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Scattering and reflection of SH waves around a slope on an elastic wedged space

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Earthquake Engineering and Engineering Vibration 2019年第2期18卷 255-266页

作者： Liu Qijian wu Zhiyu vincent w lee College of Civil Engineering Hunan University Civil and Environmental Engineering University of Southern California

The scattering and reflection of SH waves by a slope on an elastic wedged space is investigated. A series solution is obtained by using the wave function expansion method. The slope on a wedged space is divided into two subregions by an artificial, auxiliary circular arc. The wave fields with unknown complex coefficients within each sub-region are derived. Applying Graf addition theorem, the scattered waves in the sub-regions are expressed in a global coordinate system. Fourier transform is adopted to derive a consistent form of standing waves in the inner region using the orthogonality of the cosine functions. The boundary-valued problem is solved by stress and displacement continuity along the artificial, auxiliary arc to obtain the unknown complex coefficients. Parametric studies are next performed to investigate how the topography from the slope on the wedged space will affect the scattering and diffraction, and hence the amplification and de-amplification of the SH waves. Numerical results show that the surface motions on the slope of the wedged space is influenced greatly by the topography. Amplification of the surface motions near the slope vertex is significant. The corresponding phases along the wedged space surfaces are consistent with the direction that the SH waves are propagating.

关键词： earthquake ground motion wave scattering and diffraction Graf addition theorem Fourier transform

Anti-plane (SH) waves diffraction by an underground semi-circular cavity:analytical solution

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Earthquake Engineering and Engineering Vibration 2010年第3期9卷 385-396页

作者： Luo Hao vincent w. lee Liang Jianwen HNTB Corporation Santa Ana CA 92707-8797 USA Sonny Astani Department of Civil and Environmental Engineering University of Southern California Los Angeles CA 90089-2531 USA Department of Civil Engineering Tianjin University Tianjin 300072 China

Diffraction of a two-dimensional （2D） semi-circular cavity in a half-space under incident SH-waves is studied using the classic wave function expansion method with a new de-coupling technique. This so-called ＂improved cosine half- range expansion＂ algorithm exhibits an excellent performance in reducing displacement residual errors at two rim points of concern. The governing equations are developed in a manner that minimizes the residues of the boundary conditions. Detailed derivation and analysis procedures as well as truncation of infinite linear governing equations are presented. The semi-circular cavity model presented in this paper, due to its simple profile, is expected to be used in seismic wave propagation studies as a benchmark for examining the accuracies of various analytical or numerical methods for mixed-boundary wave propagation problems.

关键词： plane SH waves diffraction, semi-circular cavity half-space improved cosine half-range expansion

A series solution for surface motion amplification due to underground twin tunnels:incident SV waves

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Earthquake Engineering and Engineering Vibration 2003年第2期2卷 289-298页

作者：梁建文张浩 vincent w lee Department of Civil Engineering Tianjin UniversityTianjin 300072China Professor Department of Civil Engineering Tianjin UniversityTianjin 300072China Graduate Student Department of Civil Engineering University of Southern CaliforniaLos AngelesCA 90089-2531USA Professor

A series solution of displacement response of the ground surface in the presence of underground twin tunnels subjected to excitation of incident plane SV waves is derived by using Fourier-Bessel series expansion *** numerical parametric study shows that underground twin tunnels significantly amplify the nearby surface ground *** is suggested that the effect of subways on ground motion should be considered when the subways are planned and designed.

关键词： underground twin tunnels surface motion plane SV wave scattering series solution

Scattering of plane P waves by a semi-cylindrical hill: analytical solution

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Earthquake Engineering and Engineering Vibration 2005年第1期4卷 27-36页

作者：梁建文张彦帅 vincent w lee Department of Civil Engineering Tianjin University Tianjin 300072 ChinaProfessor Department of Civil Engineering Tianjin University Tianjin 300072 ChinaGraduateStudent Department of Civil Engineering University of Southern California Los AngelesCA 90089-2531USAProfessor

An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and incident angle on the surface motion of the hill was discussed, and it was shown that a hill greatly amplifies incident plane P waves, and maximum horizontal displacement amplitudes appear mostly at the inclined incidence of waves, which are located at the half-space; and maximum vertical displacement amplitudes emerge mostly at the vertical incidence of waves, which are situated at the hill.

