,v, ρ,v A Srface layer A A E E A B B Bae layer E Ed H 0

11 A A = ik H + + e ik H ( α ) e ( α ) α k πf α= ρv ρ V ω= ρ, ρ V, V ρv + id α = = α ρ V + id ρω π f = H= V 4H kh ( + id) D, D ( de dt) ( de dt) ( ) ( ) de dt de dt = α A A ( ded dt) ( ) ( ) d A de dt de dt = B α = ρv ρ V α = ρv ρv ( de dt) ( de dt) dew dt de dt de dt de dt ( ) ( ) w ( ) ( ) ( ) ( ) dew dt de dt = d de dt de dt ( ) ( ) de dt de dt α ( ) ( ) α = de dt de dt α = ρ V ρv α < f V 4H =.0 = 4H α > f V 4H =.0 ( dew dt) ( de dt) H =

12 de dt de dt D f V 4H =.0 de dt ( ω = n+ ) πv H n de ( n ) k H = ω H V = + π ( ) ( ) dt de dt = α f V 4H 0. 6 f V 4H. 4 de dt de dt ( ) ( ) de dt de dt α w D f V 4 H =. 0 D de dt w de w dt de dt w H ρ V D ρ V =330m/ D =0% V E D α D E E ( E Ed) ( E Ed)

13 α ( E Ed) = 0 E αρ ρ E α αρ ρ α E E E αρ ρ E 3

14 ( ) ( ) de dt de dt max max α E E α w E E w E w E E E E E E de dt de dt D ( ) ( ) max α V V V f 0 n max Vi = 4 i= Hi f V H 0 V V V E E E E w 4

15 E E E E w Ew E E w E E E E w E E w E α 89 5

16 Fondation grond,, z Et Et Shear-vibrating trctre ρt, V ρ,v E E d t H t γ z ikh B A = e ( ) γ = kaink H z e ω i( t kh ) H H t ρ ρ t Vt de dt det dt de dt de dt A A t A A α α t k k t γ de dt / 4inkt ( Ht z) αt de γ = ik 3 t Ht ikt Ht ( αt ) e ( α dt t ) e ρtv + + t V ( ) k ρ V α t de dt V t / γ de dt = γ = ω= πvt H α ρ V max / 3 t t t α α t ( ) ( ) t α t t de dt de dt = A A t t 6

17 ( ) ( ) { } 3 in t t t t t de dt k H z V γ = ρ ( ) t de dt t de dt γ γ y γ y = γ γ µ t V t ρ V ρv 7

18 E E E E ( ) d d E E w ) E E ) E E E w E E E E E w 3) 4) 5) E E E E 6) E E E E 7) E E E E w 8) E E w 9) E E 0) ) ) 3) 8

19 995 ) tenberg, B. and Richter, C.F.: Earthqake magnitde, intenity, energy and acceleration (econd paper), Blletin of Seimological Society of America, Vol.46, 956, pp ) 3) pp ) Kanai, K., Tanaka, T., Yohizawa, S.:Comparative tdie of earthqake motion on the grond and ndergrond, Blletin of the Earthqake Reearch Intitte, Tokyo Univerity, Vol.37, 959, pp.53-87,. 5) Kanai,K., Tanaka, T., Yohizawa, S., Morihita, T., Oada, K. and Szki,T.: Comparative tdie of earthqake motion on the grond and ndergrond II, Blletin of the Earthqake Reearch Intitte, Tokyo Univerity, Vol.44, 966, pp ) Schnabel, P.B., Lymer, J. & Seed, H.B.: SHAKE, A compter program for earthqake repone analyi of horizontally layered ite. Report EERC 7-, Univerity of California Berkeley, 97. 8) Kokho, T. and Motoyama, R.: Energy diipation in rface layer de to vertically propagating SH wave, Jornal of eotechnical and eoenvironmental Engineering, ASCE, Vol.8, No.4, 00, pp ) Kokho,T., Matmoto,M. and Sato,K.: Nonlinear eimic propertie back-calclated from trong motion dring Hyogoken-Namb EQ, Proc. World Conference on earthqake Engineering (Acaplco), 996, CD-pblication. 0) Sato,K., Kokho,T., Matmoto,M., and Yamada, E.Nonlinear eimic repone and oil property dring trong motion, Soil and Fondation Special Ie for the 995 Hyogoken Namb earthqake, 996, pp.4-5. Yohida, N.: Nonlinear behavior of rface depoit dring the 995 Hyogoken-Namb earthqake, Special Ie of Soil and Fondation, 998, pp.-. Romo, M. P.: Clay behavior, grond repone and oil-trctre interaction tdie in Mexico City, Proc. 3 rd International Conf. on Recent Advance in eotechnical Earthqake Engineering and Soil Dynamic, St. Loi, Vol.II, 995, pp

20 Energy Flow of Seimic Wave in Srface rond for Performance-Baed Deign KOKUSHO Takaji ), MOTOYAMA Ry-ichi ), MANTANI Shogo ) and MOTOYAMA Hirohi 3) ) Profeor, Faclty of Science & Engineering, Cho Univerity ) Ex-gradate tdent, School of Science & Enginnering, Cho Univerity 3) radate tdent, School of Science & Enginnering, Cho Univerity ABSTRACT Energy flow of eimic wave oberved dring the 995 Hyogo-ken Namb earthqake in vertical array ite i calclated by aming vertical propagation of SH wave in rface layer. In order to baically ndertand the relt, wave energy and it diipation in linear to 5 layer ytem are alo invetigated. The major finding are; () Wave energy generally tend to decreae a it goe p from bae layer to grond rface, () The amont of pward energy depend on the reonant condition, the impedance ratio, oil damping, the nmber of oil layer, etc. (3) A general perception that oft oil ite are prone to heavier damage de to energy torage effect by reonance may not be right, becae large damping ratio tend to cancel reonant effect if it ever occr. The wave energy, which i directly related to indced train in pertrctre, can play a key role for the performance-baed deign. For that prpoe, deign eimic motion hold be defined in term of wave energy. Key Word: Seimic wave energy, SH wave, Impedance ratio, Damping, Performance-baed deign 0

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