Amplification Pattern of Trapezoidal Alluvial Valley Subjected to SH-waves

Document Type : Original Research

Authors
M. Panji
S. Mojtabazadeh-Hasanlouei
Department of Civil Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran.
DOI: 10.22034/22.2.2
Abstract
In this paper, a simple numerical model is presented for analyzing trapezoidal alluvial valleys subjected to propagating obliquely incident plane SH-waves. As the literature review shows, the scattering effect of transient SH-waves on the surface of trapezoidal alluvial valleys has not yet been directly analyzed in the time-domain by half-plane BEM. In previous researches, the models were limited to the homogeneous single-material subsurface problems. Although in some researches, the mathematical formulation, numerical implementation, and transient analysis of two-dimensional non-homogeneous solids were presented as well, they were established to obtain the time-domain responses by the inverse Fourier/Laplace-transform from a mechanical problem point of view. Additionally, some researchers were used a full-plane time-domain BEM approach to present the time-domain responses for an alluvial valley. But in this study, based on an advanced half-plane time-domain BEM, the surface responses of a linear elastic trapezoidal alluvial valley are obtained due to propagating obliquely incident anti-plane SH-waves. In the use of half-plane time-domain BEM, the meshes are only concentrated around the interface of the basin. First, the problem is decomposed into two parts including a half-plane valley-shaped feature and closed filled alluvium. Then, the influence coefficients of the matrices are obtained by applying the method to each part. Finally, by satisfying the boundary/continuity conditions on the interfaces, a coupled equation is formed to determine unknown boundary values in each time-step. Then, all ground surface responses are also obtained in a secondary solution as internal points. After implementing the method in a general algorithm previously named DASBEM, several practical examples are analyzed to authenticate the obtained results beside prior published responses by other researchers. The main aims of this study are to present some applicable diagrams for use in engineering/operational projects, present a better view of alluvial valleys’ seismic behavior, and reveal the power of the developed algorithm in the analysis of complicated geotechnical problems. Thus, an advanced numerical study is performed to sensitize the surface motion of trapezoidal alluvial valleys with the variable of shape/impedance ratios as synthetic seismograms and three-dimensional (3D) amplification patterns. In the following, to complete the time-domain results, the transient response of the internal domain of the alluvium as well as the surrounding bedrock is shown by the snapshots’ views. Moreover, the sensitivity analysis is carried out to obtain the seismic amplification pattern of the surface by considering the key parameters including impedance and shape ratios, incident wave angle, and response frequency. Lastly, by collecting the maximum amplification of different scenarios and applying linear fit on the obtained values, the responses are summarized as a series of linear equations and tables. The results showed that the mentioned factors are very effective on the seismic response of the surface. The results of the present study can be used to complete the accuracy of existing codes around the subject of near-filed site effects.

