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Green's function of multi-layered poroelastic half-space for models of ground vibration due to railway traffic

Earthquake Engineering and Engineering Vibration 2017年第2期16卷 311-328页

作者： Wang Futong Tao Xiaxin Xie Lili Siddharthan Raj Institute of Engineering Mechanics China Earthquake Administration Key Laboratory of Earthquake Engineeringand Engineering Vibration of China Earthquake Administration Harbin 150080 China School of Civil Engineering and Architecture Heilongiiang University Harbin 150080 China School of Civil Engineering Harbin Institute of Technology Harbin 150090 China Department of Civil and Environmental Engineering University of Nevada Reno NV89557 USA

This study proposes a Green＇s function, an essential representation of water-saturated ground under moving excitation, to simulate ground borne vibration from trains. First, general solutions to the governing equations of poroelastic medium are derived by means of integral transform. Secondly, the transmission and reflection matrix approach is used to formulate the relationship between displacement and stress of the stratified ground, which results in the matrix of the Green＇s function. Then the Green＇s function is combined into a train-track-ground model, and is verified by typical examples and a field test. Additional simulations show that the computed ground vibration attenuates faster in the immediate vicinity of the track than in the surrounding area. The wavelength of wheel-rail unevenness has a notable effect on computed displacement and pore pressure. The variation of vibration intensity with the depth of ground is significantly influenced by the layering of the strata soil. When the train speed is equal to the velocity of the Rayleigh wave, the Mach cone appears in the simulated wave field. The proposed Green＇s function is an appropriate representation for a layered ground with shallow ground water table, and will be helpful to understand the dynamic responses of the ground to complicated moving excitation.

关键词： wave propagation poroelastic medium layered half-space train Green＇s function

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2.5D scattering of incident plane SV waves by a canyon in layered half-space

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Earthquake Engineering and Engineering Vibration 2010年第4期9卷 587-595页

作者： Ba Zhenning Liang Jianwen Department of Civil Engineering Tianjin University Tianjin 300072 China Key Laboratory of Coast Civil Structure Safety （ Tianjin University） Ministry of Education

This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green＇s fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.

关键词： layered half-space canyon plane SV wave amplification scattering surface layer indirect boundaryelement method

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Dynamic soil-tunnel interaction in layered half-space for incident plane SH waves

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Earthquake Engineering and Engineering Vibration 2016年第4期15卷 715-727页

作者： Fu Jia Liang Jianwen Qin Lin State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University Department of Civil Engineering Tianjin University

The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.

关键词： underground tunnel layered half-space plane SH wave indirect boundary element method soil-tunnel interaction site dynamic characteristics

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Time domain method for calculating free field motion of a layered half-space subjected to obliquely incident body waves

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Earthquake Engineering and Engineering Vibration 2007年第2期6卷 191-196页

作者：李山有朱海燕高淑芳 Institute of Engineering Mechanics China Earthquake Administration Earthquake Administration of Fujian Province No.703 Team of Bureau of Geological Exploration of Nonferrous Metals of Heilongjiang Province

In numerical simulation of wave scattering under oblique incident body waves using the finite element method, the free field motion at the incident lateral boundary induced by the background layered half-space complicates the computational area. In order to replace the complex frequency domain method, a time-domain method to calculate the free field motion of a layered half-space subjected to oblique incident body waves is developed in this paper. The new method decouples the equations of motion used in the finite element method and offers an interpolation formula of the free field motion. This formula is based on the fact that the apparent horizontal velocity of the free field motion is constant and can be calculated exactly. Both the theoretical analysis and numerical results demonstrate that the proposed method offers a high degree of accuracy.

关键词： layered half-space wave scattering obliquely incidence artificial botmdary explicit finite element method Snell law

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Dynamic soil-tunnel interaction in layered half-space for incident P-and SV-waves

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Earthquake Science 2015年第4期28卷 275-284页

作者： Jia Fu Jianwen Liang Lin Qin Department of Civil Engineering Tianjin University Tianjin Key Laboratory of Civil Engineering Structures & New Materials

The dynamic soil-tunnel interaction is studied by the model of a rigid tunnel embedded in layered half-space, which is simplified as a single soil layer on elastic bedrock to the excitation of P- and SV-waves. The indirect boundary element method is used, combined with the Green＇ s function of distributed loads acting on inclined lines. It is shown that the dynamic characteristics of soil-tunnel interaction in layered half-space are different much from that in homoge- neous half-space, and that the mechanism of soil-tunnel interaction is also different much from that of soil-founda- tion-superstructure interaction. For oblique incidence, the tunnel response for in-plane incident SV-waves is com- pletely different from that for incident SH-waves, while the tunnel response for vertically incident SV-wave is very similar to that of vertically incident SH-wave.

关键词： Underground tunnel layered half-space P-wave and SV-wave Indirect boundary element method Soil-tunnel interaction ~ Site dynamic characteristics

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3D seismic response of a 2D hill-valley staggered topography modeled by a 2.5D multi-domain IBEM

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Earthquake Science 2019年第3期32卷 125-142页

作者： Zhenning Ba Qiaozhi Sang Jianwen Liang Department of Civil Engineering Tianjin UniversityTianjin 300072China Key Laboratory of Coast Civil Structure Safety(Tianjin University) Ministry of EducationTianjin 300072China

A two and a half dimensional(2.5D)multi-domain indirect boundary element method(IBEM)is developed to study the wave scattering of obliquely incident P-,SV-and SH-waves by a hill-valley staggered topography in a multi-layered half-space.The IBEM algorithm includes using 2.5D full-space and half-space Green’s functions to construct scattered fields in decomposed closed and opened half-space regions,respectively,and using the dynamic stiffness method to solve the free fields.All regions are finally integrated by introducing the compatibility conditions to obtain the total wave fields.The proposed 2.5D IBEM has the flexibility in dealing with complex boundaries by directly applying the fictitious loads on the regions’boundaries,with a less storage requirement compared to the full 3D models.Besides,by combining the specific advantages of the two kinds of Green’s functions,the method is well suitable for handling coupled topographies with high accuracy.The method is validated by comparison with published results for a single valley as well as a single hill topography.The effects of height-to-width ratio of hill and layering on dynamic responses are further parametrically investigated by numerical implementations in frequency domain.Results show that the interaction between valley and hills can lead to a more significant amplification within the valley region,and dynamic responses are deeply influenced by the height-to-width of hill,simultaneously depending on incident angle and frequency.Besides,the site effects become more complex when the stratification feature is taken into account.

关键词： 2.5D multi-domain IBEM Green’s functions for moving load hill-valley staggered topography wave scattering layered half-space

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