Earthquake Ground Motion and Structural Response in Alluvial Valleys
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 125, Issue 5
Abstract
This paper is concerned with the problem of soil amplification and structural damage due to local site conditions in sedimentary valleys during earthquakes. It focuses on a small valley in Kirovakan, for which 1D wave propagation analyses have failed to provide adequate answers for the large extent and spatial distribution of damage during the 1988 Armenia earthquake. A more realistic 2D finite-element analysis is performed herein in search of an explanation for the observed behavior. Using as input an inferred rock accelerogram, the response of the valley is calculated for a vertically incident SH-wave. Synthetic accelerograms of the surface ground motion are presented for different sites; these accelerograms are then used to determine the amplification ratios of the surface response with respect to that of the free-field motion of the rock outcrop, for different frequencies and for a continuous set of sites. In addition, response spectra are evaluated for simple oscillators representing structures located at various sites. Results of the 2D simulations show striking differences with respect to those from 1D analyses. In particular, (1) while the resonant frequencies exhibited by a 1D model for a given site also appear in the 2D model, the peak ground response and structural response are almost twice as large for the 2D as for the 1D model; (2) the 2D model exhibits, in addition, a new set of resonant frequencies and concomitant “mode shapes” across the valley, which are directly related to its finite width; and (3) due to these additional resonances the ground amplification ratio tends to oscillate very rapidly, both spatially and with frequency, leading to the observation that two identical structures located in the same vicinity or two slightly different structures located essentially on the same site can be subjected to significantly different seismic forces, even if the underlying soils have very similar characteristics. These results provide a meaningful explanation for the observed damage, and thus serve to exemplify a situation in which site effects caused by the finite lateral extent of a valley must be taken into consideration in order to model satisfactorily seismic behavior.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Aki, K. ( 1988). “Local site effects on ground motion.” Earthquake engineering and soil dynamics II—recent advances in ground motion evaluation, J. L. V. Thun, ed., ASCE, Reston, Va., 103–155.
2.
Aki, K. ( 1993). “Local site effects on weak and strong ground motion.” Tectonophysics, 218, 93–111.
3.
Aki, K., and Larner, K. L. ( 1970). “Surface motion of a layered medium having an irregular interface due to incident plane SH-waves.” J. Geophys. Res., 75, 933–954.
4.
Alterman, Z. S., and Karal, F. C. ( 1968). “Propagation of elastic waves in layered media by finite difference methods.” Bull. Seismological Soc. of Am., 58, 367–398.
5.
“Archimedes home page.” (1998). 〈http://ww.cs.cmu.edu/uake/ archimedes.html〉.
6.
Bao, H., et al. ( 1996). “Earthquake ground motion modeling on parallel computers.” Proc., 1996 ACM/IEEE Supercomputing Conf., available from 〈http://www.supercomp.org/sc96/proceedings/SC96PROC/ OGHATTAS/INDEX.HTM〉.
7.
Bard, P. Y., and Bouchon, M. ( 1980a). “The seismic response of sediment-filled valleys, part I. The case of incident SH waves.” Bull. Seismological Soc. of Am., 70, 1263–1286.
8.
Bard, P. Y., and Bouchon, M. ( 1980b). “The seismic response of sediment-filled valleys, part II. The case of incident P-SV waves.” Bull. Seismological Soc. of Am., 70, 1921–1941.
9.
Bard, P. Y., and Bouchon, M. ( 1985). “The two-dimensional resonance of sediment-filled valleys.” Bull. Seismological Soc. of Am., 75, 519–541.
10.
Bardet, J. P., and Davis, C. ( 1996). “Engineering observations on ground motion at the Van Norman Complex after the 1994 Northridge earthquake.” Bull. Seismological Soc. of Am., 86(1B), S333–S349.
11.
Bayliss, A., and Turkel, E. ( 1980). “Radiation boundary conditions for wave-like equations.” Comm. Pure Appl. Math, 33, 707–725.
12.
