{"title":"计算具有不规则表面的均质半空间隧道地面振动的半解析法","authors":"","doi":"10.1016/j.jsv.2024.118615","DOIUrl":null,"url":null,"abstract":"<div><p>This paper proposes a novel two-dimensional (2D) semi-analytical method for calculating ground vibrations from a tunnel situated in a homogeneous half-space with an irregular surface. The circular tunnel is conceptualized as an elastic solid, while the soil is modelled as an elastic, isotropic, and homogeneous half-space with an irregular surface. A virtual horizontal interface is introduced to divide the soil domain into an irregular region with an arbitrary-shaped surface and a half-space with a circular hollow. The wavefield scattered by the irregular surface is simulated by the boundary integral equation. Through the application of the discrete wavenumber approach and expansion of wavefield on the irregular surface, the boundary integral equation is transformed into a set of simultaneous matrix equations containing unknown expansion coefficients. By utilizing the transformation between cylindrical and plane waves, the boundary conditions on soil-tunnel interface are satisfied, yielding a solution for a harmonic point load acting on the tunnel in a half-space with an irregular surface. The proposed method can simulate topographies with arbitrary shapes and only requires the discretization of the irregular part of the ground surface, which provides a highly efficient tool to investigate the propagation characteristics of train-induced vibrations in complex topographies. The proposed method is verified through comparisons with the existing analytical methods and the finite element method. The dynamic responses of a tunnel embedded in a half-space with a Gaussian-shaped surface are meticulously investigated. A case study involving a site for the Shenzhen metro line 5 is performed. The numerical results demonstrate that the presence of irregular topography alters the distribution of ground vibrations, leading to significant differences in responses within the irregular region and certain disparities in the regular region. The effect of the location, size, and undulating direction of the irregular topography on ground vibrations is frequency-dependent.</p></div>","PeriodicalId":17233,"journal":{"name":"Journal of Sound and Vibration","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Semi-analytical method for calculating ground vibrations from a tunnel in a homogeneous half-space with an irregular surface\",\"authors\":\"\",\"doi\":\"10.1016/j.jsv.2024.118615\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper proposes a novel two-dimensional (2D) semi-analytical method for calculating ground vibrations from a tunnel situated in a homogeneous half-space with an irregular surface. The circular tunnel is conceptualized as an elastic solid, while the soil is modelled as an elastic, isotropic, and homogeneous half-space with an irregular surface. A virtual horizontal interface is introduced to divide the soil domain into an irregular region with an arbitrary-shaped surface and a half-space with a circular hollow. The wavefield scattered by the irregular surface is simulated by the boundary integral equation. Through the application of the discrete wavenumber approach and expansion of wavefield on the irregular surface, the boundary integral equation is transformed into a set of simultaneous matrix equations containing unknown expansion coefficients. By utilizing the transformation between cylindrical and plane waves, the boundary conditions on soil-tunnel interface are satisfied, yielding a solution for a harmonic point load acting on the tunnel in a half-space with an irregular surface. The proposed method can simulate topographies with arbitrary shapes and only requires the discretization of the irregular part of the ground surface, which provides a highly efficient tool to investigate the propagation characteristics of train-induced vibrations in complex topographies. The proposed method is verified through comparisons with the existing analytical methods and the finite element method. The dynamic responses of a tunnel embedded in a half-space with a Gaussian-shaped surface are meticulously investigated. A case study involving a site for the Shenzhen metro line 5 is performed. The numerical results demonstrate that the presence of irregular topography alters the distribution of ground vibrations, leading to significant differences in responses within the irregular region and certain disparities in the regular region. The effect of the location, size, and undulating direction of the irregular topography on ground vibrations is frequency-dependent.</p></div>\",\"PeriodicalId\":17233,\"journal\":{\"name\":\"Journal of Sound and Vibration\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2024-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Sound and Vibration\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022460X24003778\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Sound and Vibration","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022460X24003778","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ACOUSTICS","Score":null,"Total":0}
Semi-analytical method for calculating ground vibrations from a tunnel in a homogeneous half-space with an irregular surface
This paper proposes a novel two-dimensional (2D) semi-analytical method for calculating ground vibrations from a tunnel situated in a homogeneous half-space with an irregular surface. The circular tunnel is conceptualized as an elastic solid, while the soil is modelled as an elastic, isotropic, and homogeneous half-space with an irregular surface. A virtual horizontal interface is introduced to divide the soil domain into an irregular region with an arbitrary-shaped surface and a half-space with a circular hollow. The wavefield scattered by the irregular surface is simulated by the boundary integral equation. Through the application of the discrete wavenumber approach and expansion of wavefield on the irregular surface, the boundary integral equation is transformed into a set of simultaneous matrix equations containing unknown expansion coefficients. By utilizing the transformation between cylindrical and plane waves, the boundary conditions on soil-tunnel interface are satisfied, yielding a solution for a harmonic point load acting on the tunnel in a half-space with an irregular surface. The proposed method can simulate topographies with arbitrary shapes and only requires the discretization of the irregular part of the ground surface, which provides a highly efficient tool to investigate the propagation characteristics of train-induced vibrations in complex topographies. The proposed method is verified through comparisons with the existing analytical methods and the finite element method. The dynamic responses of a tunnel embedded in a half-space with a Gaussian-shaped surface are meticulously investigated. A case study involving a site for the Shenzhen metro line 5 is performed. The numerical results demonstrate that the presence of irregular topography alters the distribution of ground vibrations, leading to significant differences in responses within the irregular region and certain disparities in the regular region. The effect of the location, size, and undulating direction of the irregular topography on ground vibrations is frequency-dependent.
期刊介绍:
The Journal of Sound and Vibration (JSV) is an independent journal devoted to the prompt publication of original papers, both theoretical and experimental, that provide new information on any aspect of sound or vibration. There is an emphasis on fundamental work that has potential for practical application.
JSV was founded and operates on the premise that the subject of sound and vibration requires a journal that publishes papers of a high technical standard across the various subdisciplines, thus facilitating awareness of techniques and discoveries in one area that may be applicable in others.