Keywords

Subjects

[1] Bouchon M. 1973 Effect of topography on surface motion. Bull Seism Soc Am, 63(3), 715-732.
[2] Sánchez-Sesma FJ. 1987 Site effects on strong ground motion. Soil Dyn Earthq Eng. 6(2), 124-132.
[3] Davis LL, West LR. 1973 Observed effects of topography on ground motion. Bull Seism Soc Am, 63(1), 283-298.
[4] Bard PY, Bouchon M. 1980 The seismic response of sediment-filled valleys, Part 2. The case of incident P and SV-waves. Bull Seism Soc Am, 70, 1921-1941.
[5] Manoogian ME, Lee VW. 1999 Antiplane deformations near arbitrary-shape alluvial valleys. ISET J Earthq Tech. 36(2), 107-120.
[6] Sánchez-Sesma FJ, Palencia VJ, Luzón F. 2002 Estimation of local site effects during earthquakes: An overview. ISET J of Earthq Tech, 39)3(, 167-193.
[7] Trifunac MD. 1973 Scattering of plane SH-waves by a semi-cylindrical canyon. Earthq Eng Struct Dyn, 1, 267-281.
[8] Wong HL, Trifunac MD. 1974 Scattering of plane SH-waves by a semi-elliptical canyon. Earthq Eng Struct Dyn, 3(2), 157-169.
[9] Lee VW. 1984 Three-dimensional diffraction of plane P, SV & SH-waves by a hemispherical alluvial valley. Int J Soil Dyn Earthq Eng. 3(3), 199-144.
[10] Todorovska MI, Lee VW. 1991 Surface motion of shallow circular alluvial valleys for incident plane SH-waves (Analytical solution). Soil Dyn Earthq Eng, 10(4), 192-200.
[11] Yuan X, Liao Z. 1995 Scattering of plane SH-waves by a cylindrical alluvial valley of circular-arc cross-section. Earthq Eng Struct Dyn, 24(10), 1303-1313.
[12] Sherif RI, Lee VW. 1996 Diffraction around a circular alluvial valley in an elastic wedge-shaped medium due to Plane SH-waves. Europ Earthq Eng, 3, 21-28.
[13] Tsaur DH, Chang KH. 2009 Scattering of SH-waves by truncated semi-cylindrical canyon. J Eng Mech, ASCE, 135, 862-870.
[14] Zhang N, Gao Y, Cai Y, Li D, Wu Y. 2012 Scattering of SH-waves induced by a non-symmetrical V-shaped canyon. Geophys J Int, 191(1), 243-256.
[15] Chang KH, Tsaur DH, Wang JH. 2015 Response of a shallow asymmetric V-shaped canyon to anti-plane elastic waves. Proc Math Phys Eng Sci, 471(2174), 20140215.
[16] Faik-Kara H, Trifunac MD. 2014 Two-dimensional earthquake vibrations in sedimentary basins, SH-waves. Soil Dyn Earthq Eng. 63, 69-82.
[17] Jalali RS, Tokmechi Z, Trifunac MD. 2015 A note on the surface motion of a semi-cylindrical alluvial valley for incident-cylindrical SH-waves radiating from a fault with arbitrary orientation. Soil Dyn Earthq Eng. 79(A), 80-88.
[18] Zhang C, Liu Q, Deng P. 2015 Antiplane scattering of SH-waves by a trapezoidal valley with a circular-arc alluvium in an elastic half space. J Earthq Tsu. 9(3), 1550008. 10.1142/S1793431115500086.
[19] Le T, Lee VW, Trifunac MD. 2017 SH-waves in a moon-shaped valley. Soil Dyn Earthq Eng, 101, 162-175.
[20] Zhang N, Gao Y, Pak RYS. 2017 Soil and topographic effects on ground motion of a surficially inhomogeneous semi-cylindrical canyon under oblique incident SH-waves. Soil Dyn Earthq Eng. 95, 17-28.
[21] Tsaur DH, Chang KH. 2018 Exact solution to scattering of SH-waves by an elliptic-arc canyon in the corner of an elastic quarter space. Soil Dyn Earthq Eng. 110, 137-140.
[22] Faik-Kara H. 2020 Dynamic response of an alluvial valley consists of three types of soil. Earthq Eng Eng Vib, 19, 289-305, 10.1007/s11803-020-0562-1.
[23] Chang K, Wang W, Hsu, S. 2020 Antiplane response of a flat-bottomed semicircular canyon to cylindrical elastic waves. J Eng Math, 121, 125-139.
[24] Sánchez-Sesma FJ, Rosenblueth E. 1979 Ground motions at canyons of arbitrary shapes under incident SH-waves. Earthq Eng Struct Dyn, 7, 441-450.
[25] Lysmer J, Drake LA. 1972 A finite element method for seismology, Method Comp Phys. Ed Bolt BA, Academic Press, New York. 11, 181-216.
[26] Kawase H, Sato T. 1992 Simulation analysis of strong motions in the Ashigara valley considering one- and two-dimensional geological structures. J Phys Earth. 40, 27-56.
[27] Bielak J, Xu J, Ghattas O. 1999 Earthquake ground motion and structural response in alluvial valleys. J Geotech Geoenviron Eng, ASCE, 125(5), 413-423.
[28] Shyu WS, Teng TJ, Chou CS. 2016 Anti-plane response induced by an irregular alluvial valley using a hybrid method with modified transfinite interpolation. Soil Dyn Earthq Eng, 90, 250-264.
[29] Nohegoo‑Shahvari A, Kamalian M, Panji M. 2018 Two-dimensional dynamic analysis of alluvial valleys subjected to vertically propagating incident SH-waves. Int J Civ Eng, 17, 823-839.
[30] Nohegoo‑Shahvari A, Kamalian M, Panji M. 2019 A hybrid time-domain half-plane FE/BE approach for SH-wave scattering of alluvial sites. Eng Analy BE, 105, 194-206.