关键词： hill plane P waves scattering analytical solution amplification

Diffraction of anti-plane SH waves by a semi-circular cylindrical hill with an inside concentric semi-circular tunnel

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Earthquake Engineering and Engineering Vibration 2004年第2期3卷 249-262页

作者： vincent w.lee 罗昊梁建文 Dept.of Civil and Environmental Engineering Univ.of Southern CaliforniaLos AngelesCA 90089-2531USA Professor Civil Engineering and Architecture Experiment Center Dept.of Civil EngineeringShanghai Jiaotong Univ.800 Dongchuan Rd.Shanghai 200240China Dept.of Civil EngineeringTianjin Univ.Tianjin 300072China Assistant Engineer Dept.of Civil Engineering Tianjin Univ.Tianjin 300072China Professor

A closed-form analytic solution of two-dimensional scattering and diffraction of plane SH waves by a semi- cylindrical hill with a semi-cylindrical concentric tunnel inside an elastic half-space is presented using the cylindrical wave functions expansion *** solution is reduced to solving a set of infinite linear algebraic *** expansion theorem with the form of complex exponential function and cosine function is *** solutions are obtained by truncation of the infinite *** accuracy of the presented numerical results is carefully verified.

关键词： SH waves hill tunnels close-form analytic solution amplifications

Anti-plane deformations around arbitrary-shaped canyons on a wedge-shape half-space:moment method solutions

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Earthquake Engineering and Engineering Vibration 2003年第2期2卷 281-287页

作者： Nazaret Dermendjian vincent w.lee 梁建文 Department of Civil Engineering & Applied Mechanics California State UniversityNorthridgeCalifornia 91330-8347USA Assistant Professor Department of Civil& Environmental Engineering University of Southern CaliforniaLos AngelesCalifornia90089-2531USA Profcssor School of Civil Engineering Tianjin UniversityTianjin 300072China Professor

The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been *** computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the *** analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.

关键词： weighted-residual moment method wedge half-space arbitrary-shaped cicular elliptic rectangular canyons

Diffraction of plane SH waves by a semi-circular cavity in half-space

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Earthquake Science 2010年第1期23卷 5-12页

作者： Jianwen Liang Hao Luo vincent w lee Department of Civil Engineering Tianjin University Tianjin 300072 China HNTB Corporation SantaAna CA 92707 USA University of Southern California Los Angeles CA 90089-2531 USA

This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.

关键词： diffraction SH wave semi-circular cavity wave function expansion method closed-form solution

Scattering of plane SH waves by a circular-arc hill with a circular tunnel

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Acta Seismologica Sinica(English Edition) 2004年第5期17卷 549-563页

作者： LIANG Jian-wen(梁建文) LUO Hao(罗昊) vincent w. lee Department of Civil Engineering Tianjin UniversityTianjin300072China Department of Civil EngineeringUniversity of Southern CaliforniaLos AngelesCA 90089-2531U.S.A. Department of Civil EngineeringUniversity of Southern CaliforniaLos AngelesCA90089-2531U.S.A.

No abstract available

关键词： hill tunnel scattering plane SH waves analytical solution

Out-of-plane (SH) soil-structure interaction： a shear wall with rigid and flexible ring foundation

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Earthquake Science 2016年第1期29卷 45-55页

作者： Thang Le vincent w. lee Hao Luo Sonny Astani Civil & Environmental Engineering Department University of Southern California Los Angeles CA 90089 USA HNTB Corporation 200 E Sandpointe Ave #200 Santa AnaCA 92707 USA

Soil-structure interaction （SSI） of a building and shear wall above a foundation in an elastic half-space has long been an important research subject for earthquake engineers and strong-motion seismologists. Numerous papers have been published since the early 1970s; however, very few of these papers have analytic closed-form solu- tions available. The soil-structure interaction problem is one of the most classic problems connecting the two dis- ciplines of earthquake engineering and civil engineering. The interaction effect represents the mechanism of energy transfer and dissipation among the elements of the dynamic system, namely the soil subgrade, foundation, and super- structure. This interaction effect is important across many structure, foundation, and subgrade types but is most pro- nounced when a rigid superstructure is founded on a rela- tively soft lower foundation and subgrade. This effect may only be ignored when the subgrade is much harder than a flexible superstructure： for instance a flexible moment frame superstructure founded on a thin compacted soil layer on top of very stiff bedrock below. This paper will study the interaction effect of the subgrade and the super- structure. The analytical solution of the interaction of a shear wall, flexible-rigid foundation, and an elastic half- space is derived for incident SH waves with various angles of incidence. It found that the flexible ring （soft layer） cannot be used as an isolation mechanism to decouple asuperstructure from its substructure resting on a shaking half-space.

关键词： Out-of-plane SH waves Closed-formanalytic solution Rigid-flexible foundation Fourier-bessel series Soil-structure interaction