{"title":"Dynamic response of a circular tunnel buried in the half-space unsaturated soil to elastic waves","authors":"Yong-Hong Miao, Jian-Fei Lu","doi":"10.1007/s00707-025-04401-x","DOIUrl":null,"url":null,"abstract":"<div><p>Based on the wave function expansion (WFE) method and expansion of the cylindrical wave into plane wave (ECPW) method, an analytical method for a circular lined tunnel embedded in the half-space unsaturated soil is developed. To develop the analytical method, the governing equations and corresponding potentials for the unsaturated soil are introduced first. The wavefield in the soil is decomposed into the free wavefield and scattered wavefield. The free wavefield in the unsaturated soil is determined by the incident waves as well as reflected waves from the surface of the soil. The scattered wavefield in the soil can be further divided into the direct and secondary scattered wavefields. The direct scattered waves due to the presence of the tunnel are cylindrical waves emitted from the tunnel, while the secondary scattered waves are the reflected waves of the direct scattered waves from the surface of the soil. To determine the secondary scattered waves for the tunnel, the ECPW method for the unsaturated half-space soil is proposed in this study. The wavefield in the tunnel lining consists of standing waves represented by Bessel functions. By using the expressions for the above wavefields, the equations for the unknown coefficients of the wavefunctions are derived. With the developed analytical method for the circular tunnel, some numerical results are presented.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 8","pages":"4795 - 4821"},"PeriodicalIF":2.9000,"publicationDate":"2025-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00707-025-04401-x","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
Based on the wave function expansion (WFE) method and expansion of the cylindrical wave into plane wave (ECPW) method, an analytical method for a circular lined tunnel embedded in the half-space unsaturated soil is developed. To develop the analytical method, the governing equations and corresponding potentials for the unsaturated soil are introduced first. The wavefield in the soil is decomposed into the free wavefield and scattered wavefield. The free wavefield in the unsaturated soil is determined by the incident waves as well as reflected waves from the surface of the soil. The scattered wavefield in the soil can be further divided into the direct and secondary scattered wavefields. The direct scattered waves due to the presence of the tunnel are cylindrical waves emitted from the tunnel, while the secondary scattered waves are the reflected waves of the direct scattered waves from the surface of the soil. To determine the secondary scattered waves for the tunnel, the ECPW method for the unsaturated half-space soil is proposed in this study. The wavefield in the tunnel lining consists of standing waves represented by Bessel functions. By using the expressions for the above wavefields, the equations for the unknown coefficients of the wavefunctions are derived. With the developed analytical method for the circular tunnel, some numerical results are presented.
期刊介绍:
Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.