[31] Zhou H, Chen XF. 2006 A new approach to simulate scattering of SH-waves by an irregular topography. Geophys J Int, 164, 449-459.
[32] Wang L, Xu Y, Xia J, Luo Y. 2015 Effect of near-surface topography on high-frequency Rayleigh-wave propagation. J Appl Geophys, 116, 93-103.
[33] Zhu C, Thambiratnam D. 2016 Interaction of geometry and mechanical property of trapezoidal sedimentary basins with incident SH-waves. Bull Earthq Eng. 14, 2977-3002.
[34] Zhu C, Thambiratnam D, Gallage C. 2019 Inherent Characteristics of 2D Alluvial Formations Subjected to In-Plane Motion, J Earthq Eng, 23(9), 1512-1530.
[35] Kamalian, M., Jafari, M.K., Sohrabi-Bidar, A., Razmkhah, A., Gatmiri, B. 2006 Time-domain two-dimensional site response analysis of non-homogeneous topographic structures by a hybrid FE/BE method. Soil Dyn Earthq Eng. 26(8), 753-765.
[36] Kamalian M, Gatmiri B, Sohrabi-Bidar A, Khalaj A. 2007 Amplification pattern of 2D semi-sine shaped valleys subjected to vertically propagating incident waves. Commun Numer Methods Eng. 23(10), 871-887.
[37] Panji M, Kamalian M, Asgari Marnani J, Jafari MK. 2012 A Literature Review of Seismic Analysis of Topographic Features Subjected to Incident SH-Waves (In Persian). Bull Earthq Sci Eng, 15, 21-35.
[38] Reinoso E, Wrobel LC, Power H. 1993 Preliminary results of the modeling of the Mexico City valley with a two-dimensional boundary element method for the scattering of SH-waves. Soil Dyn Earthq Eng. 12(8), 457-468.
[39] Fishman KL, Ahmad S. 1995 Seismic response for alluvial valleys subjected to SH, P and SV-waves. Soil Dyn Earthq Eng, 14(4), 249-258.
[40] Sánchez-Sesma FJ, Luzon F. 1995 Seismic response of three-dimensional alluvial valleys for incident P, S and Rayleigh-waves. Bull Seism Soc Am, 85(1), 269-284.
[41] Ausilio E, Conte E, Dente G. 2008 Seismic response of alluvial valleys to SH-waves. In: Seism Eng Conf, AIP Conf Proc, 1020, 199-206.
[42] Ba Z, Yin X. 2016 Wave scattering of complex local site in a layered half-space by using a multidomain IBEM: Incident plane SH-waves. Geophys J Int, 205(3), 1382-1405.
[43] Liu ZX, Liang JW, Huang YH, Liu L. 2016 IBIEM modelling of the amplification of seismic waves by a three-dimensional layered alluvial basin, Geophys J Int. 204(2), 999-1023.
[44] Ba Z, Wang Y, Liang J, Lee V. 2020 Wave scattering of plane P, SV, SH-waves by a 3D alluvial basin in a multilayered half-space. Bull Seismol Soc Am, 110, 10.1785/0120190090.
[45] Panji M, Kamalian M, Asgari Marnani J, Jafari MK. 2013a Transient analysis of wave propagation problems by half-plane BEM. Geophys J Int, 194, 1849-1865.
[46] Panji M, Kamalian M, Asgari Marnani J, Jafari MK. 2013b Amplification pattern of semi-sine shaped valleys subjected to vertically propagating incident SH-waves. J Comp Meth in Eng, 32(2), 87-111.
[47] Panji M, Kamalian M, Asgari Marnani J, Jafari MK. 2014 Antiplane seismic response from semi-sine shaped valley above embedded truncated circular cavity: a time-domain half-plane BEM. Int J Civil Eng, 12(2 and B), 160-173.
[48] Panji M, Mojtabazadeh-Hasanlouei S. 2019 Transient response of irregular surface by periodically distributed semi-sine shaped valleys: Incident SH-waves. J Earthq Tsu, 4(1), 2050005.
[49] Panji M, Mojtabazadeh-Hasanlouei S. 2020a Surface motion of alluvial valleys subjected to obliquely incident plane SH-wave propagation. J Earthq Eng. Accepted.
[50] Ohtsu M., Uesugi S. 1985 Analysis of SH-wave scattering in a half space and its applications to seismic responses of geological structures. Eng Analy, 2(4), 198-204.
[51] Ricker N. 1953 The form and laws of propagation of seismic wavelet. Geophys. 18(1), 10-40.
[52] Eringen AC, Suhubi ES. 1975 Elastodynamics. Academic Press.
[53] Brebbia CA, Dominguez J. 1989 Boundary Elements, an Introductory Course. Comp Mech Pub. Southampton: Boston.
[54] Dominguez J. 1993 Boundary elements in dynamics. Comp Mech Pub, Southampton, Boston.
[55] Panji M, Mojtabazadeh-Hasanlouei S. 2020b Seismic antiplane response of gaussian-shaped alluvial valley. Sharif J Civ Eng. Under Review.
[56] Panji M, Mojtabazadeh-Hasanlouei S, Yasemi F. 2020 A half-plane time-domain BEM for SH-wave scattering by a subsurface inclusion. Comp Geosci, 134, 104342.
[57] Shyu WS, Teng, TJ. 2014 Hybrid method combines transfinite interpolation with series expansion to simulate the anti-plane response of a surface irregularity. J Mech. 30:349-360. 10.1017/jmech.2014.27.
Modares Civil Engineering journal
Volume 22, Issue 2
May and June 2022
Pages 1-25