CHARACTERISTICS OF LOVE WAVE GENERATED AROUND A DIPPING BASEMENT By Susumu NAKAMURA, Iwao SUETOMI, Shinichi AKIYAMA and Nozomu YOSHIDA Source mechanis

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1 CHARACTERISTICS OF LOVE WAVE GENERATED AROUND A DIPPING BASEMENT By Susumu NAKAMURA, Iwao SUETOMI, Shinichi AKIYAMA and Nozomu YOSHIDA Source mechanism and characteristics of the horizontally propagating waves generated around a dipping basement due to the incident SH wave are investigated. A new analitical method which combines boundary elements, finite elements and energy transmitting boundary is proposed. Two layered media, the upper layer of which has semi-infinite boundary in one side and a dipping interface in the other side, is used in the analysis. It is found that the incident SH wave is mostly transformed into Love wave whose period is close to Airy phase at the horizontal part of the surface layer in the case that both the ratio of wave impedance and the inclination of basement are small ; all reflected SH wave is predominant in the other case. Keywords : love wave, all reflected SH wave, dipping basement, new coupling method of BE and FE

2 Bedrock BE Region Incident SB Wave Fig. 1 Illustration of the analitical model. Kff Kft Kib Ktf Ktt Ktb Kb. f Kbt Kbb Uf Ut Ub Qt [M]Qb [M] 1 F I Z i I lfir Vsr t o. K11 f Kt1 Ktt K1t KJb Ktb Kb/ Kbt Kbb Uf Ut Ub [M]qb

3 [A]=hiGi/3[ ] Fig. 2 Comparison of phase velocity by the proposed method to that by Haskell's method. Kff Kft Kfb Uf Ktf Ktt Ktb Ut Kbf Kbt Kbb Ub H CUb(XO, Z)+ / (Q(r)Ub(x, z) - U (r)qb (x, z))d'= U, (Xo, Z) (8) U (r)= i (HZ (kr)+hz (kr')) -EM] -[G] Qb Uf

4 A: =1. tf /m' Vs2=1, m/sec Fig. 3 The analitical model and the material properties. Table 1 Differences ratio of displacement at ground surface. Fig. 4 Comparison of displacements at ground surface obtained by the proposed method and by the B. E. M. pz =1. t+/m3 Fig. 5 The analitical model and the material constants.

5 Table 2 Analitical Parameters. (b) (c) Fig, 6 Comparison of phase velocity computed by the proposed method to that by Haskell's method.

6 Fig. 7 Comparison of phase velocity computed by the proposed method to that by Haskell's method. (b) Fig. 8 Amplitude of displacement at the ground surface.

7 (b) (c) (e) Fig. 9 Frequency characteristics of magnification factor. (r) Fig. 1 Ratio of maximum amplitude versus inclination of basement. Table 3 Predominant Period versus inclination of basement (a=. 2, Bt=85).

8 v /L1 y-v SI1/ v(l/ cost Fig. 11 Coefficient of influence due to Love wave (AS (t)=as (t)) Fig. 12 Coefficient of influence due to Love wave versus inclination of basement.

9 Fig. 13 Coefficient of influence due to Love wave versus incident angle of SH wave. Fig. 14 Coefficient of influence due to Love wave versus ratio of wave impedance.

10 1) Scawthorn, C., Celebi, M, and Prince, J. : Performance Characteristics of Structure, 1985 Mexico City earthquake, The Mexico Earthquake 1985, pp , ) Bard, Y. P. and Bouchon, M. : The Seismic Response of Sediment-Filled Valleys Part. 1 The case of Incident SB wave, Bull. Seis. Soc. Am., Vol. 7, No. 4, pp , ) Bard, Y. P. and Bouchon, M. : The Two-Dimensional Response of Sediment-Filled Valleys, Bull. Seis. Soc. Am., Vol. 75, No. 2, pp , ) Aki, K. and Lamer, L. K. : Surface motion of a layered medium having Irregular Interface due to Incident SH Waves, J. Geophys. Res., Vol. 75, No. 5, pp , ) Lysmer, J., Udake, T., Tsai, T. C. and Seed, H. B. Flush-A Computer Program for Approximate 3-D Analysis of Soil-Structure Interaction Problem, Report No. EERC 75-3, Earthquake Engineering Research Center, University of California, ) Lysmer, J, and Waas, G. : Shear Waves in Plane Infinite Structure, A. S. C. E, EM 1, pp , ) Chen, C. J., Lysmer, J. and Seed, H. B. : Analysis of Local Vaivrations in Free Field seismic ground motion, Earthquake Engineering Research Center, Report No. EERC 81-3, University of California, ) Tazime, K. : Maximum Group Velocity, Maximum Amplitude and Quarter Wave-Length Law, J. Phys. Earth, Vol. 5, No. 1, pp. 43-5, ) Haskell, N. A. : The Dispersion of Surface Waves on Multilayered Media, Bull. Seis. Soc. Am., Vol. 43, No. 2, pp , 1953.

mbb mb9 xb Fig. 1 Soil-Structure Interaction System.

mbb mb9 xb Fig. 1 Soil-Structure Interaction System. In this paper the authors developed a new subsystem modes synthesis method as one of the dynamic substructure methods for the analysis of soil-foundation-superstructure for seismic motions. This method