Bielak, J., and Christiano, P. ( 1984). “On the effective seismic input for nonlinear soil-structure interaction systems.” Earthquake Engrg. and Struct. Dyn., 12, 107–119.
13.
Bielak, J., MacCamy, R. C., McGhee D. S., and Barry, A. (1991). “Unified symmetric BEM-FEM for site effects on ground motion—SH waves.”J. Engrg. Mech., ASCE, 117(10), 2265–2285.
14.
Bommer, J. J., and Ambraseys, N. N. ( 1989). “The Spitak (Armenia, USSR) earthquake of 7 December 1988: A summary engineering seismology report.” Earthquake Engrg. and Struct. Dyn., 18, 921–925.
15.
Boore, D. M. ( 1972). “Finite difference methods for seismic wave propagation in heterogeneous materials.” Methods in computational physics, B. A. Bolt, ed., Vol. 11, Academic Press, New York.
16.
Boore, D. M., Larner, K. L., and Aki, K. ( 1971). “Comparison of two independent methods for the solution of wave-scattering problems: Response of a sedimentary basin to vertically incident SH-waves.” J. Geophys. Res., 76, 558–569.
17.
Borcherdt, R. ( 1989). “Results and data from seismologic and geologic studies following earthquake of December 7, 1988, near Spitak, Armenia.” Tech. Rep. No. 89-163A, U.S. Geological Survey, Menlo Park, Calif.
18.
Bouchon, M., and Aki, K. ( 1977). “Discrete wavenumber representation of seismic source wavefield.” Bull. Seismological Soc. of Am., 67, 259–277.
19.
Cisternas, A., et al. ( 1989). “The Spitak (Armenia) earthquake of 7 December 1988: Field observations, seismology and tectonics.” Nature, 339, 675–679.
20.
Cremonini, M. G., Christiano, P., and Bielak, J. ( 1988). “Implementation of effective seismic input for soil-structure interaction systems.” Earthquake Engrg. and Struct. Dyn., 16, 615–625.
21.
Foss, K. A. ( 1958). “Co-ordinates which uncouple the equations of motion of damped linear dynamic systems.” J. Appl. Mech., 25, 361–364.
22.
Frankel, A. ( 1993). “Three-dimensional simulations of ground motions in the San Bernardino Valley, California, for hypothetical earthquakes on the San Andreas fault.” Bull. Seismological Soc. of Am., 83, 1020–1041.
23.
Hadjian, A. H. ( 1993). “The Spitak, Armenia earthquake of 7 December 1988—why so much destruction.” Soil Dyn. and Earthquake Engrg., 12, 1–24.
24.
Hartzell, S., Leeds, A., Frankel, A., and Michael, J. ( 1996). “Site response for urban Los Angeles using aftershocks of the Northridge earthquake.” Bull. Seismological Soc. of Am., 86(1B), S168–S192.
25.
Jennings, P. C. ( 1997). “Earthquake response of tall regular buildings.” Tech. Rep. No. EERL 97-01, California Institute of Technology, Pasadena, Calif.
26.
Kallivokas, L. F., Bielak, J., and MacCamy, R. C. (1991). “Symmetric local absorbing boundaries in time and space.”J. Engrg. Mech., ASCE, 117(9), 2027–2048.
27.
Kawase, H. ( 1988). “Time-domain response of a semi-circular canyon for incident SV, P, and Rayleigh waves calculated by the discrete wavenumber boundary element method.” Bull. Seismological Soc. of Am., 78, 1415–1423.
28.
Lee, V. W. ( 1990). “Scattering of plane SH waves by a semi-parabolic cylindrical canyon in an elastic half-space.” Int. J. Geophys., 100, 79–86.
29.
Li, X., Bielak, J., and Ghattas, O. ( 1992). “Three-dimensional earthquake response on a CM-2.” Proc., 10th World Conf. Earthquake Engrg., Vol. 2, Balkema, Rotterdam, The Netherlands, 959–964.
30.
Lysmer, J., and Drake, L. A. ( 1971). “The propagation of Love waves across nonhorizontally layered structures.” Bull. Seismological Soc. of Am., 61, 1233–1252.
31.
Mossessian, T., and Dravinski, M. ( 1987). “Application of a hybrid method for scattering of P, SV, and Rayleigh waves by near-surface irregularities.” Bull. Seismological Soc. of Am., 77, 1784–1803.
32.
Sánchez-Sesma, F. J. ( 1983). “Diffraction of elastic waves by three-dimensional surface irregularities.” Bull. Seismological Soc. of Am., 73, 1621–1636.
33.
Sánchez-Sesma, F. J., and Esquivel, J. A. ( 1979). “Ground motion on alluvial valleys under incident plane SH waves.” Bull. Seismological Soc. of Am., 69, 1107–1120.
34.
Sánchez-Sesma, F. J., Ramos-Martínez, J., and Campillo, M. ( 1993). “An indirect boundary element method applied to simulate the seismic response of alluvial valleys for incident P, S and Rayleigh waves.” Earthquake Engrg. and Struct. Dyn., 22, 279–295.
35.
Shewchuk, J. R. ( 1996). “Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator.” Applied computational geometry: Towards geometric engineering, (Lecture notes in computer science, Vol. 1148), M. C. Lin and D. Manocha, eds., Springer, New York, 203–222.
36.
Smith, W. D. ( 1975). “The application of finite element analysis to body wave propagation problems.” J. Geophys., 44, 747–768.
37.
Spudich, P., and Iida, M. ( 1993). “The seismic coda, site effects, and scattering in alluvial basins studied using aftershocks of the 1986 North Palm Springs, California earthquake as source arrays.” Bull. Seismological Soc. of Am., 83, 1721–1724.
38.
Toshinawa, T., and Ohmachi, T. ( 1992). “Love wave propagation in a three-dimensional sedimentary basin.” Bull. Seismological Soc. of Am., 82, 1661–1667.
39.
Trifunac, M. D. ( 1971). “Surface motion of a semi-cylindrical alluvial valley for incident plane SH waves.” Bull. Seismological Soc. of Am., 61, 1755–1770.
40.
Vidale, J. E., and Helmberger, D. V. ( 1988). “Elastic finite-difference modeling of the 1971 San Fernando, California earthquake.” Bull. Seismological Soc. of Am., 78, 122–141.
41.
Wong, H. L., and Trifunac, M. D. ( 1974). “Surface motion of semi-elliptical alluvial valley for incident plane SH wave.” Bull. Seismological Soc. of Am., 64, 1389–1408.
42.
Wyllie, L. J., and Filson, J. ( 1989). “Armenia earthquake reconnaissance report.” Earthquake Spectra, Spec. Supplement.
43.
Yegian, M. K., Ghahraman, V. G., and Gazetas, G. (1994a). “1988 Armenia earthquake. I: seismological, geotechnical, and structural overview.”J. Geotech. Engrg., ASCE, 120(1), 1–20.
44.
Yegian, M. K., Ghahraman, V. G., and Gazetas, G. (1994b). “1988 Armenia earthquake. II: Damage statistics versus geologic and soil profiles.”J. Geotech. Engrg., ASCE, 120(1), 21–45.
45.
Yegian, M. K., Ghahraman, V. G., and Gazetas, G. (1994c). “Ground-motion and soil-response analyses for Leninakan, 1988 Armenia earthquake.”J. Geotech. Engrg., ASCE, 120(2), 330–348.
46.
Yegian, M. K., Ghahraman, V. G., and Gazetas, G. (1994d). “Seismological, soil and valley effects in Kirovakan, 1988 Armenia earthquake.”J. Geotech. Engrg., ASCE, 120(2), 349–365.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 125 • Issue 5 • May 1999
Pages: 413 - 423
History
Received: Jun 13, 1997
Published online: May 1, 1999
Published in print: May 1999
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.